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[axolotl.cli.config.load_cfg:259] [PID:1659682] config: +{ + "activation_offloading": false, + "axolotl_config_path": "/home/jiaruil5/math_rl/mix_teachers/mix_teachers/train/math_operations_sft/configs/.tmp_jo6r_r7k.yaml", + "base_model": "/home/jiaruil5/math_rl/mix_teachers/r3lit_rl/models/Qwen/Qwen3-4B-Instruct-2507", + "base_model_config": "/home/jiaruil5/math_rl/mix_teachers/r3lit_rl/models/Qwen/Qwen3-4B-Instruct-2507", + "batch_size": 8, + "bf16": true, + "capabilities": { + "bf16": true, + "compute_capability": "sm_86", + "fp8": false, + "n_gpu": 1, + "n_node": 1 + }, + "chat_template": "chatml", + "context_parallel_size": 1, + "dataloader_num_workers": 1, + "dataloader_pin_memory": true, + "dataloader_prefetch_factor": 256, + "dataset_num_proc": 128, + "datasets": [ + { + "message_property_mappings": { + "content": "content", + "role": "role" + }, + "path": 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"load_best_model_at_end": true, + "load_in_4bit": false, + "load_in_8bit": false, + "local_rank": 0, + "logging_steps": 10, + "lora_dropout": 0.0, + "loraplus_lr_embedding": 1e-06, + "lr_scheduler": "constant_with_warmup", + "mean_resizing_embeddings": false, + "micro_batch_size": 1, + "model_config_type": "qwen3", + "num_epochs": 3.0, + "optimizer": "adamw_torch_fused", + "otel_metrics_host": "localhost", + "otel_metrics_port": 8000, + "output_dir": "/home/jiaruil5/math_rl/mix_teachers/r3lit_rl/mix_teachers/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308", + "pad_to_sequence_len": true, + "pretrain_multipack_attn": true, + "profiler_steps_start": 0, + "qlora_sharded_model_loading": false, + "ray_num_workers": 1, + "resources_per_worker": { + "GPU": 1 + }, + "sample_packing": true, + "sample_packing_bin_size": 200, + "sample_packing_group_size": 100000, + "save_only_model": false, + "save_safetensors": true, + "save_steps": 0.3333333333333333, + "save_total_limit": 3, + "saves_per_epoch": 1, + "sequence_len": 2048, + "shuffle_before_merging_datasets": false, + "shuffle_merged_datasets": true, + "skip_prepare_dataset": false, + "streaming_multipack_buffer_size": 10000, + "strict": false, + "tensor_parallel_size": 1, + "test_datasets": [ + { + "message_property_mappings": { + "content": "content", + "role": "role" + }, + "path": "/home/jiaruil5/math_rl/mix_teachers/r3lit_rl/mix_teachers/data/math_operations/primitive_atomic_balanced_sft_50k/balanced_val_alpaca.jsonl", + "trust_remote_code": false, + "type": "alpaca" + } + ], + "tf32": true, + "tiled_mlp_use_original_mlp": true, + "tokenizer_config": "/home/jiaruil5/math_rl/mix_teachers/r3lit_rl/models/Qwen/Qwen3-4B-Instruct-2507", + "tokenizer_save_jinja_files": true, + "torch_dtype": "torch.bfloat16", + "train_on_inputs": false, + "trl": { + "log_completions": false, + "mask_truncated_completions": false, + "ref_model_mixup_alpha": 0.9, + "ref_model_sync_steps": 64, + "scale_rewards": true, + "sync_ref_model": false, + "use_vllm": false, + "vllm_server_host": "0.0.0.0", + "vllm_server_port": 8000 + }, + "use_otel_metrics": false, + "use_ray": false, + "use_wandb": true, + "val_set_size": 0.0, + "vllm": { + "device": "auto", + "dtype": "auto", + "gpu_memory_utilization": 0.9, + "host": "0.0.0.0", + "port": 8000 + }, + "wandb_log_model": "false", + "wandb_name": "primitive-atomic-full-sft-50k-lr1e4-t20260308", + "wandb_project": "math_operations_sft", + "warmup_ratio": 0.1, + "weight_decay": 0.01, + "world_size": 1 +} +[2026-03-08 15:53:43,978] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:285] [PID:1659682] EOS: 151645 / <|im_end|> +[2026-03-08 15:53:43,979] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:286] [PID:1659682] BOS: None / None +[2026-03-08 15:53:43,979] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:287] [PID:1659682] PAD: 151643 / <|endoftext|> +[2026-03-08 15:53:43,979] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:288] [PID:1659682] UNK: None / None +[2026-03-08 15:53:43,981] [INFO] [axolotl.utils.data.shared.load_preprocessed_dataset:481] [PID:1659682] Unable to find prepared dataset in last_run_prepared/c5b2dcf69e91df42a1bb115dcc61090d +[2026-03-08 15:53:43,981] [INFO] [axolotl.utils.data.sft._load_raw_datasets:320] [PID:1659682] Loading raw datasets... +[2026-03-08 15:53:43,981] [WARNING] [axolotl.utils.data.sft._load_raw_datasets:322] [PID:1659682] Processing datasets during training can lead to VRAM instability. Please pre-process your dataset using `axolotl preprocess path/to/config.yml`. +[2026-03-08 15:53:44,834] [INFO] [axolotl.utils.data.wrappers.get_dataset_wrapper:87] [PID:1659682] Loading dataset: /home/jiaruil5/math_rl/mix_teachers/r3lit_rl/mix_teachers/data/math_operations/primitive_atomic_balanced_sft_50k/balanced_train_alpaca.jsonl with base_type: alpaca and prompt_style: None +[2026-03-08 15:53:48,061] [INFO] [axolotl.utils.data.utils.handle_long_seq_in_dataset:224] [PID:1659682] min_input_len: 257 +[2026-03-08 15:53:48,062] [INFO] [axolotl.utils.data.utils.handle_long_seq_in_dataset:226] [PID:1659682] max_input_len: 371 + Dropping Long Sequences (>2048) (num_proc=128): 0%| | 0/50000 [00:002048) (num_proc=128): 1%| | 391/50000 [00:01<03:08, 262.70 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 7%|▋ | 3519/50000 [00:01<00:15, 2950.35 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 13%|█▎ | 6647/50000 [00:01<00:07, 5827.45 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 21%|██ | 10557/50000 [00:01<00:03, 9923.09 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 31%|███▏ | 15640/50000 [00:01<00:02, 15964.67 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 38%|███▊ | 19159/50000 [00:02<00:01, 18319.56 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 46%|████▌ | 23068/50000 [00:02<00:01, 21593.10 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 52%|█████▏ | 26196/50000 [00:02<00:01, 21007.95 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 77%|███████▋ | 38689/50000 [00:02<00:00, 42705.24 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 100%|██████████| 50000/50000 [00:03<00:00, 16564.97 examples/s] + Drop Samples with Zero Trainable Tokens (num_proc=128): 0%| | 0/50000 [00:002048) (num_proc=128): 0%| | 0/200 [00:002048) (num_proc=128): 1%| | 2/200 [00:01<02:16, 1.45 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 13%|█▎ | 26/200 [00:01<00:07, 23.70 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 25%|██▌ | 50/200 [00:01<00:03, 48.06 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 36%|███▌ | 72/200 [00:01<00:01, 72.15 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 74%|███████▍ | 149/200 [00:01<00:00, 187.42 examples/s] Dropping Long Sequences (>2048) (num_proc=128): 100%|██████████| 200/200 [00:02<00:00, 87.41 examples/s] + Drop Samples with Zero Trainable Tokens (num_proc=128): 0%| | 0/200 [00:00 +[2026-03-08 15:54:18,529] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:286] [PID:1659682] BOS: None / None +[2026-03-08 15:54:18,529] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:287] [PID:1659682] PAD: 151643 / <|endoftext|> +[2026-03-08 15:54:18,529] [DEBUG] [axolotl.loaders.tokenizer.load_tokenizer:288] [PID:1659682] UNK: None / None +[2026-03-08 15:54:18,529] [DEBUG] [axolotl.train.setup_model_and_tokenizer:82] [PID:1659682] Loading model +[2026-03-08 15:54:18,574] [DEBUG] [axolotl.monkeypatch.transformers.trainer_loss_calc.patch_evaluation_loop:87] [PID:1659682] Patched Trainer.evaluation_loop with nanmean loss calculation +[2026-03-08 15:54:18,576] [DEBUG] [axolotl.monkeypatch.transformers.trainer_loss_calc.patch_maybe_log_save_evaluate:138] [PID:1659682] Patched Trainer._maybe_log_save_evaluate with nanmean loss calculation +[2026-03-08 15:54:18,576] [INFO] [axolotl.loaders.patch_manager._apply_multipack_patches:346] [PID:1659682] Applying multipack dataloader patch for sample packing... + Fetching 22 files: 0%| | 0/22 [00:00user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 5^2 + 8^2 = 25 - 4 + 64 - 25 + 64 = 124\nG(52858) = |124| = 124\n\n\\boxed{124}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 17, 20, 488, 220, 21, 19, 284, 220, 16, 17, 19, 198, 38, 7, 20, 17, 23, 20, 23, 8, 284, 760, 16, 17, 19, 91, 284, 220, 16, 17, 19, 271, 59, 79075, 90, 16, 17, 19, 92, 151645], "meta_info": {"id": "ff11c0b2bdc74e44a8e1efc045e8df87", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.1520233154296875, "response_sent_to_client_ts": 1773877212.9390454}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "55889", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n5 is prime: 5^2 = 25\n9 is not prime: 9\n8 is not prime: 8\nP(58598) = 25 + 8 + 25 + 9 + 8 = 75\n\n\\boxed{75}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 47, 7, 20, 23, 20, 24, 23, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 17, 20, 488, 220, 24, 488, 220, 23, 284, 220, 22, 20, 271, 59, 79075, 90, 22, 20, 92, 151645], "meta_info": {"id": "49173166c71342c991f63257ec0dbe06", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.238176107406616, "response_sent_to_client_ts": 1773877213.0251894}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2430", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nB(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 33, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "e0b5fabe5ab64c1ba23f699b83903b4f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 205, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.453560829162598, "response_sent_to_client_ts": 1773877213.2406173}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nAlternating sum of squares = 6^2 - 5^2 + 3^2 - 3^2 + 3^2 = 36 - 25 + 9 - 9 + 9 = 20\nG(65333) = |20| = 20\n\n\\boxed{20}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 24, 481, 220, 24, 488, 220, 24, 284, 220, 17, 15, 198, 38, 7, 21, 20, 18, 18, 18, 8, 284, 760, 17, 15, 91, 284, 220, 17, 15, 271, 59, 79075, 90, 17, 15, 92, 151645], "meta_info": {"id": "49860859156c43febefc2cdedbbd6bf4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.018996238708496, "response_sent_to_client_ts": 1773877212.80605}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nC(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 34, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "8e800964f50548a090d70a5acbf72822", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.764068603515625, "response_sent_to_client_ts": 1773877213.5511417}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nC(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 34, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "0b24e8c19d40478e984d6b939548197e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.408428907394409, "response_sent_to_client_ts": 1773877213.1954634}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nM(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 44, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "7ad91d892fdc4db093d85464219c177b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.6776204109191895, "response_sent_to_client_ts": 1773877213.4646685}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9232", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 2329 is \"2329\".\nRotations: 2329, 3292, 2923, 9232\nI(2329) = min(2329, 3292, 2923, 9232) = 2329\n\n\\boxed{2329}", "output_ids": [785, 15723, 914, 315, 220, 17, 18, 17, 24, 374, 330, 17, 18, 17, 24, 22956, 36936, 804, 25, 220, 17, 18, 17, 24, 11, 220, 18, 17, 24, 17, 11, 220, 17, 24, 17, 18, 11, 220, 24, 17, 18, 17, 198, 40, 7, 17, 18, 17, 24, 8, 284, 1308, 7, 17, 18, 17, 24, 11, 220, 18, 17, 24, 17, 11, 220, 17, 24, 17, 18, 11, 220, 24, 17, 18, 17, 8, 284, 220, 17, 18, 17, 24, 271, 59, 79075, 90, 17, 18, 17, 24, 92, 151645], "meta_info": {"id": "576a20c9f2ce437cb338a0c07e813472", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 92, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 3.802885055541992, "response_sent_to_client_ts": 1773877212.5899115}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nC(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 34, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "1ddd1a2d41424f74a558a03391a26ec0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.677637100219727, "response_sent_to_client_ts": 1773877213.4646804}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nN(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 45, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "0eb668d89e85430d971bfdb60d78f1af", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.803585052490234, "response_sent_to_client_ts": 1773877213.590603}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "88653", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 85638 is \"85638\".\nRotations: 85638, 56388, 63885, 38856, 88563\nQ(85638) = min(85638, 56388, 63885, 38856, 88563) = 38856\n\n\\boxed{38856}", "output_ids": [785, 15723, 914, 315, 220, 23, 20, 21, 18, 23, 374, 330, 23, 20, 21, 18, 23, 22956, 36936, 804, 25, 220, 23, 20, 21, 18, 23, 11, 220, 20, 21, 18, 23, 23, 11, 220, 21, 18, 23, 23, 20, 11, 220, 18, 23, 23, 20, 21, 11, 220, 23, 23, 20, 21, 18, 198, 48, 7, 23, 20, 21, 18, 23, 8, 284, 1308, 7, 23, 20, 21, 18, 23, 11, 220, 20, 21, 18, 23, 23, 11, 220, 21, 18, 23, 23, 20, 11, 220, 18, 23, 23, 20, 21, 11, 220, 23, 23, 20, 21, 18, 8, 284, 220, 18, 23, 23, 20, 21, 271, 59, 79075, 90, 18, 23, 23, 20, 21, 92, 151645], "meta_info": {"id": "d7522a7af1f54fcf9cc28afcf83e1831", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.390235424041748, "response_sent_to_client_ts": 1773877213.177307}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "85220", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 58220 is \"58220\".\nRotations: 58220, 82205, 22058, 20582, 5822\nQ(58220) = min(58220, 82205, 22058, 20582, 5822) = 5822\n\n\\boxed{5822}", "output_ids": [785, 15723, 914, 315, 220, 20, 23, 17, 17, 15, 374, 330, 20, 23, 17, 17, 15, 22956, 36936, 804, 25, 220, 20, 23, 17, 17, 15, 11, 220, 23, 17, 17, 15, 20, 11, 220, 17, 17, 15, 20, 23, 11, 220, 17, 15, 20, 23, 17, 11, 220, 20, 23, 17, 17, 198, 48, 7, 20, 23, 17, 17, 15, 8, 284, 1308, 7, 20, 23, 17, 17, 15, 11, 220, 23, 17, 17, 15, 20, 11, 220, 17, 17, 15, 20, 23, 11, 220, 17, 15, 20, 23, 17, 11, 220, 20, 23, 17, 17, 8, 284, 220, 20, 23, 17, 17, 271, 59, 79075, 90, 20, 23, 17, 17, 92, 151645], "meta_info": {"id": "3e297c897f34470494f678d09a04daeb", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.304403305053711, "response_sent_to_client_ts": 1773877213.0914714}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nAlternating sum of squares = 5^2 - 4^2 + 0^2 - 4^2 + 6^2 = 25 - 16 + 0 - 16 + 36 = 29\nD(54046) = |29| = 29\n\n\\boxed{29}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 19, 61, 17, 488, 220, 15, 61, 17, 481, 220, 19, 61, 17, 488, 220, 21, 61, 17, 284, 220, 17, 20, 481, 220, 16, 21, 488, 220, 15, 481, 220, 16, 21, 488, 220, 18, 21, 284, 220, 17, 24, 198, 35, 7, 20, 19, 15, 19, 21, 8, 284, 760, 17, 24, 91, 284, 220, 17, 24, 271, 59, 79075, 90, 17, 24, 92, 151645], "meta_info": {"id": "df98635212144227b6aaffc1a6a54253", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.0648033618927, "response_sent_to_client_ts": 1773877212.8518307}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2285", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 58220 is \"58220\".\nRotations: 58220, 82205, 22058, 20582, 5822\nI(58220) = min(58220, 82205, 22058, 20582, 5822) = 5822\n\n\\boxed{5822}", "output_ids": [785, 15723, 914, 315, 220, 20, 23, 17, 17, 15, 374, 330, 20, 23, 17, 17, 15, 22956, 36936, 804, 25, 220, 20, 23, 17, 17, 15, 11, 220, 23, 17, 17, 15, 20, 11, 220, 17, 17, 15, 20, 23, 11, 220, 17, 15, 20, 23, 17, 11, 220, 20, 23, 17, 17, 198, 40, 7, 20, 23, 17, 17, 15, 8, 284, 1308, 7, 20, 23, 17, 17, 15, 11, 220, 23, 17, 17, 15, 20, 11, 220, 17, 17, 15, 20, 23, 11, 220, 17, 15, 20, 23, 17, 11, 220, 20, 23, 17, 17, 8, 284, 220, 20, 23, 17, 17, 271, 59, 79075, 90, 20, 23, 17, 17, 92, 151645], "meta_info": {"id": "7cd75fd7139044e19ae19857125beeec", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.304423809051514, "response_sent_to_client_ts": 1773877213.0914834}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "15", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nT(58733) = 25 + 8 + 49 + 9 + 9 = 90\n\n\\boxed{90}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 51, 7, 20, 23, 22, 18, 18, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 488, 220, 24, 284, 220, 24, 15, 271, 59, 79075, 90, 24, 15, 92, 151645], "meta_info": {"id": "622981a278fb4b31b73dcfefb74152ba", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 120, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.393443584442139, "response_sent_to_client_ts": 1773877213.1804445}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nC(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 34, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "4214df999af4410f95d9a6c6b20d073c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.304433345794678, "response_sent_to_client_ts": 1773877213.0914898}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "139", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nO(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 46, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "ea41ea790e6a4e46abd8ad1a9eac2dea", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.707491874694824, "response_sent_to_client_ts": 1773877213.49456}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nAlternating sum of squares = 9^2 - 7^2 + 6^2 - 7^2 + 9^2 = 81 - 49 + 36 - 49 + 81 = 60\nG(97679) = |60| = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 24, 61, 17, 481, 220, 22, 61, 17, 488, 220, 21, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 23, 16, 481, 220, 19, 24, 488, 220, 18, 21, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 21, 15, 198, 38, 7, 24, 22, 21, 22, 24, 8, 284, 760, 21, 15, 91, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "e5ee685642004ba8ab61d2ffd228279a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.0871593952178955, "response_sent_to_client_ts": 1773877212.8741894}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "35431", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 13453 is \"13453\".\nRotations: 13453, 34531, 45313, 53134, 31345\nI(13453) = min(13453, 34531, 45313, 53134, 31345) = 13453\n\n\\boxed{13453}", "output_ids": [785, 15723, 914, 315, 220, 16, 18, 19, 20, 18, 374, 330, 16, 18, 19, 20, 18, 22956, 36936, 804, 25, 220, 16, 18, 19, 20, 18, 11, 220, 18, 19, 20, 18, 16, 11, 220, 19, 20, 18, 16, 18, 11, 220, 20, 18, 16, 18, 19, 11, 220, 18, 16, 18, 19, 20, 198, 40, 7, 16, 18, 19, 20, 18, 8, 284, 1308, 7, 16, 18, 19, 20, 18, 11, 220, 18, 19, 20, 18, 16, 11, 220, 19, 20, 18, 16, 18, 11, 220, 20, 18, 16, 18, 19, 11, 220, 18, 16, 18, 19, 20, 8, 284, 220, 16, 18, 19, 20, 18, 271, 59, 79075, 90, 16, 18, 19, 20, 18, 92, 151645], "meta_info": {"id": "7752f2fd7bfb49aea821988df091e2f8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.39025616645813, "response_sent_to_client_ts": 1773877213.1773205}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\n1 is not prime: 1\n1 is not prime: 1\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n6 is not prime: 6\nK(11536) = 1 + 1 + 25 + 9 + 6 = 42\n\n\\boxed{42}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 42, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 17, 20, 488, 220, 24, 488, 220, 21, 284, 220, 19, 17, 271, 59, 79075, 90, 19, 17, 92, 151645], "meta_info": {"id": "4a3b74cb1f2a402c950dd1e9c2740aa8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.195106267929077, "response_sent_to_client_ts": 1773877212.9821208}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nR(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 49, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "c5562188135149c08d21147eb6faac40", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 0, "cached_tokens_details": null, "e2e_latency": 4.707508325576782, "response_sent_to_client_ts": 1773877213.494571}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nM(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 44, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "05ecbb6064394b5cb3bb411116c5482b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.453581094741821, "response_sent_to_client_ts": 1773877213.2406313}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nL(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 43, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "1d4aca31dc5f442a8ee68134564355f5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.7640838623046875, "response_sent_to_client_ts": 1773877213.5511515}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "25588", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n5 is prime: 5^2 = 25\n8 is not prime: 8\nP(52858) = 25 + 4 + 8 + 25 + 8 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 47, 7, 20, 17, 23, 20, 23, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 17, 20, 488, 220, 23, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "e95a53b7193c4728b75496e0611ab9e4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.325423002243042, "response_sent_to_client_ts": 1773877213.1124382}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "21", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nA(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 32, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "a1ff19a1a6544c21a9d9d174467497a9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.707517147064209, "response_sent_to_client_ts": 1773877213.494577}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "36", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\n6 is not prime: 6\n0 is not prime: 0\n1 is not prime: 1\n7 is prime: 7^2 = 49\n4 is not prime: 4\nS(60174) = 6 + 0 + 1 + 49 + 4 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 50, 7, 21, 15, 16, 22, 19, 8, 284, 220, 21, 488, 220, 15, 488, 220, 16, 488, 220, 19, 24, 488, 220, 19, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "b91a8bc429b64cd48c551f2bcba37e11", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.108885288238525, "response_sent_to_client_ts": 1773877212.895896}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "11", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nJ(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 41, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "0c72d7b95b6c428f8c9ecdfa6d878060", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.677646636962891, "response_sent_to_client_ts": 1773877213.4646893}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "16", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nJ(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 41, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "c4862b4cc45e4a84930a3972aafbfea2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.7640931606292725, "response_sent_to_client_ts": 1773877213.551158}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "15", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nJ(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 41, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "7af44170f5c64e41b82eaf7bb99330a3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 195, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.453591823577881, "response_sent_to_client_ts": 1773877213.2406394}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "45127", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 72154 is \"72154\".\nRotations: 72154, 21547, 15472, 54721, 47215\nI(72154) = min(72154, 21547, 15472, 54721, 47215) = 15472\n\n\\boxed{15472}", "output_ids": [785, 15723, 914, 315, 220, 22, 17, 16, 20, 19, 374, 330, 22, 17, 16, 20, 19, 22956, 36936, 804, 25, 220, 22, 17, 16, 20, 19, 11, 220, 17, 16, 20, 19, 22, 11, 220, 16, 20, 19, 22, 17, 11, 220, 20, 19, 22, 17, 16, 11, 220, 19, 22, 17, 16, 20, 198, 40, 7, 22, 17, 16, 20, 19, 8, 284, 1308, 7, 22, 17, 16, 20, 19, 11, 220, 17, 16, 20, 19, 22, 11, 220, 16, 20, 19, 22, 17, 11, 220, 20, 19, 22, 17, 16, 11, 220, 19, 22, 17, 16, 20, 8, 284, 220, 16, 20, 19, 22, 17, 271, 59, 79075, 90, 16, 20, 19, 22, 17, 92, 151645], "meta_info": {"id": "f4e745659e1e46bc9f5790ac67e3482f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.390265464782715, "response_sent_to_client_ts": 1773877213.1773274}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nAlternating sum of squares = 5^2 - 8^2 + 7^2 - 3^2 + 3^2 = 25 - 64 + 49 - 9 + 9 = 10\nF(58733) = |10| = 10\n\n\\boxed{10}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 24, 481, 220, 24, 488, 220, 24, 284, 220, 16, 15, 198, 37, 7, 20, 23, 22, 18, 18, 8, 284, 760, 16, 15, 91, 284, 220, 16, 15, 271, 59, 79075, 90, 16, 15, 92, 151645], "meta_info": {"id": "ed5420b9e358409981f6239e0d50d585", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.042636394500732, "response_sent_to_client_ts": 1773877212.8296843}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nAlternating sum of squares = 6^2 - 0^2 + 1^2 - 7^2 + 4^2 = 36 - 0 + 1 - 49 + 16 = 4\nG(60174) = |4| = 4\n\n\\boxed{4}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 481, 220, 22, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 15, 488, 220, 16, 481, 220, 19, 24, 488, 220, 16, 21, 284, 220, 19, 198, 38, 7, 21, 15, 16, 22, 19, 8, 284, 760, 19, 91, 284, 220, 19, 271, 59, 79075, 90, 19, 92, 151645], "meta_info": {"id": "27486c3dbd724516a19602047eb6e335", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 99, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 3.9525277614593506, "response_sent_to_client_ts": 1773877212.739544}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "82694", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 49628 is \"49628\".\nRotations: 49628, 96284, 62849, 28496, 84962\nI(49628) = min(49628, 96284, 62849, 28496, 84962) = 28496\n\n\\boxed{28496}", "output_ids": [785, 15723, 914, 315, 220, 19, 24, 21, 17, 23, 374, 330, 19, 24, 21, 17, 23, 22956, 36936, 804, 25, 220, 19, 24, 21, 17, 23, 11, 220, 24, 21, 17, 23, 19, 11, 220, 21, 17, 23, 19, 24, 11, 220, 17, 23, 19, 24, 21, 11, 220, 23, 19, 24, 21, 17, 198, 40, 7, 19, 24, 21, 17, 23, 8, 284, 1308, 7, 19, 24, 21, 17, 23, 11, 220, 24, 21, 17, 23, 19, 11, 220, 21, 17, 23, 19, 24, 11, 220, 17, 23, 19, 24, 21, 11, 220, 23, 19, 24, 21, 17, 8, 284, 220, 17, 23, 19, 24, 21, 271, 59, 79075, 90, 17, 23, 19, 24, 21, 92, 151645], "meta_info": {"id": "edbbee4c704e4f419fd2842c36ef6105", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.3902740478515625, "response_sent_to_client_ts": 1773877213.1773334}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "192", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nB(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 33, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "0ddbfef3b9724666a20f55c08be5535e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.707526683807373, "response_sent_to_client_ts": 1773877213.4945834}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nL(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 43, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "3a01193eaa164b268287bcdf67c54ff5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.764102935791016, "response_sent_to_client_ts": 1773877213.5511634}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "12", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nA(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 32, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "a2ba5f7be5fd4fdc9cfe9edcdc21605c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.647384166717529, "response_sent_to_client_ts": 1773877213.4343927}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nR(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 49, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "c5005c29669b4d2f815299a0cf52fefe", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 108, "cached_tokens_details": null, "e2e_latency": 4.304443597793579, "response_sent_to_client_ts": 1773877213.0914962}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nC(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 34, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "e537da42f1724bc080695aec52afbf25", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.707536220550537, "response_sent_to_client_ts": 1773877213.4945886}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "10", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nJ(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 41, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "0d9287783c734c6dbbfbfb4c09e5bcac", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.764111280441284, "response_sent_to_client_ts": 1773877213.551169}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nAlternating sum of squares = 1^2 - 1^2 + 5^2 - 3^2 + 6^2 = 1 - 1 + 25 - 9 + 36 = 52\nG(11536) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 16, 61, 17, 488, 220, 20, 61, 17, 481, 220, 18, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 481, 220, 16, 488, 220, 17, 20, 481, 220, 24, 488, 220, 18, 21, 284, 220, 20, 17, 198, 38, 7, 16, 16, 20, 18, 21, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "9c2fbb82e209442ab6e1feac2d91e0d2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.019012451171875, "response_sent_to_client_ts": 1773877212.806061}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "23", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nO(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 46, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "9292d87ed9b54839a33792e52febe025", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.617649555206299, "response_sent_to_client_ts": 1773877213.404664}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "64045", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 54046 is \"54046\".\nRotations: 54046, 40465, 4654, 46540, 65404\nI(54046) = min(54046, 40465, 4654, 46540, 65404) = 4654\n\n\\boxed{4654}", "output_ids": [785, 15723, 914, 315, 220, 20, 19, 15, 19, 21, 374, 330, 20, 19, 15, 19, 21, 22956, 36936, 804, 25, 220, 20, 19, 15, 19, 21, 11, 220, 19, 15, 19, 21, 20, 11, 220, 19, 21, 20, 19, 11, 220, 19, 21, 20, 19, 15, 11, 220, 21, 20, 19, 15, 19, 198, 40, 7, 20, 19, 15, 19, 21, 8, 284, 1308, 7, 20, 19, 15, 19, 21, 11, 220, 19, 15, 19, 21, 20, 11, 220, 19, 21, 20, 19, 11, 220, 19, 21, 20, 19, 15, 11, 220, 21, 20, 19, 15, 19, 8, 284, 220, 19, 21, 20, 19, 271, 59, 79075, 90, 19, 21, 20, 19, 92, 151645], "meta_info": {"id": "a1da5d7d437048c19b07861461bd4985", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.304453134536743, "response_sent_to_client_ts": 1773877213.0915015}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nAlternating sum of squares = 5^2 - 8^2 + 7^2 - 3^2 + 3^2 = 25 - 64 + 49 - 9 + 9 = 10\nG(58733) = |10| = 10\n\n\\boxed{10}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 24, 481, 220, 24, 488, 220, 24, 284, 220, 16, 15, 198, 38, 7, 20, 23, 22, 18, 18, 8, 284, 760, 16, 15, 91, 284, 220, 16, 15, 271, 59, 79075, 90, 16, 15, 92, 151645], "meta_info": {"id": "8b8b4ebca5d34f6da81a1d95d37ad2ee", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.04265570640564, "response_sent_to_client_ts": 1773877212.8296964}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nAlternating sum of squares = 6^2 - 6^2 + 4^2 - 4^2 + 4^2 = 36 - 36 + 16 - 16 + 16 = 36\nH(66444) = |36| = 36\n\n\\boxed{36}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 21, 61, 17, 488, 220, 19, 61, 17, 481, 220, 19, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 18, 21, 488, 220, 16, 21, 481, 220, 16, 21, 488, 220, 16, 21, 284, 220, 18, 21, 198, 39, 7, 21, 21, 19, 19, 19, 8, 284, 760, 18, 21, 91, 284, 220, 18, 21, 271, 59, 79075, 90, 18, 21, 92, 151645], "meta_info": {"id": "ebf79d2872c747b3b0656fce9f24c363", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.087174415588379, "response_sent_to_client_ts": 1773877212.8741996}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4669", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\n4 is not prime: 4\n6 is not prime: 6\n9 is not prime: 9\n6 is not prime: 6\nP(4696) = 4 + 6 + 9 + 6 = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 47, 7, 19, 21, 24, 21, 8, 284, 220, 19, 488, 220, 21, 488, 220, 24, 488, 220, 21, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "75eaea1f49d44104851e22ddfe9374bf", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 84, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 3.6305956840515137, "response_sent_to_client_ts": 1773877212.4176173}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 5^2 + 8^2 = 25 - 4 + 64 - 25 + 64 = 124\nF(52858) = |124| = 124\n\n\\boxed{124}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 17, 20, 488, 220, 21, 19, 284, 220, 16, 17, 19, 198, 37, 7, 20, 17, 23, 20, 23, 8, 284, 760, 16, 17, 19, 91, 284, 220, 16, 17, 19, 271, 59, 79075, 90, 16, 17, 19, 92, 151645], "meta_info": {"id": "e35bea345a104bc186ee63c9fb75b434", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.152039527893066, "response_sent_to_client_ts": 1773877212.939057}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nAlternating sum of squares = 4^2 - 1^2 + 4^2 - 2^2 + 6^2 = 16 - 1 + 16 - 4 + 36 = 63\nF(41426) = |63| = 63\n\n\\boxed{63}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 16, 61, 17, 488, 220, 19, 61, 17, 481, 220, 17, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 16, 488, 220, 16, 21, 481, 220, 19, 488, 220, 18, 21, 284, 220, 21, 18, 198, 37, 7, 19, 16, 19, 17, 21, 8, 284, 760, 21, 18, 91, 284, 220, 21, 18, 271, 59, 79075, 90, 21, 18, 92, 151645], "meta_info": {"id": "e75b506a713b46ecbce2238c2b7340b2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.0426647663116455, "response_sent_to_client_ts": 1773877212.8297026}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nN(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 45, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "5531fd4807024a41b736c887be8f3a6d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 4.677655220031738, "response_sent_to_client_ts": 1773877213.4646952}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nAlternating sum of squares = 1^2 - 5^2 + 5^2 - 5^2 + 9^2 = 1 - 25 + 25 - 25 + 81 = 57\nH(15559) = |57| = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 20, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 284, 220, 16, 481, 220, 17, 20, 488, 220, 17, 20, 481, 220, 17, 20, 488, 220, 23, 16, 284, 220, 20, 22, 198, 39, 7, 16, 20, 20, 20, 24, 8, 284, 760, 20, 22, 91, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "545bbc1b51584d2f86accfb1b65c5a03", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 155, "cached_tokens_details": null, "e2e_latency": 4.064817667007446, "response_sent_to_client_ts": 1773877212.8518405}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nAlternating sum of squares = 6^2 - 5^2 + 9^2 - 9^2 = 36 - 25 + 81 - 81 = 11\nG(6599) = |11| = 11\n\n\\boxed{11}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 481, 220, 24, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 23, 16, 481, 220, 23, 16, 284, 220, 16, 16, 198, 38, 7, 21, 20, 24, 24, 8, 284, 760, 16, 16, 91, 284, 220, 16, 16, 271, 59, 79075, 90, 16, 16, 92, 151645], "meta_info": {"id": "ad2eb53bc2ac41f9a03d19d489bd3ca9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.781015634536743, "response_sent_to_client_ts": 1773877212.5680199}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nAlternating sum of squares = 9^2 - 7^2 + 6^2 - 7^2 + 9^2 = 81 - 49 + 36 - 49 + 81 = 60\nD(97679) = |60| = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 24, 61, 17, 481, 220, 22, 61, 17, 488, 220, 21, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 23, 16, 481, 220, 19, 24, 488, 220, 18, 21, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 21, 15, 198, 35, 7, 24, 22, 21, 22, 24, 8, 284, 760, 21, 15, 91, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "03e26dac556b46f9855798bc88e3a406", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 4.087182998657227, "response_sent_to_client_ts": 1773877212.8742054}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nAlternating sum of squares = 3^2 - 0^2 + 8^2 - 0^2 + 1^2 = 9 - 0 + 64 - 0 + 1 = 74\nD(30801) = |74| = 74\n\n\\boxed{74}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 18, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 284, 220, 24, 481, 220, 15, 488, 220, 21, 19, 481, 220, 15, 488, 220, 16, 284, 220, 22, 19, 198, 35, 7, 18, 15, 23, 15, 16, 8, 284, 760, 22, 19, 91, 284, 220, 22, 19, 271, 59, 79075, 90, 22, 19, 92, 151645], "meta_info": {"id": "0863b6494e5e4a4aab10f6ec0bb65de2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 101, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.996225357055664, "response_sent_to_client_ts": 1773877212.7832382}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nR(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 49, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "3acdfe20a17647ac8a52ed8068b88c27", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 108, "cached_tokens_details": null, "e2e_latency": 4.76412034034729, "response_sent_to_client_ts": 1773877213.5511746}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nM(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 44, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "675b3e90ace945f1979c6f31e3f34103", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 4.7641284465789795, "response_sent_to_client_ts": 1773877213.55118}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nC(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 34, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "3029b724aaea43309d9ac6e9f5e29e39", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 4.74893045425415, "response_sent_to_client_ts": 1773877213.5359442}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nAlternating sum of squares = 7^2 - 3^2 + 0^2 - 2^2 + 4^2 = 49 - 9 + 0 - 4 + 16 = 52\nH(73024) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 15, 61, 17, 481, 220, 17, 61, 17, 488, 220, 19, 61, 17, 284, 220, 19, 24, 481, 220, 24, 488, 220, 15, 481, 220, 19, 488, 220, 16, 21, 284, 220, 20, 17, 198, 39, 7, 22, 18, 15, 17, 19, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "78334b50be404e5288e457c76b3a3a8e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 155, "cached_tokens_details": null, "e2e_latency": 4.019021034240723, "response_sent_to_client_ts": 1773877212.806067}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nL(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 43, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "e829899d076942f59daad07ae7c7c595", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.408447980880737, "response_sent_to_client_ts": 1773877213.1954765}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nAlternating sum of squares = 6^2 - 5^2 + 3^2 - 3^2 + 3^2 = 36 - 25 + 9 - 9 + 9 = 20\nF(65333) = |20| = 20\n\n\\boxed{20}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 24, 481, 220, 24, 488, 220, 24, 284, 220, 17, 15, 198, 37, 7, 21, 20, 18, 18, 18, 8, 284, 760, 17, 15, 91, 284, 220, 17, 15, 271, 59, 79075, 90, 17, 15, 92, 151645], "meta_info": {"id": "40ed8f04745c4927ae7134b2faab50a4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 4.0190346240997314, "response_sent_to_client_ts": 1773877212.8060725}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n9 is not prime: 9\n9 is not prime: 9\nE(6599) = 6 + 25 + 9 + 9 = 49\n\n\\boxed{49}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 36, 7, 21, 20, 24, 24, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 284, 220, 19, 24, 271, 59, 79075, 90, 19, 24, 92, 151645], "meta_info": {"id": "e06d838e55b74cc4a934b8b3028aa104", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 90, "cached_tokens": 18, "cached_tokens_details": null, "e2e_latency": 3.759408712387085, "response_sent_to_client_ts": 1773877212.5464249}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "259", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nO(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 46, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "ebee1564341042b8b9b5a6280541e1ff", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 4.8036017417907715, "response_sent_to_client_ts": 1773877213.5906146}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 7^2 + 9^2 = 25 - 4 + 64 - 49 + 81 = 97\nH(52879) = |97| = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 24, 22, 198, 39, 7, 20, 17, 23, 22, 24, 8, 284, 760, 24, 22, 91, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "d337abfeac9f42c2927b241477ccbf88", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 155, "cached_tokens_details": null, "e2e_latency": 4.064826488494873, "response_sent_to_client_ts": 1773877212.851847}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "223", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nO(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 46, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "499ff5ab39e545c5a833e48aab9a9de8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 203, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 4.453601837158203, "response_sent_to_client_ts": 1773877213.2406464}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "168", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nB(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 33, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "3d122c4f2d4b4e4b8708b169a1d74d42", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 4.707544565200806, "response_sent_to_client_ts": 1773877213.4945939}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nAlternating sum of squares = 1^2 - 3^2 + 4^2 - 5^2 + 3^2 = 1 - 9 + 16 - 25 + 9 = -8\nG(13453) = |-8| = 8\n\n\\boxed{8}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 18, 61, 17, 488, 220, 19, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 284, 220, 16, 481, 220, 24, 488, 220, 16, 21, 481, 220, 17, 20, 488, 220, 24, 284, 481, 23, 198, 38, 7, 16, 18, 19, 20, 18, 8, 284, 44561, 23, 91, 284, 220, 23, 271, 59, 79075, 90, 23, 92, 151645], "meta_info": {"id": "c22a995d918241a2b2862cc25e74a1cf", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 98, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.9307167530059814, "response_sent_to_client_ts": 1773877212.7177355}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "26", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nA(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 32, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "d3692a6da5c241ada276ecc9318537bf", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.038944959640503, "response_sent_to_client_ts": 1773877216.6321192}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n1 is not prime: 1\n0 is not prime: 0\n8 is not prime: 8\nD(75108) = 49 + 25 + 1 + 0 + 8 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 35, 7, 22, 20, 16, 15, 23, 8, 284, 220, 19, 24, 488, 220, 17, 20, 488, 220, 16, 488, 220, 15, 488, 220, 23, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "c19dc0d295454397a027d6eee08a7d6c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.574505090713501, "response_sent_to_client_ts": 1773877216.1676755}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nM(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 44, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "beaba766c008405c8e908a0d2d8e5a74", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.0389628410339355, "response_sent_to_client_ts": 1773877216.6321335}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nAlternating sum of squares = 9^2 - 7^2 + 6^2 - 7^2 + 9^2 = 81 - 49 + 36 - 49 + 81 = 60\nH(97679) = |60| = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 24, 61, 17, 481, 220, 22, 61, 17, 488, 220, 21, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 23, 16, 481, 220, 19, 24, 488, 220, 18, 21, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 21, 15, 198, 39, 7, 24, 22, 21, 22, 24, 8, 284, 760, 21, 15, 91, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "84a8cc9a2dcc47399c7d3f6bb6a25253", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.420321464538574, "response_sent_to_client_ts": 1773877216.0134766}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "78", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nO(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 46, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "07c06915e4f147f79f8be1e2c2ec3f18", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.0092711448669434, "response_sent_to_client_ts": 1773877216.602455}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "60", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n6 is not prime: 6\n3 is prime: 3^2 = 9\n8 is not prime: 8\nS(85638) = 8 + 25 + 6 + 9 + 8 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 50, 7, 23, 20, 21, 18, 23, 8, 284, 220, 23, 488, 220, 17, 20, 488, 220, 21, 488, 220, 24, 488, 220, 23, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "2dd1a9c0e110453d83b1677a2ba2e4a3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.5304031372070312, "response_sent_to_client_ts": 1773877216.1235292}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nAlternating sum of squares = 1^2 - 0^2 + 3^2 - 3^2 + 2^2 = 1 - 0 + 9 - 9 + 4 = 5\nD(10332) = |5| = 5\n\n\\boxed{5}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 284, 220, 16, 481, 220, 15, 488, 220, 24, 481, 220, 24, 488, 220, 19, 284, 220, 20, 198, 35, 7, 16, 15, 18, 18, 17, 8, 284, 760, 20, 91, 284, 220, 20, 271, 59, 79075, 90, 20, 92, 151645], "meta_info": {"id": "a95241fb9f7c4b13ac88a3760e0eaaa5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.2249388694763184, "response_sent_to_client_ts": 1773877215.818061}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "42", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n1 is not prime: 1\n0 is not prime: 0\n8 is not prime: 8\nS(75108) = 49 + 25 + 1 + 0 + 8 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 50, 7, 22, 20, 16, 15, 23, 8, 284, 220, 19, 24, 488, 220, 17, 20, 488, 220, 16, 488, 220, 15, 488, 220, 23, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "179e16cddad64210815123d8dfd6f40b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.5745246410369873, "response_sent_to_client_ts": 1773877216.1676903}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nL(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 43, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "bcff4a91c18c48419ed468d7ed740f38", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0668857097625732, "response_sent_to_client_ts": 1773877216.660011}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nN(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 45, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "dbab214dce4c48ffa89ea850a72928be", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.0092899799346924, "response_sent_to_client_ts": 1773877216.6024666}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "99210", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 29190 is \"29190\".\nRotations: 29190, 91902, 19029, 90291, 2919\nQ(29190) = min(29190, 91902, 19029, 90291, 2919) = 2919\n\n\\boxed{2919}", "output_ids": [785, 15723, 914, 315, 220, 17, 24, 16, 24, 15, 374, 330, 17, 24, 16, 24, 15, 22956, 36936, 804, 25, 220, 17, 24, 16, 24, 15, 11, 220, 24, 16, 24, 15, 17, 11, 220, 16, 24, 15, 17, 24, 11, 220, 24, 15, 17, 24, 16, 11, 220, 17, 24, 16, 24, 198, 48, 7, 17, 24, 16, 24, 15, 8, 284, 1308, 7, 17, 24, 16, 24, 15, 11, 220, 24, 16, 24, 15, 17, 11, 220, 16, 24, 15, 17, 24, 11, 220, 24, 15, 17, 24, 16, 11, 220, 17, 24, 16, 24, 8, 284, 220, 17, 24, 16, 24, 271, 59, 79075, 90, 17, 24, 16, 24, 92, 151645], "meta_info": {"id": "42872ba92a0a4595bf6f8e917a87d473", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.6403274536132812, "response_sent_to_client_ts": 1773877216.233489}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "98855", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 58598 is \"58598\".\nRotations: 58598, 85985, 59858, 98585, 85859\nQ(58598) = min(58598, 85985, 59858, 98585, 85859) = 58598\n\n\\boxed{58598}", "output_ids": [785, 15723, 914, 315, 220, 20, 23, 20, 24, 23, 374, 330, 20, 23, 20, 24, 23, 22956, 36936, 804, 25, 220, 20, 23, 20, 24, 23, 11, 220, 23, 20, 24, 23, 20, 11, 220, 20, 24, 23, 20, 23, 11, 220, 24, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 24, 198, 48, 7, 20, 23, 20, 24, 23, 8, 284, 1308, 7, 20, 23, 20, 24, 23, 11, 220, 23, 20, 24, 23, 20, 11, 220, 20, 24, 23, 20, 23, 11, 220, 24, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 24, 8, 284, 220, 20, 23, 20, 24, 23, 271, 59, 79075, 90, 20, 23, 20, 24, 23, 92, 151645], "meta_info": {"id": "9b6049e5bceb4221b10735e1ceadd222", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.7081682682037354, "response_sent_to_client_ts": 1773877216.301294}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nAlternating sum of squares = 6^2 - 0^2 + 1^2 - 7^2 + 4^2 = 36 - 0 + 1 - 49 + 16 = 4\nH(60174) = |4| = 4\n\n\\boxed{4}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 481, 220, 22, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 15, 488, 220, 16, 481, 220, 19, 24, 488, 220, 16, 21, 284, 220, 19, 198, 39, 7, 21, 15, 16, 22, 19, 8, 284, 760, 19, 91, 284, 220, 19, 271, 59, 79075, 90, 19, 92, 151645], "meta_info": {"id": "09ef21698f3a4198afc87f38cca3dd8f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 99, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.289567470550537, "response_sent_to_client_ts": 1773877215.8826861}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nN(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 45, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "923c5a4326a94b19bdca91217140878f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.640346050262451, "response_sent_to_client_ts": 1773877216.2335017}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "97679", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 97679 is \"97679\".\nRotations: 97679, 76799, 67997, 79976, 99767\nI(97679) = min(97679, 76799, 67997, 79976, 99767) = 67997\n\n\\boxed{67997}", "output_ids": [785, 15723, 914, 315, 220, 24, 22, 21, 22, 24, 374, 330, 24, 22, 21, 22, 24, 22956, 36936, 804, 25, 220, 24, 22, 21, 22, 24, 11, 220, 22, 21, 22, 24, 24, 11, 220, 21, 22, 24, 24, 22, 11, 220, 22, 24, 24, 22, 21, 11, 220, 24, 24, 22, 21, 22, 198, 40, 7, 24, 22, 21, 22, 24, 8, 284, 1308, 7, 24, 22, 21, 22, 24, 11, 220, 22, 21, 22, 24, 24, 11, 220, 21, 22, 24, 24, 22, 11, 220, 22, 24, 24, 22, 21, 11, 220, 24, 24, 22, 21, 22, 8, 284, 220, 21, 22, 24, 24, 22, 271, 59, 79075, 90, 21, 22, 24, 24, 22, 92, 151645], "meta_info": {"id": "b85faacba46d46ad8ef6051b3fb766fd", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.708181858062744, "response_sent_to_client_ts": 1773877216.3013046}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nAlternating sum of squares = 6^2 - 6^2 + 4^2 - 4^2 + 4^2 = 36 - 36 + 16 - 16 + 16 = 36\nF(66444) = |36| = 36\n\n\\boxed{36}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 21, 61, 17, 488, 220, 19, 61, 17, 481, 220, 19, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 18, 21, 488, 220, 16, 21, 481, 220, 16, 21, 488, 220, 16, 21, 284, 220, 18, 21, 198, 37, 7, 21, 21, 19, 19, 19, 8, 284, 760, 18, 21, 91, 284, 220, 18, 21, 271, 59, 79075, 90, 18, 21, 92, 151645], "meta_info": {"id": "cebfff63787441d5a5ec5de7f7f1e6ca", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.420340061187744, "response_sent_to_client_ts": 1773877216.0134878}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "19", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nA(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 32, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "bde331d60021479ea31f3e6610fc7224", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0389726161956787, "response_sent_to_client_ts": 1773877216.6321394}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "20", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nA(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 32, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "af793716d1324cb8b8011bb4ce40e641", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0092992782592773, "response_sent_to_client_ts": 1773877216.6024733}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nR(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 49, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "15c3b26970e544a5b798275f0c4d3139", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.066903591156006, "response_sent_to_client_ts": 1773877216.6600223}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nJ(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 41, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "9db371c6f3014a2392a6a6fe5596fd49", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 2.9780633449554443, "response_sent_to_client_ts": 1773877216.5711708}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "138", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\n3 is prime: 3^2 = 9\n0 is not prime: 0\n8 is not prime: 8\n0 is not prime: 0\n1 is not prime: 1\nP(30801) = 9 + 0 + 8 + 0 + 1 = 18\n\n\\boxed{18}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 47, 7, 18, 15, 23, 15, 16, 8, 284, 220, 24, 488, 220, 15, 488, 220, 23, 488, 220, 15, 488, 220, 16, 284, 220, 16, 23, 271, 59, 79075, 90, 16, 23, 92, 151645], "meta_info": {"id": "cace0c6a2c69415ca6da7818b7c6d9d0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.397961139678955, "response_sent_to_client_ts": 1773877215.9911056}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nR(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 49, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "c6b1d29a7fcf4b90ae41b7f6b469574a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0807716846466064, "response_sent_to_client_ts": 1773877216.6738937}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nN(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 45, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "b6571094934d478c830eb5a056fdd00e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.782689332962036, "response_sent_to_client_ts": 1773877216.3758051}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 5^2 + 8^2 = 25 - 4 + 64 - 25 + 64 = 124\nD(52858) = |124| = 124\n\n\\boxed{124}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 17, 20, 488, 220, 21, 19, 284, 220, 16, 17, 19, 198, 35, 7, 20, 17, 23, 20, 23, 8, 284, 760, 16, 17, 19, 91, 284, 220, 16, 17, 19, 271, 59, 79075, 90, 16, 17, 19, 92, 151645], "meta_info": {"id": "7b880195fd074286ada68d2ec98a8d53", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.485872745513916, "response_sent_to_client_ts": 1773877216.079006}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nR(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 49, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "8bdbc28b86fb4d3e9fa54df385a059c1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0093088150024414, "response_sent_to_client_ts": 1773877216.6024787}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "90", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nB(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 33, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "eeb4ef206ad14ce8aa560fde6e14f994", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 3.009317636489868, "response_sent_to_client_ts": 1773877216.6024842}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nAlternating sum of squares = 6^2 - 6^2 + 4^2 - 4^2 + 4^2 = 36 - 36 + 16 - 16 + 16 = 36\nD(66444) = |36| = 36\n\n\\boxed{36}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 21, 61, 17, 488, 220, 19, 61, 17, 481, 220, 19, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 18, 21, 488, 220, 16, 21, 481, 220, 16, 21, 488, 220, 16, 21, 284, 220, 18, 21, 198, 35, 7, 21, 21, 19, 19, 19, 8, 284, 760, 18, 21, 91, 284, 220, 18, 21, 271, 59, 79075, 90, 18, 21, 92, 151645], "meta_info": {"id": "87e2d52d3dc747faab0b7dcedf1ea814", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.420349359512329, "response_sent_to_client_ts": 1773877216.013495}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nAlternating sum of squares = 2^2 - 3^2 + 2^2 - 9^2 = 4 - 9 + 4 - 81 = -82\nH(2329) = |-82| = 82\n\n\\boxed{82}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 481, 220, 24, 61, 17, 284, 220, 19, 481, 220, 24, 488, 220, 19, 481, 220, 23, 16, 284, 481, 23, 17, 198, 39, 7, 17, 18, 17, 24, 8, 284, 44561, 23, 17, 91, 284, 220, 23, 17, 271, 59, 79075, 90, 23, 17, 92, 151645], "meta_info": {"id": "35dafa7b19b9456e8c4990cf226ec5b2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 88, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.053431510925293, "response_sent_to_client_ts": 1773877215.6465526}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\n6 is not prime: 6\n0 is not prime: 0\n1 is not prime: 1\n7 is prime: 7^2 = 49\n4 is not prime: 4\nK(60174) = 6 + 0 + 1 + 49 + 4 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 42, 7, 21, 15, 16, 22, 19, 8, 284, 220, 21, 488, 220, 15, 488, 220, 16, 488, 220, 19, 24, 488, 220, 19, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "a75b9643e16843fb9c8feffccdcd9b62", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.443047285079956, "response_sent_to_client_ts": 1773877216.0362043}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9192", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 29190 is \"29190\".\nRotations: 29190, 91902, 19029, 90291, 2919\nI(29190) = min(29190, 91902, 19029, 90291, 2919) = 2919\n\n\\boxed{2919}", "output_ids": [785, 15723, 914, 315, 220, 17, 24, 16, 24, 15, 374, 330, 17, 24, 16, 24, 15, 22956, 36936, 804, 25, 220, 17, 24, 16, 24, 15, 11, 220, 24, 16, 24, 15, 17, 11, 220, 16, 24, 15, 17, 24, 11, 220, 24, 15, 17, 24, 16, 11, 220, 17, 24, 16, 24, 198, 40, 7, 17, 24, 16, 24, 15, 8, 284, 1308, 7, 17, 24, 16, 24, 15, 11, 220, 24, 16, 24, 15, 17, 11, 220, 16, 24, 15, 17, 24, 11, 220, 24, 15, 17, 24, 16, 11, 220, 17, 24, 16, 24, 8, 284, 220, 17, 24, 16, 24, 271, 59, 79075, 90, 17, 24, 16, 24, 92, 151645], "meta_info": {"id": "59ac66b7128f4444a56a6dd51605920c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6403560638427734, "response_sent_to_client_ts": 1773877216.2335083}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nAlternating sum of squares = 2^2 - 9^2 + 1^2 - 9^2 + 0^2 = 4 - 81 + 1 - 81 + 0 = -117\nH(29190) = |-117| = 117\n\n\\boxed{117}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 24, 61, 17, 488, 220, 16, 61, 17, 481, 220, 24, 61, 17, 488, 220, 15, 61, 17, 284, 220, 19, 481, 220, 23, 16, 488, 220, 16, 481, 220, 23, 16, 488, 220, 15, 284, 481, 16, 16, 22, 198, 39, 7, 17, 24, 16, 24, 15, 8, 284, 44561, 16, 16, 22, 91, 284, 220, 16, 16, 22, 271, 59, 79075, 90, 16, 16, 22, 92, 151645], "meta_info": {"id": "e86d6a616aee4a8fa95d87bff6d28e50", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.4430654048919678, "response_sent_to_client_ts": 1773877216.036216}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nAlternating sum of squares = 6^2 - 5^2 + 9^2 - 9^2 = 36 - 25 + 81 - 81 = 11\nD(6599) = |11| = 11\n\n\\boxed{11}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 481, 220, 24, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 23, 16, 481, 220, 23, 16, 284, 220, 16, 16, 198, 35, 7, 21, 20, 24, 24, 8, 284, 760, 16, 16, 91, 284, 220, 16, 16, 271, 59, 79075, 90, 16, 16, 92, 151645], "meta_info": {"id": "9c5d366b3bb84e22ad95441253d42116", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.118302822113037, "response_sent_to_client_ts": 1773877215.7114236}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\n1 is not prime: 1\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n9 is not prime: 9\nE(15559) = 1 + 25 + 25 + 25 + 9 = 85\n\n\\boxed{85}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 36, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 24, 284, 220, 23, 20, 271, 59, 79075, 90, 23, 20, 92, 151645], "meta_info": {"id": "ca7a57fc360f4b2599ad95d77c6c5e93", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.7054996490478516, "response_sent_to_client_ts": 1773877216.2986445}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "33210", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 10332 is \"10332\".\nRotations: 10332, 3321, 33210, 32103, 21033\nQ(10332) = min(10332, 3321, 33210, 32103, 21033) = 3321\n\n\\boxed{3321}", "output_ids": [785, 15723, 914, 315, 220, 16, 15, 18, 18, 17, 374, 330, 16, 15, 18, 18, 17, 22956, 36936, 804, 25, 220, 16, 15, 18, 18, 17, 11, 220, 18, 18, 17, 16, 11, 220, 18, 18, 17, 16, 15, 11, 220, 18, 17, 16, 15, 18, 11, 220, 17, 16, 15, 18, 18, 198, 48, 7, 16, 15, 18, 18, 17, 8, 284, 1308, 7, 16, 15, 18, 18, 17, 11, 220, 18, 18, 17, 16, 11, 220, 18, 18, 17, 16, 15, 11, 220, 18, 17, 16, 15, 18, 11, 220, 17, 16, 15, 18, 18, 8, 284, 220, 18, 18, 17, 16, 271, 59, 79075, 90, 18, 18, 17, 16, 92, 151645], "meta_info": {"id": "3167b1201c074af0a2ea55b0c4dbc49d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.6403648853302, "response_sent_to_client_ts": 1773877216.233514}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1233", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\n1 is not prime: 1\n0 is not prime: 0\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\nP(10332) = 1 + 0 + 9 + 9 + 4 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 47, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 24, 488, 220, 24, 488, 220, 19, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "fc47d365ab6f4f5dabaa644883c5179a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.5745396614074707, "response_sent_to_client_ts": 1773877216.167698}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 7^2 + 9^2 = 25 - 4 + 64 - 49 + 81 = 97\nG(52879) = |97| = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 24, 22, 198, 38, 7, 20, 17, 23, 22, 24, 8, 284, 760, 24, 22, 91, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "3100c280ee034d6fa8cdc1d3cfc598d1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 2.3979814052581787, "response_sent_to_client_ts": 1773877215.9911182}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "14", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nJ(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 41, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "79ca51c832004e94af0c7022e64e86d8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 3.1091699600219727, "response_sent_to_client_ts": 1773877216.7023065}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "102", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nO(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 46, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "819da75acc9641508b421b2c183b1127", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.0389814376831055, "response_sent_to_client_ts": 1773877216.6321456}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "10", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nJ(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 41, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "a91bd5ded4af48b1be7ca00908f4312c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0389904975891113, "response_sent_to_client_ts": 1773877216.6321514}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "198", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nO(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 46, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "33fed733743b4819bedb8d45ed9a233a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 3.0949392318725586, "response_sent_to_client_ts": 1773877216.6880713}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nAlternating sum of squares = 1^2 - 3^2 + 4^2 - 5^2 + 3^2 = 1 - 9 + 16 - 25 + 9 = -8\nD(13453) = |-8| = 8\n\n\\boxed{8}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 18, 61, 17, 488, 220, 19, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 284, 220, 16, 481, 220, 24, 488, 220, 16, 21, 481, 220, 17, 20, 488, 220, 24, 284, 481, 23, 198, 35, 7, 16, 18, 19, 20, 18, 8, 284, 44561, 23, 91, 284, 220, 23, 271, 59, 79075, 90, 23, 92, 151645], "meta_info": {"id": "cbed727506c242d8bac2869e81500c6a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 98, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.267683744430542, "response_sent_to_client_ts": 1773877215.8608005}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nM(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 44, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "f80671028bc4477987284f2c58794035", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1091864109039307, "response_sent_to_client_ts": 1773877216.7023172}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nAlternating sum of squares = 3^2 - 0^2 + 8^2 - 0^2 + 1^2 = 9 - 0 + 64 - 0 + 1 = 74\nG(30801) = |74| = 74\n\n\\boxed{74}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 18, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 284, 220, 24, 481, 220, 15, 488, 220, 21, 19, 481, 220, 15, 488, 220, 16, 284, 220, 22, 19, 198, 38, 7, 18, 15, 23, 15, 16, 8, 284, 760, 22, 19, 91, 284, 220, 22, 19, 271, 59, 79075, 90, 22, 19, 92, 151645], "meta_info": {"id": "be9a31c3b375430281d2c2d04ddfc04c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 101, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.33296537399292, "response_sent_to_client_ts": 1773877215.9260798}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1578", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n1 is not prime: 1\n0 is not prime: 0\n8 is not prime: 8\nP(75108) = 49 + 25 + 1 + 0 + 8 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 47, 7, 22, 20, 16, 15, 23, 8, 284, 220, 19, 24, 488, 220, 17, 20, 488, 220, 16, 488, 220, 15, 488, 220, 23, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "2f3158b61472410cb1cd1e211d93b291", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.574549436569214, "response_sent_to_client_ts": 1773877216.167704}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nAlternating sum of squares = 8^2 - 5^2 + 6^2 - 3^2 + 8^2 = 64 - 25 + 36 - 9 + 64 = 130\nG(85638) = |130| = 130\n\n\\boxed{130}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 21, 61, 17, 481, 220, 18, 61, 17, 488, 220, 23, 61, 17, 284, 220, 21, 19, 481, 220, 17, 20, 488, 220, 18, 21, 481, 220, 24, 488, 220, 21, 19, 284, 220, 16, 18, 15, 198, 38, 7, 23, 20, 21, 18, 23, 8, 284, 760, 16, 18, 15, 91, 284, 220, 16, 18, 15, 271, 59, 79075, 90, 16, 18, 15, 92, 151645], "meta_info": {"id": "df3b65b61f004ced9034f9079ca15e90", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.4858922958374023, "response_sent_to_client_ts": 1773877216.0790186}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nM(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 44, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "d247611bffcf4732acb9d0edf72acfd6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1497642993927, "response_sent_to_client_ts": 1773877216.742901}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "23814", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nB(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 33, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "11a0a0473bee4db09f2b6b8f872242c7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 3.1497817039489746, "response_sent_to_client_ts": 1773877216.7429113}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4456", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\n5 is prime: 5^2 = 25\n4 is not prime: 4\n0 is not prime: 0\n4 is not prime: 4\n6 is not prime: 6\nP(54046) = 25 + 4 + 0 + 4 + 6 = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 47, 7, 20, 19, 15, 19, 21, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 15, 488, 220, 19, 488, 220, 21, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "bade594fb36a498f80c94058934547f2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.443074941635132, "response_sent_to_client_ts": 1773877216.0362227}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nC(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 34, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "d14bbab316b941c78aff3e2f23b30543", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.948336601257324, "response_sent_to_client_ts": 1773877216.5414689}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nE(65333) = 6 + 25 + 9 + 9 + 9 = 58\n\n\\boxed{58}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 36, 7, 21, 20, 18, 18, 18, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 488, 220, 24, 284, 220, 20, 23, 271, 59, 79075, 90, 20, 23, 92, 151645], "meta_info": {"id": "828bbf1fa79243e6920fc1caffc53859", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.705519199371338, "response_sent_to_client_ts": 1773877216.298658}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nN(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 45, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "c92d00daed4b40bf8910a6feca84f233", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1091954708099365, "response_sent_to_client_ts": 1773877216.702323}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "40", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n5 is prime: 5^2 = 25\n8 is not prime: 8\nT(52858) = 25 + 4 + 8 + 25 + 8 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 51, 7, 20, 17, 23, 20, 23, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 17, 20, 488, 220, 23, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "44c97bce346440faae47bbe5f70a2596", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.662492036819458, "response_sent_to_client_ts": 1773877216.255652}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nR(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 49, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "8fa7aa30179748b0b72696214c10f661", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0949606895446777, "response_sent_to_client_ts": 1773877216.688082}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nAlternating sum of squares = 5^2 - 8^2 + 5^2 - 9^2 + 8^2 = 25 - 64 + 25 - 81 + 64 = -31\nG(58598) = |-31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 20, 61, 17, 481, 220, 24, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 17, 20, 481, 220, 23, 16, 488, 220, 21, 19, 284, 481, 18, 16, 198, 38, 7, 20, 23, 20, 24, 23, 8, 284, 44561, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "9f7b92ec360f4509b1e6e317fce757ae", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.4203579425811768, "response_sent_to_client_ts": 1773877216.013502}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "810", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nB(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 33, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "8226706cdd9245e1aae2b547bca79e1c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 181, "cached_tokens_details": null, "e2e_latency": 3.009326457977295, "response_sent_to_client_ts": 1773877216.6024902}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nJ(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 41, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "a22434f7da35407da44ba6270948de2e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 2.948357582092285, "response_sent_to_client_ts": 1773877216.5414822}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "35", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nA(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 32, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "8c90f216a6ab41749dd042b6775b9cb4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.1362922191619873, "response_sent_to_client_ts": 1773877216.7294264}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\n5 is prime: 5^2 = 25\n4 is not prime: 4\n0 is not prime: 0\n4 is not prime: 4\n6 is not prime: 6\nK(54046) = 25 + 4 + 0 + 4 + 6 = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 42, 7, 20, 19, 15, 19, 21, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 15, 488, 220, 19, 488, 220, 21, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "44f580f1b4d24ec79718afd8473fa633", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.443082809448242, "response_sent_to_client_ts": 1773877216.0362287}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\n1 is not prime: 1\n3 is prime: 3^2 = 9\n4 is not prime: 4\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\nT(13453) = 1 + 9 + 4 + 25 + 9 = 48\n\n\\boxed{48}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 51, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 24, 488, 220, 19, 488, 220, 17, 20, 488, 220, 24, 284, 220, 19, 23, 271, 59, 79075, 90, 19, 23, 92, 151645], "meta_info": {"id": "849f2cdca7b34c749ba92e389b4f536c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.617750406265259, "response_sent_to_client_ts": 1773877216.2108831}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "13", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nJ(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 41, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "284c06326c6e44f7827bf5476af0cf31", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 3.1363120079040527, "response_sent_to_client_ts": 1773877216.7294388}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n5 is prime: 5^2 = 25\n4 is not prime: 4\nK(72154) = 49 + 4 + 1 + 25 + 4 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 42, 7, 22, 17, 16, 20, 19, 8, 284, 220, 19, 24, 488, 220, 19, 488, 220, 16, 488, 220, 17, 20, 488, 220, 19, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "0e7ce1beda7f4b209e96928ff194c23c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.662513494491577, "response_sent_to_client_ts": 1773877216.2556663}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "65311", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 11536 is \"11536\".\nRotations: 11536, 15361, 53611, 36115, 61153\nQ(11536) = min(11536, 15361, 53611, 36115, 61153) = 11536\n\n\\boxed{11536}", "output_ids": [785, 15723, 914, 315, 220, 16, 16, 20, 18, 21, 374, 330, 16, 16, 20, 18, 21, 22956, 36936, 804, 25, 220, 16, 16, 20, 18, 21, 11, 220, 16, 20, 18, 21, 16, 11, 220, 20, 18, 21, 16, 16, 11, 220, 18, 21, 16, 16, 20, 11, 220, 21, 16, 16, 20, 18, 198, 48, 7, 16, 16, 20, 18, 21, 8, 284, 1308, 7, 16, 16, 20, 18, 21, 11, 220, 16, 20, 18, 21, 16, 11, 220, 20, 18, 21, 16, 16, 11, 220, 18, 21, 16, 16, 20, 11, 220, 21, 16, 16, 20, 18, 8, 284, 220, 16, 16, 20, 18, 21, 271, 59, 79075, 90, 16, 16, 20, 18, 21, 92, 151645], "meta_info": {"id": "2838ed11da7a4cfe8336500c8399972a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.7081916332244873, "response_sent_to_client_ts": 1773877216.3013115}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nL(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 43, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "7868b12e6fff4857b4709c622b7a316d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.038998603820801, "response_sent_to_client_ts": 1773877216.6321566}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nAlternating sum of squares = 4^2 - 9^2 + 6^2 - 2^2 + 8^2 = 16 - 81 + 36 - 4 + 64 = 31\nH(49628) = |31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 24, 61, 17, 488, 220, 21, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 284, 220, 16, 21, 481, 220, 23, 16, 488, 220, 18, 21, 481, 220, 19, 488, 220, 21, 19, 284, 220, 18, 16, 198, 39, 7, 19, 24, 21, 17, 23, 8, 284, 760, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "351b9584c3c4445e86759aad2737732e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.3979907035827637, "response_sent_to_client_ts": 1773877215.9911246}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nAlternating sum of squares = 2^2 - 9^2 + 1^2 - 9^2 + 0^2 = 4 - 81 + 1 - 81 + 0 = -117\nF(29190) = |-117| = 117\n\n\\boxed{117}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 24, 61, 17, 488, 220, 16, 61, 17, 481, 220, 24, 61, 17, 488, 220, 15, 61, 17, 284, 220, 19, 481, 220, 23, 16, 488, 220, 16, 481, 220, 23, 16, 488, 220, 15, 284, 481, 16, 16, 22, 198, 37, 7, 17, 24, 16, 24, 15, 8, 284, 44561, 16, 16, 22, 91, 284, 220, 16, 16, 22, 271, 59, 79075, 90, 16, 16, 22, 92, 151645], "meta_info": {"id": "f683028bd58740d0a70f1a8a0b7f6fa3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.452343225479126, "response_sent_to_client_ts": 1773877219.1977713}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nM(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 44, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "0a6cbd0ac71644f9a52a833b7079dab9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.9968531131744385, "response_sent_to_client_ts": 1773877219.7422886}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nM(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 44, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "04a4c8e68f9740f38a7ad8a015ff877e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.7273154258728027, "response_sent_to_client_ts": 1773877219.4727244}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nA(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 32, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "0fd18a46f39b477090eba2078d81514e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.0853216648101807, "response_sent_to_client_ts": 1773877219.8307796}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "21", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nA(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 32, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "996811b49762437796e3a4679a330772", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.0273616313934326, "response_sent_to_client_ts": 1773877219.772827}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "81", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\n9 is not prime: 9\n7 is prime: 7^2 = 49\n6 is not prime: 6\n7 is prime: 7^2 = 49\n9 is not prime: 9\nT(97679) = 9 + 49 + 6 + 49 + 9 = 122\n\n\\boxed{122}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 24, 374, 537, 10250, 25, 220, 24, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 51, 7, 24, 22, 21, 22, 24, 8, 284, 220, 24, 488, 220, 19, 24, 488, 220, 21, 488, 220, 19, 24, 488, 220, 24, 284, 220, 16, 17, 17, 271, 59, 79075, 90, 16, 17, 17, 92, 151645], "meta_info": {"id": "a5c71044b9554fcd9fb5a1bd23177143", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.628488063812256, "response_sent_to_client_ts": 1773877219.3739626}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\n9 is not prime: 9\n7 is prime: 7^2 = 49\n6 is not prime: 6\n7 is prime: 7^2 = 49\n9 is not prime: 9\nK(97679) = 9 + 49 + 6 + 49 + 9 = 122\n\n\\boxed{122}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 24, 374, 537, 10250, 25, 220, 24, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 42, 7, 24, 22, 21, 22, 24, 8, 284, 220, 24, 488, 220, 19, 24, 488, 220, 21, 488, 220, 19, 24, 488, 220, 24, 284, 220, 16, 17, 17, 271, 59, 79075, 90, 16, 17, 17, 92, 151645], "meta_info": {"id": "cf9b258e89274ba1b76682a6b5c91002", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.628507137298584, "response_sent_to_client_ts": 1773877219.3739748}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nAlternating sum of squares = 1^2 - 1^2 + 5^2 - 3^2 + 6^2 = 1 - 1 + 25 - 9 + 36 = 52\nD(11536) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 16, 61, 17, 488, 220, 20, 61, 17, 481, 220, 18, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 481, 220, 16, 488, 220, 17, 20, 481, 220, 24, 488, 220, 18, 21, 284, 220, 20, 17, 198, 35, 7, 16, 16, 20, 18, 21, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "1d84a104533b46afa4c74db991092aaa", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.36338210105896, "response_sent_to_client_ts": 1773877219.108819}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n6 is not prime: 6\n3 is prime: 3^2 = 9\n8 is not prime: 8\nK(85638) = 8 + 25 + 6 + 9 + 8 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 42, 7, 23, 20, 21, 18, 23, 8, 284, 220, 23, 488, 220, 17, 20, 488, 220, 21, 488, 220, 24, 488, 220, 23, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "01f305b44a05446d91bdba0bbc7e8e01", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.540174722671509, "response_sent_to_client_ts": 1773877219.2856143}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nM(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 44, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "fa091ddc10fb4f44a7c795029732d488", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.085336685180664, "response_sent_to_client_ts": 1773877219.8307893}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "72", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nO(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 46, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "cfeb76b2d9ee444eb8331f72cf05a0fe", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 2.9968700408935547, "response_sent_to_client_ts": 1773877219.7423003}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\n3 is prime: 3^2 = 9\n0 is not prime: 0\n8 is not prime: 8\n0 is not prime: 0\n1 is not prime: 1\nS(30801) = 9 + 0 + 8 + 0 + 1 = 18\n\n\\boxed{18}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 50, 7, 18, 15, 23, 15, 16, 8, 284, 220, 24, 488, 220, 15, 488, 220, 23, 488, 220, 15, 488, 220, 16, 284, 220, 16, 23, 271, 59, 79075, 90, 16, 23, 92, 151645], "meta_info": {"id": "515ccb51f5ea42919d661fc2f971a6cc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.4082698822021484, "response_sent_to_client_ts": 1773877219.1537488}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nAlternating sum of squares = 7^2 - 5^2 + 1^2 - 0^2 + 8^2 = 49 - 25 + 1 - 0 + 64 = 89\nF(75108) = |89| = 89\n\n\\boxed{89}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 20, 61, 17, 488, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 284, 220, 19, 24, 481, 220, 17, 20, 488, 220, 16, 481, 220, 15, 488, 220, 21, 19, 284, 220, 23, 24, 198, 37, 7, 22, 20, 16, 15, 23, 8, 284, 760, 23, 24, 91, 284, 220, 23, 24, 271, 59, 79075, 90, 23, 24, 92, 151645], "meta_info": {"id": "1c2343d6ef4948b6a768fad096b61673", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.3852603435516357, "response_sent_to_client_ts": 1773877219.1306849}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nR(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 49, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "270eb91615cf494d9a356131ed289541", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9968793392181396, "response_sent_to_client_ts": 1773877219.7423067}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nC(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 34, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "940253ba8aa144e5bc7bb27c216dfe4e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0273783206939697, "response_sent_to_client_ts": 1773877219.7728384}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nAlternating sum of squares = 5^2 - 8^2 + 7^2 - 3^2 + 3^2 = 25 - 64 + 49 - 9 + 9 = 10\nH(58733) = |10| = 10\n\n\\boxed{10}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 24, 481, 220, 24, 488, 220, 24, 284, 220, 16, 15, 198, 39, 7, 20, 23, 22, 18, 18, 8, 284, 760, 16, 15, 91, 284, 220, 16, 15, 271, 59, 79075, 90, 16, 15, 92, 151645], "meta_info": {"id": "1b062ecfa2684078a5d4050e6d33047d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3852763175964355, "response_sent_to_client_ts": 1773877219.1306958}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nAlternating sum of squares = 5^2 - 8^2 + 5^2 - 9^2 + 8^2 = 25 - 64 + 25 - 81 + 64 = -31\nF(58598) = |-31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 20, 61, 17, 481, 220, 24, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 17, 20, 481, 220, 23, 16, 488, 220, 21, 19, 284, 481, 18, 16, 198, 37, 7, 20, 23, 20, 24, 23, 8, 284, 44561, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "5da6e8cb96564c3ab5c4018ad0aeb2d6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.430250644683838, "response_sent_to_client_ts": 1773877219.1756625}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nAlternating sum of squares = 1^2 - 0^2 + 3^2 - 3^2 + 2^2 = 1 - 0 + 9 - 9 + 4 = 5\nF(10332) = |5| = 5\n\n\\boxed{5}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 284, 220, 16, 481, 220, 15, 488, 220, 24, 481, 220, 24, 488, 220, 19, 284, 220, 20, 198, 37, 7, 16, 15, 18, 18, 17, 8, 284, 760, 20, 91, 284, 220, 20, 271, 59, 79075, 90, 20, 92, 151645], "meta_info": {"id": "50c9f143af4c4593aa62be1b273b9642", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.2344038486480713, "response_sent_to_client_ts": 1773877218.979822}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "65333", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 65333 is \"65333\".\nRotations: 65333, 53336, 33365, 33653, 36533\nQ(65333) = min(65333, 53336, 33365, 33653, 36533) = 33365\n\n\\boxed{33365}", "output_ids": [785, 15723, 914, 315, 220, 21, 20, 18, 18, 18, 374, 330, 21, 20, 18, 18, 18, 22956, 36936, 804, 25, 220, 21, 20, 18, 18, 18, 11, 220, 20, 18, 18, 18, 21, 11, 220, 18, 18, 18, 21, 20, 11, 220, 18, 18, 21, 20, 18, 11, 220, 18, 21, 20, 18, 18, 198, 48, 7, 21, 20, 18, 18, 18, 8, 284, 1308, 7, 21, 20, 18, 18, 18, 11, 220, 20, 18, 18, 18, 21, 11, 220, 18, 18, 18, 21, 20, 11, 220, 18, 18, 21, 20, 18, 11, 220, 18, 21, 20, 18, 18, 8, 284, 220, 18, 18, 18, 21, 20, 271, 59, 79075, 90, 18, 18, 18, 21, 20, 92, 151645], "meta_info": {"id": "e5e6697bf637495c932339a7e713de93", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.697850465774536, "response_sent_to_client_ts": 1773877219.4432983}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nL(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 43, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "9d23cd6ef90d4e6b8c1f9c47fb5bcaa6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 3.09869647026062, "response_sent_to_client_ts": 1773877219.8441138}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\n1 is not prime: 1\n0 is not prime: 0\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\nK(10332) = 1 + 0 + 9 + 9 + 4 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 42, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 24, 488, 220, 24, 488, 220, 19, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "8ae4adb5791347aeaf108c3e215587df", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.584028959274292, "response_sent_to_client_ts": 1773877219.3294537}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "34", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\n4 is not prime: 4\n1 is not prime: 1\n4 is not prime: 4\n2 is prime: 2^2 = 4\n6 is not prime: 6\nS(41426) = 4 + 1 + 4 + 4 + 6 = 19\n\n\\boxed{19}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 50, 7, 19, 16, 19, 17, 21, 8, 284, 220, 19, 488, 220, 16, 488, 220, 19, 488, 220, 19, 488, 220, 21, 284, 220, 16, 24, 271, 59, 79075, 90, 16, 24, 92, 151645], "meta_info": {"id": "66bb56953f6742ff94537e1ccbaf6a6d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.408285140991211, "response_sent_to_client_ts": 1773877219.15376}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "89585", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 58598 is \"58598\".\nRotations: 58598, 85985, 59858, 98585, 85859\nI(58598) = min(58598, 85985, 59858, 98585, 85859) = 58598\n\n\\boxed{58598}", "output_ids": [785, 15723, 914, 315, 220, 20, 23, 20, 24, 23, 374, 330, 20, 23, 20, 24, 23, 22956, 36936, 804, 25, 220, 20, 23, 20, 24, 23, 11, 220, 23, 20, 24, 23, 20, 11, 220, 20, 24, 23, 20, 23, 11, 220, 24, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 24, 198, 40, 7, 20, 23, 20, 24, 23, 8, 284, 1308, 7, 20, 23, 20, 24, 23, 11, 220, 23, 20, 24, 23, 20, 11, 220, 20, 24, 23, 20, 23, 11, 220, 24, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 24, 8, 284, 220, 20, 23, 20, 24, 23, 271, 59, 79075, 90, 20, 23, 20, 24, 23, 92, 151645], "meta_info": {"id": "b8ee84f2c00d4e56afa464489c4e4d92", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.6978678703308105, "response_sent_to_client_ts": 1773877219.4433112}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nAlternating sum of squares = 6^2 - 5^2 + 9^2 - 9^2 = 36 - 25 + 81 - 81 = 11\nF(6599) = |11| = 11\n\n\\boxed{11}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 481, 220, 24, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 23, 16, 481, 220, 23, 16, 284, 220, 16, 16, 198, 37, 7, 21, 20, 24, 24, 8, 284, 760, 16, 16, 91, 284, 220, 16, 16, 271, 59, 79075, 90, 16, 16, 92, 151645], "meta_info": {"id": "2dd8757f18a54697ab5c3a4d3d8b74a0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.1276614665985107, "response_sent_to_client_ts": 1773877218.8730924}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nR(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 49, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "9584ad77bec34c8db6a9cd76f31915ca", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.027388095855713, "response_sent_to_client_ts": 1773877219.7728453}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nL(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 43, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "8aa434e94f3b4cdeb8babed5e7d142c4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0853469371795654, "response_sent_to_client_ts": 1773877219.8307965}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nN(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 45, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "d2fdff5dc1a842a18e134810100d1263", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0273969173431396, "response_sent_to_client_ts": 1773877219.7728515}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "34", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\n0 is not prime: 0\nS(58220) = 25 + 8 + 4 + 4 + 0 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 50, 7, 20, 23, 17, 17, 15, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 488, 220, 19, 488, 220, 15, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "9f36b89fcc0b4c40aacc1753a5f5db54", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.628516912460327, "response_sent_to_client_ts": 1773877219.3739822}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nM(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 44, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "61bc75ad0ff14600a593ccfe37e00d64", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.056103467941284, "response_sent_to_client_ts": 1773877219.8015404}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "19", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nA(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 32, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "9a9d8221d2b04303b997feaae4737c55", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.0561203956604004, "response_sent_to_client_ts": 1773877219.801552}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nR(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 49, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "0d3b9cf01d1b4f5984d3921a9fd4ef21", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0987093448638916, "response_sent_to_client_ts": 1773877219.8441226}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "29", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nA(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 32, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "c38b5800ea92469ab7f54e1418edb3d7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.7720136642456055, "response_sent_to_client_ts": 1773877219.5174208}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 7^2 + 9^2 = 25 - 4 + 64 - 49 + 81 = 97\nF(52879) = |97| = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 24, 22, 198, 37, 7, 20, 17, 23, 22, 24, 8, 284, 760, 24, 22, 91, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "1966d956743f408c908fd465f5f4a060", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 2.408294200897217, "response_sent_to_client_ts": 1773877219.1537662}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "18", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nJ(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 41, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "16f7c22bb404468bbc9f2f2476155e03", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 3.1387057304382324, "response_sent_to_client_ts": 1773877219.884116}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nL(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 43, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "3760b8ece8d0477d86657a2555704913", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.96653413772583, "response_sent_to_client_ts": 1773877219.7119873}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nL(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 43, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "f930fe8730ca41ffac9ce44f023d6c47", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0274059772491455, "response_sent_to_client_ts": 1773877219.7728572}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nN(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 45, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "a41e7b8d3049433b9ece03555621fff9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.027414321899414, "response_sent_to_client_ts": 1773877219.7728627}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nM(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 44, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "10b5bb0ab80c44128dfdc14af6fccdfc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0701897144317627, "response_sent_to_client_ts": 1773877219.8156066}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nAlternating sum of squares = 7^2 - 3^2 + 0^2 - 2^2 + 4^2 = 49 - 9 + 0 - 4 + 16 = 52\nF(73024) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 15, 61, 17, 481, 220, 17, 61, 17, 488, 220, 19, 61, 17, 284, 220, 19, 24, 481, 220, 24, 488, 220, 15, 481, 220, 19, 488, 220, 16, 21, 284, 220, 20, 17, 198, 37, 7, 22, 18, 15, 17, 19, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "17c87ac064cd4ad2a804e8d67a5b414c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.3633980751037598, "response_sent_to_client_ts": 1773877219.1088297}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "83658", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 85638 is \"85638\".\nRotations: 85638, 56388, 63885, 38856, 88563\nI(85638) = min(85638, 56388, 63885, 38856, 88563) = 38856\n\n\\boxed{38856}", "output_ids": [785, 15723, 914, 315, 220, 23, 20, 21, 18, 23, 374, 330, 23, 20, 21, 18, 23, 22956, 36936, 804, 25, 220, 23, 20, 21, 18, 23, 11, 220, 20, 21, 18, 23, 23, 11, 220, 21, 18, 23, 23, 20, 11, 220, 18, 23, 23, 20, 21, 11, 220, 23, 23, 20, 21, 18, 198, 40, 7, 23, 20, 21, 18, 23, 8, 284, 1308, 7, 23, 20, 21, 18, 23, 11, 220, 20, 21, 18, 23, 23, 11, 220, 21, 18, 23, 23, 20, 11, 220, 18, 23, 23, 20, 21, 11, 220, 23, 23, 20, 21, 18, 8, 284, 220, 18, 23, 23, 20, 21, 271, 59, 79075, 90, 18, 23, 23, 20, 21, 92, 151645], "meta_info": {"id": "0df26987d6a4472b91b202c5bc11112b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.6978769302368164, "response_sent_to_client_ts": 1773877219.4433172}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1467", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\n6 is not prime: 6\n0 is not prime: 0\n1 is not prime: 1\n7 is prime: 7^2 = 49\n4 is not prime: 4\nP(60174) = 6 + 0 + 1 + 49 + 4 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 47, 7, 21, 15, 16, 22, 19, 8, 284, 220, 21, 488, 220, 15, 488, 220, 16, 488, 220, 19, 24, 488, 220, 19, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "a2c638501bec4cd6ac096c58cff1e8b4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.452360153198242, "response_sent_to_client_ts": 1773877219.1977823}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24689", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\n4 is not prime: 4\n9 is not prime: 9\n6 is not prime: 6\n2 is prime: 2^2 = 4\n8 is not prime: 8\nP(49628) = 4 + 9 + 6 + 4 + 8 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 47, 7, 19, 24, 21, 17, 23, 8, 284, 220, 19, 488, 220, 24, 488, 220, 21, 488, 220, 19, 488, 220, 23, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "23f57180eaa0436a8b6f35ab6366e6e2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.408301830291748, "response_sent_to_client_ts": 1773877219.1537716}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nAlternating sum of squares = 5^2 - 8^2 + 2^2 - 2^2 + 0^2 = 25 - 64 + 4 - 4 + 0 = -39\nH(58220) = |-39| = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 17, 61, 17, 481, 220, 17, 61, 17, 488, 220, 15, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 481, 220, 19, 488, 220, 15, 284, 481, 18, 24, 198, 39, 7, 20, 23, 17, 17, 15, 8, 284, 44561, 18, 24, 91, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "7836454a94ee4d9fb1965a50a2a65dae", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3634066581726074, "response_sent_to_client_ts": 1773877219.108836}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "63511", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 11536 is \"11536\".\nRotations: 11536, 15361, 53611, 36115, 61153\nI(11536) = min(11536, 15361, 53611, 36115, 61153) = 11536\n\n\\boxed{11536}", "output_ids": [785, 15723, 914, 315, 220, 16, 16, 20, 18, 21, 374, 330, 16, 16, 20, 18, 21, 22956, 36936, 804, 25, 220, 16, 16, 20, 18, 21, 11, 220, 16, 20, 18, 21, 16, 11, 220, 20, 18, 21, 16, 16, 11, 220, 18, 21, 16, 16, 20, 11, 220, 21, 16, 16, 20, 18, 198, 40, 7, 16, 16, 20, 18, 21, 8, 284, 1308, 7, 16, 16, 20, 18, 21, 11, 220, 16, 20, 18, 21, 16, 11, 220, 20, 18, 21, 16, 16, 11, 220, 18, 21, 16, 16, 20, 11, 220, 21, 16, 16, 20, 18, 8, 284, 220, 16, 16, 20, 18, 21, 271, 59, 79075, 90, 16, 16, 20, 18, 21, 92, 151645], "meta_info": {"id": "9b409bcd673c4749bcfd109fbcb57d28", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6978862285614014, "response_sent_to_client_ts": 1773877219.4433234}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "87510", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 75108 is \"75108\".\nRotations: 75108, 51087, 10875, 8751, 87510\nQ(75108) = min(75108, 51087, 10875, 8751, 87510) = 8751\n\n\\boxed{8751}", "output_ids": [785, 15723, 914, 315, 220, 22, 20, 16, 15, 23, 374, 330, 22, 20, 16, 15, 23, 22956, 36936, 804, 25, 220, 22, 20, 16, 15, 23, 11, 220, 20, 16, 15, 23, 22, 11, 220, 16, 15, 23, 22, 20, 11, 220, 23, 22, 20, 16, 11, 220, 23, 22, 20, 16, 15, 198, 48, 7, 22, 20, 16, 15, 23, 8, 284, 1308, 7, 22, 20, 16, 15, 23, 11, 220, 20, 16, 15, 23, 22, 11, 220, 16, 15, 23, 22, 20, 11, 220, 23, 22, 20, 16, 11, 220, 23, 22, 20, 16, 15, 8, 284, 220, 23, 22, 20, 16, 271, 59, 79075, 90, 23, 22, 20, 16, 92, 151645], "meta_info": {"id": "047267652bed42df8beb5ddbb6905bf6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.649852991104126, "response_sent_to_client_ts": 1773877219.3952882}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "28", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nA(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 32, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "968995a118bd4825a588284709f786c3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.085355758666992, "response_sent_to_client_ts": 1773877219.830803}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nC(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 34, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "965e441f9f92422bb25c58c242bf25f7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.09871768951416, "response_sent_to_client_ts": 1773877219.8441284}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nAlternating sum of squares = 1^2 - 5^2 + 5^2 - 5^2 + 9^2 = 1 - 25 + 25 - 25 + 81 = 57\nD(15559) = |57| = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 20, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 284, 220, 16, 481, 220, 17, 20, 488, 220, 17, 20, 481, 220, 17, 20, 488, 220, 23, 16, 284, 220, 20, 22, 198, 35, 7, 16, 20, 20, 20, 24, 8, 284, 760, 20, 22, 91, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "e9cb674e7e9e420780cf1076e373ef82", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.408311128616333, "response_sent_to_client_ts": 1773877219.1537771}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nL(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 43, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "df00335903e6409c9fb3fb225fe5d73f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.649869441986084, "response_sent_to_client_ts": 1773877219.3952994}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3200", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nB(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 33, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "c595bbb019904edea1580d83fc93b992", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 3.085364580154419, "response_sent_to_client_ts": 1773877219.8308084}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "12446", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\n4 is not prime: 4\n1 is not prime: 1\n4 is not prime: 4\n2 is prime: 2^2 = 4\n6 is not prime: 6\nP(41426) = 4 + 1 + 4 + 4 + 6 = 19\n\n\\boxed{19}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 47, 7, 19, 16, 19, 17, 21, 8, 284, 220, 19, 488, 220, 16, 488, 220, 19, 488, 220, 19, 488, 220, 21, 284, 220, 16, 24, 271, 59, 79075, 90, 16, 24, 92, 151645], "meta_info": {"id": "9264de665f3c4838abdf05befac40164", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.408318281173706, "response_sent_to_client_ts": 1773877219.1537826}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "32", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\n1 is not prime: 1\n3 is prime: 3^2 = 9\n4 is not prime: 4\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\nS(13453) = 1 + 9 + 4 + 25 + 9 = 48\n\n\\boxed{48}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 50, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 24, 488, 220, 19, 488, 220, 17, 20, 488, 220, 24, 284, 220, 19, 23, 271, 59, 79075, 90, 19, 23, 92, 151645], "meta_info": {"id": "49ef9331c08c40f995e29431a6190e27", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.628526210784912, "response_sent_to_client_ts": 1773877219.3739886}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\n2 is prime: 2^2 = 4\n9 is not prime: 9\n1 is not prime: 1\n9 is not prime: 9\n0 is not prime: 0\nK(29190) = 4 + 9 + 1 + 9 + 0 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 42, 7, 17, 24, 16, 24, 15, 8, 284, 220, 19, 488, 220, 24, 488, 220, 16, 488, 220, 24, 488, 220, 15, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "b13cf40563f94a1391277b3003eb97b6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.408325433731079, "response_sent_to_client_ts": 1773877219.1537876}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nAlternating sum of squares = 8^2 - 5^2 + 6^2 - 3^2 + 8^2 = 64 - 25 + 36 - 9 + 64 = 130\nH(85638) = |130| = 130\n\n\\boxed{130}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 21, 61, 17, 481, 220, 18, 61, 17, 488, 220, 23, 61, 17, 284, 220, 21, 19, 481, 220, 17, 20, 488, 220, 18, 21, 481, 220, 24, 488, 220, 21, 19, 284, 220, 16, 18, 15, 198, 39, 7, 23, 20, 21, 18, 23, 8, 284, 760, 16, 18, 15, 91, 284, 220, 16, 18, 15, 271, 59, 79075, 90, 16, 18, 15, 92, 151645], "meta_info": {"id": "e3057a7d15894333a4956e666109ba1a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.495743989944458, "response_sent_to_client_ts": 1773877219.2411716}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "47106", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 60174 is \"60174\".\nRotations: 60174, 1746, 17460, 74601, 46017\nI(60174) = min(60174, 1746, 17460, 74601, 46017) = 1746\n\n\\boxed{1746}", "output_ids": [785, 15723, 914, 315, 220, 21, 15, 16, 22, 19, 374, 330, 21, 15, 16, 22, 19, 22956, 36936, 804, 25, 220, 21, 15, 16, 22, 19, 11, 220, 16, 22, 19, 21, 11, 220, 16, 22, 19, 21, 15, 11, 220, 22, 19, 21, 15, 16, 11, 220, 19, 21, 15, 16, 22, 198, 40, 7, 21, 15, 16, 22, 19, 8, 284, 1308, 7, 21, 15, 16, 22, 19, 11, 220, 16, 22, 19, 21, 11, 220, 16, 22, 19, 21, 15, 11, 220, 22, 19, 21, 15, 16, 11, 220, 19, 21, 15, 16, 22, 8, 284, 220, 16, 22, 19, 21, 271, 59, 79075, 90, 16, 22, 19, 21, 92, 151645], "meta_info": {"id": "69164d6620cf41b692b99a4374b113ee", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.6498775482177734, "response_sent_to_client_ts": 1773877219.3953056}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "50", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\n4 is not prime: 4\n6 is not prime: 6\n9 is not prime: 9\n6 is not prime: 6\nS(4696) = 4 + 6 + 9 + 6 = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 50, 7, 19, 21, 24, 21, 8, 284, 220, 19, 488, 220, 21, 488, 220, 24, 488, 220, 21, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "d5e55f934310405dbdde495998271bef", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 199, "weight_version": "default", "total_retractions": 0, "completion_tokens": 84, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 1.9780118465423584, "response_sent_to_client_ts": 1773877218.7234325}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9965", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 6599 is \"6599\".\nRotations: 6599, 5996, 9965, 9659\nQ(6599) = min(6599, 5996, 9965, 9659) = 5996\n\n\\boxed{5996}", "output_ids": [785, 15723, 914, 315, 220, 21, 20, 24, 24, 374, 330, 21, 20, 24, 24, 22956, 36936, 804, 25, 220, 21, 20, 24, 24, 11, 220, 20, 24, 24, 21, 11, 220, 24, 24, 21, 20, 11, 220, 24, 21, 20, 24, 198, 48, 7, 21, 20, 24, 24, 8, 284, 1308, 7, 21, 20, 24, 24, 11, 220, 20, 24, 24, 21, 11, 220, 24, 24, 21, 20, 11, 220, 24, 21, 20, 24, 8, 284, 220, 20, 24, 24, 21, 271, 59, 79075, 90, 20, 24, 24, 21, 92, 151645], "meta_info": {"id": "c950a4ef2c2b4cafb424983e87669ab6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 92, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.1492502689361572, "response_sent_to_client_ts": 1773877218.894667}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nC(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 34, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "fe8dea51562a495cb7a98a276b6721a2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0561299324035645, "response_sent_to_client_ts": 1773877219.8015587}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n0 is not prime: 0\n2 is prime: 2^2 = 4\n4 is not prime: 4\nD(73024) = 49 + 9 + 0 + 4 + 4 = 66\n\n\\boxed{66}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 35, 7, 22, 18, 15, 17, 19, 8, 284, 220, 19, 24, 488, 220, 24, 488, 220, 15, 488, 220, 19, 488, 220, 19, 284, 220, 21, 21, 271, 59, 79075, 90, 21, 21, 92, 151645], "meta_info": {"id": "58b87375c1f14883bac7f5ed01cfb3a8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.6285340785980225, "response_sent_to_client_ts": 1773877219.373995}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\n1 is not prime: 1\n1 is not prime: 1\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n6 is not prime: 6\nT(11536) = 1 + 1 + 25 + 9 + 6 = 42\n\n\\boxed{42}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 51, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 17, 20, 488, 220, 24, 488, 220, 21, 284, 220, 19, 17, 271, 59, 79075, 90, 19, 17, 92, 151645], "meta_info": {"id": "027007943711451db5c4054ad18aed93", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.540194511413574, "response_sent_to_client_ts": 1773877219.2856271}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nAlternating sum of squares = 4^2 - 6^2 + 9^2 - 6^2 = 16 - 36 + 81 - 36 = 25\nD(4696) = |25| = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 21, 61, 17, 488, 220, 24, 61, 17, 481, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 18, 21, 488, 220, 23, 16, 481, 220, 18, 21, 284, 220, 17, 20, 198, 35, 7, 19, 21, 24, 21, 8, 284, 760, 17, 20, 91, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "164844d098c74acb9a78d147884f207d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.1276800632476807, "response_sent_to_client_ts": 1773877218.8731058}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nAlternating sum of squares = 3^2 - 0^2 + 8^2 - 0^2 + 1^2 = 9 - 0 + 64 - 0 + 1 = 74\nH(30801) = |74| = 74\n\n\\boxed{74}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 18, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 284, 220, 24, 481, 220, 15, 488, 220, 21, 19, 481, 220, 15, 488, 220, 16, 284, 220, 22, 19, 198, 39, 7, 18, 15, 23, 15, 16, 8, 284, 760, 22, 19, 91, 284, 220, 22, 19, 271, 59, 79075, 90, 22, 19, 92, 151645], "meta_info": {"id": "62a3e2df70cf40599e4ec3b05491d408", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 101, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.3411545753479004, "response_sent_to_client_ts": 1773877219.0865667}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nN(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 45, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "f7c9aefe72a348899242cc322df97597", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0853729248046875, "response_sent_to_client_ts": 1773877219.8308134}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nL(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 43, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "be49421a293c420a8569b1717b459299", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1387219429016113, "response_sent_to_client_ts": 1773877219.8841271}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nM(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 44, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "502c9905683f4d179575751853567b25", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0168144702911377, "response_sent_to_client_ts": 1773877222.903472}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "42", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\n2 is prime: 2^2 = 4\n9 is not prime: 9\n1 is not prime: 1\n9 is not prime: 9\n0 is not prime: 0\nS(29190) = 4 + 9 + 1 + 9 + 0 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 50, 7, 17, 24, 16, 24, 15, 8, 284, 220, 19, 488, 220, 24, 488, 220, 16, 488, 220, 24, 488, 220, 15, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "c8a541259ca54325b074d63396f8da4c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.4006996154785156, "response_sent_to_client_ts": 1773877222.2873423}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n0 is not prime: 0\n2 is prime: 2^2 = 4\n4 is not prime: 4\nE(73024) = 49 + 9 + 0 + 4 + 4 = 66\n\n\\boxed{66}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 36, 7, 22, 18, 15, 17, 19, 8, 284, 220, 19, 24, 488, 220, 24, 488, 220, 15, 488, 220, 19, 488, 220, 19, 284, 220, 21, 21, 271, 59, 79075, 90, 21, 21, 92, 151645], "meta_info": {"id": "ec17c21186f944eb9509d9cb9173b218", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.6159615516662598, "response_sent_to_client_ts": 1773877222.50257}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "11", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nJ(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 41, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "2ddebc4abd604fba92d46648b3f74e51", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0438764095306396, "response_sent_to_client_ts": 1773877222.9304717}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "480", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nB(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 33, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "f359c2b70ef041379999db0800f2b28f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.0438907146453857, "response_sent_to_client_ts": 1773877222.9304817}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nC(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 34, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "4a10bf482de24a94b07d7f82b0483e56", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9871466159820557, "response_sent_to_client_ts": 1773877222.8737676}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nAlternating sum of squares = 5^2 - 4^2 + 0^2 - 4^2 + 6^2 = 25 - 16 + 0 - 16 + 36 = 29\nH(54046) = |29| = 29\n\n\\boxed{29}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 19, 61, 17, 488, 220, 15, 61, 17, 481, 220, 19, 61, 17, 488, 220, 21, 61, 17, 284, 220, 17, 20, 481, 220, 16, 21, 488, 220, 15, 481, 220, 16, 21, 488, 220, 18, 21, 284, 220, 17, 24, 198, 39, 7, 20, 19, 15, 19, 21, 8, 284, 760, 17, 24, 91, 284, 220, 17, 24, 271, 59, 79075, 90, 17, 24, 92, 151645], "meta_info": {"id": "823dcc52a80e42979d4e5a96cf9fe27c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.4007155895233154, "response_sent_to_client_ts": 1773877222.2873545}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9664", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 4696 is \"4696\".\nRotations: 4696, 6964, 9646, 6469\nQ(4696) = min(4696, 6964, 9646, 6469) = 4696\n\n\\boxed{4696}", "output_ids": [785, 15723, 914, 315, 220, 19, 21, 24, 21, 374, 330, 19, 21, 24, 21, 22956, 36936, 804, 25, 220, 19, 21, 24, 21, 11, 220, 21, 24, 21, 19, 11, 220, 24, 21, 19, 21, 11, 220, 21, 19, 21, 24, 198, 48, 7, 19, 21, 24, 21, 8, 284, 1308, 7, 19, 21, 24, 21, 11, 220, 21, 24, 21, 19, 11, 220, 24, 21, 19, 21, 11, 220, 21, 19, 21, 24, 8, 284, 220, 19, 21, 24, 21, 271, 59, 79075, 90, 19, 21, 24, 21, 92, 151645], "meta_info": {"id": "7a28deecd77d418e84bbbc3f2c5c08d0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 92, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.139143228530884, "response_sent_to_client_ts": 1773877222.0257547}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\n4 is not prime: 4\n1 is not prime: 1\n4 is not prime: 4\n2 is prime: 2^2 = 4\n6 is not prime: 6\nK(41426) = 4 + 1 + 4 + 4 + 6 = 19\n\n\\boxed{19}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 42, 7, 19, 16, 19, 17, 21, 8, 284, 220, 19, 488, 220, 16, 488, 220, 19, 488, 220, 19, 488, 220, 21, 284, 220, 16, 24, 271, 59, 79075, 90, 16, 24, 92, 151645], "meta_info": {"id": "9c1b059e7ca140e0bae96bedcc613fb7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.400723934173584, "response_sent_to_client_ts": 1773877222.2873602}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nK(58733) = 25 + 8 + 49 + 9 + 9 = 90\n\n\\boxed{90}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 42, 7, 20, 23, 22, 18, 18, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 488, 220, 24, 284, 220, 24, 15, 271, 59, 79075, 90, 24, 15, 92, 151645], "meta_info": {"id": "07e58390a5054706a3483a14482319fc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 120, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.706364393234253, "response_sent_to_client_ts": 1773877222.5929608}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2239", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n9 is not prime: 9\nP(2329) = 4 + 9 + 4 + 9 = 26\n\n\\boxed{26}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 47, 7, 17, 18, 17, 24, 8, 284, 220, 19, 488, 220, 24, 488, 220, 19, 488, 220, 24, 284, 220, 17, 21, 271, 59, 79075, 90, 17, 21, 92, 151645], "meta_info": {"id": "7bca64f706a045edad61f34dd3d595cc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.2247815132141113, "response_sent_to_client_ts": 1773877222.1114042}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\n4 is not prime: 4\n6 is not prime: 6\n9 is not prime: 9\n6 is not prime: 6\nT(4696) = 4 + 6 + 9 + 6 = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 51, 7, 19, 21, 24, 21, 8, 284, 220, 19, 488, 220, 21, 488, 220, 24, 488, 220, 21, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "afecd3fbdffd4822b8dfc09a12dfb402", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 84, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 1.9677882194519043, "response_sent_to_client_ts": 1773877221.8543913}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nJ(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 41, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "9fd2465cfb72429bbcc85b1a04b9a06a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 2.9871623516082764, "response_sent_to_client_ts": 1773877222.8737776}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "54", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n9 is not prime: 9\n9 is not prime: 9\nT(6599) = 6 + 25 + 9 + 9 = 49\n\n\\boxed{49}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 51, 7, 21, 20, 24, 24, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 284, 220, 19, 24, 271, 59, 79075, 90, 19, 24, 92, 151645], "meta_info": {"id": "6d20dfeddb8d4914b94cc9a7822c117e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 90, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.0954480171203613, "response_sent_to_client_ts": 1773877221.9820487}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\n9 is not prime: 9\n7 is prime: 7^2 = 49\n6 is not prime: 6\n7 is prime: 7^2 = 49\n9 is not prime: 9\nE(97679) = 9 + 49 + 6 + 49 + 9 = 122\n\n\\boxed{122}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 24, 374, 537, 10250, 25, 220, 24, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 36, 7, 24, 22, 21, 22, 24, 8, 284, 220, 24, 488, 220, 19, 24, 488, 220, 21, 488, 220, 19, 24, 488, 220, 24, 284, 220, 16, 17, 17, 271, 59, 79075, 90, 16, 17, 17, 92, 151645], "meta_info": {"id": "d95de3d9158642dfad50c6da89f4401f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.615975856781006, "response_sent_to_client_ts": 1773877222.5025795}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nA(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 32, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "5c7c92e29cee4c508478763e8ab5a3ff", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 2.9277544021606445, "response_sent_to_client_ts": 1773877222.814344}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "80157", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 75108 is \"75108\".\nRotations: 75108, 51087, 10875, 8751, 87510\nI(75108) = min(75108, 51087, 10875, 8751, 87510) = 8751\n\n\\boxed{8751}", "output_ids": [785, 15723, 914, 315, 220, 22, 20, 16, 15, 23, 374, 330, 22, 20, 16, 15, 23, 22956, 36936, 804, 25, 220, 22, 20, 16, 15, 23, 11, 220, 20, 16, 15, 23, 22, 11, 220, 16, 15, 23, 22, 20, 11, 220, 23, 22, 20, 16, 11, 220, 23, 22, 20, 16, 15, 198, 40, 7, 22, 20, 16, 15, 23, 8, 284, 1308, 7, 22, 20, 16, 15, 23, 11, 220, 20, 16, 15, 23, 22, 11, 220, 16, 15, 23, 22, 20, 11, 220, 23, 22, 20, 16, 11, 220, 23, 22, 20, 16, 15, 8, 284, 220, 23, 22, 20, 16, 271, 59, 79075, 90, 23, 22, 20, 16, 92, 151645], "meta_info": {"id": "a1f2580c3f2b42069bdee758ebbee0e1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6373136043548584, "response_sent_to_client_ts": 1773877222.5239112}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n1 is not prime: 1\n0 is not prime: 0\n8 is not prime: 8\nE(75108) = 49 + 25 + 1 + 0 + 8 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 36, 7, 22, 20, 16, 15, 23, 8, 284, 220, 19, 24, 488, 220, 17, 20, 488, 220, 16, 488, 220, 15, 488, 220, 23, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "92fd470b9de04ef180ab06800cb8215a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.5711441040039062, "response_sent_to_client_ts": 1773877222.4577618}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "182", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nO(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 46, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "4c746648e25f426a8d41a6cd4266f8e9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.0710620880126953, "response_sent_to_client_ts": 1773877222.9576542}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "13345", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\n1 is not prime: 1\n3 is prime: 3^2 = 9\n4 is not prime: 4\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\nP(13453) = 1 + 9 + 4 + 25 + 9 = 48\n\n\\boxed{48}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 47, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 24, 488, 220, 19, 488, 220, 17, 20, 488, 220, 24, 284, 220, 19, 23, 271, 59, 79075, 90, 19, 23, 92, 151645], "meta_info": {"id": "9893715dab854ee6b3bb249563035af5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.615985155105591, "response_sent_to_client_ts": 1773877222.502586}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nR(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 49, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "5026abfb5d5343beaabebdc8c4dd9ecc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0168306827545166, "response_sent_to_client_ts": 1773877222.9034824}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nL(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 43, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "b5b8c353d5c94b55a58e9c5f5ea58826", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0168395042419434, "response_sent_to_client_ts": 1773877222.9034884}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "56", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n1 is not prime: 1\n0 is not prime: 0\n8 is not prime: 8\nT(75108) = 49 + 25 + 1 + 0 + 8 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 51, 7, 22, 20, 16, 15, 23, 8, 284, 220, 19, 24, 488, 220, 17, 20, 488, 220, 16, 488, 220, 15, 488, 220, 23, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "84c73fdf1a644b9ca09908172acb6640", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.5711617469787598, "response_sent_to_client_ts": 1773877222.4577725}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "35688", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n6 is not prime: 6\n3 is prime: 3^2 = 9\n8 is not prime: 8\nP(85638) = 8 + 25 + 6 + 9 + 8 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 47, 7, 23, 20, 21, 18, 23, 8, 284, 220, 23, 488, 220, 17, 20, 488, 220, 21, 488, 220, 24, 488, 220, 23, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "fbfd715fc9f14e9ab79b3b7105cacc53", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.5279605388641357, "response_sent_to_client_ts": 1773877222.414588}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "10", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nJ(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 41, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "a2e7a227a85a407b988d21daac74113d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 3.016848087310791, "response_sent_to_client_ts": 1773877222.9034941}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nR(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 49, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "ead87de7a9514fa38c7ed4c014ee1346", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.9574131965637207, "response_sent_to_client_ts": 1773877222.8440118}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nR(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 49, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "37f84106a96946419c1b44c88a85ec84", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9871716499328613, "response_sent_to_client_ts": 1773877222.8737843}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2304", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nB(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 33, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "91582ac34db8460f843290689c48b9f4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.0710763931274414, "response_sent_to_client_ts": 1773877222.957663}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9956", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 6599 is \"6599\".\nRotations: 6599, 5996, 9965, 9659\nI(6599) = min(6599, 5996, 9965, 9659) = 5996\n\n\\boxed{5996}", "output_ids": [785, 15723, 914, 315, 220, 21, 20, 24, 24, 374, 330, 21, 20, 24, 24, 22956, 36936, 804, 25, 220, 21, 20, 24, 24, 11, 220, 20, 24, 24, 21, 11, 220, 24, 24, 21, 20, 11, 220, 24, 21, 20, 24, 198, 40, 7, 21, 20, 24, 24, 8, 284, 1308, 7, 21, 20, 24, 24, 11, 220, 20, 24, 24, 21, 11, 220, 24, 24, 21, 20, 11, 220, 24, 21, 20, 24, 8, 284, 220, 20, 24, 24, 21, 271, 59, 79075, 90, 20, 24, 24, 21, 92, 151645], "meta_info": {"id": "a5cd199bcde046cfba2121594bd73850", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 92, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.1391611099243164, "response_sent_to_client_ts": 1773877222.0257661}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "18", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\n1 is not prime: 1\n0 is not prime: 0\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\nS(10332) = 1 + 0 + 9 + 9 + 4 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 50, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 24, 488, 220, 24, 488, 220, 19, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "446fb82a977d478aaf8fe9e7056d4554", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.5711710453033447, "response_sent_to_client_ts": 1773877222.4577792}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n5 is prime: 5^2 = 25\n4 is not prime: 4\nD(72154) = 49 + 4 + 1 + 25 + 4 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 35, 7, 22, 17, 16, 20, 19, 8, 284, 220, 19, 24, 488, 220, 19, 488, 220, 16, 488, 220, 17, 20, 488, 220, 19, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "a19b5fb74e384f2dbe6d72ba3d071a0f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.6587390899658203, "response_sent_to_client_ts": 1773877222.5453355}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "95", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nO(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 46, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "36f86bc51a304210827395381e5f0bc5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.0168569087982178, "response_sent_to_client_ts": 1773877222.9034996}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n6 is not prime: 6\n3 is prime: 3^2 = 9\n8 is not prime: 8\nE(85638) = 8 + 25 + 6 + 9 + 8 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 36, 7, 23, 20, 21, 18, 23, 8, 284, 220, 23, 488, 220, 17, 20, 488, 220, 21, 488, 220, 24, 488, 220, 23, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "fe0f65e018f24faaa94695a0f3b4f79f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.5279793739318848, "response_sent_to_client_ts": 1773877222.4146013}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "18", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nT(65333) = 6 + 25 + 9 + 9 + 9 = 58\n\n\\boxed{58}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 51, 7, 21, 20, 18, 18, 18, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 488, 220, 24, 284, 220, 20, 23, 271, 59, 79075, 90, 20, 23, 92, 151645], "meta_info": {"id": "2ef7af5a3d004e24bbbd30a285b57eff", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.6762962341308594, "response_sent_to_client_ts": 1773877222.5629084}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1125", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nB(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 33, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "e5a899cc3cbe4f44b4782e3e91637126", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.0574610233306885, "response_sent_to_client_ts": 1773877222.9440546}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nM(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 44, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "88670bb65e39451b9bf3fc354f52539c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0168657302856445, "response_sent_to_client_ts": 1773877222.9035046}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nAlternating sum of squares = 5^2 - 4^2 + 0^2 - 4^2 + 6^2 = 25 - 16 + 0 - 16 + 36 = 29\nG(54046) = |29| = 29\n\n\\boxed{29}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 19, 61, 17, 488, 220, 15, 61, 17, 481, 220, 19, 61, 17, 488, 220, 21, 61, 17, 284, 220, 17, 20, 481, 220, 16, 21, 488, 220, 15, 481, 220, 16, 21, 488, 220, 18, 21, 284, 220, 17, 24, 198, 38, 7, 20, 19, 15, 19, 21, 8, 284, 760, 17, 24, 91, 284, 220, 17, 24, 271, 59, 79075, 90, 17, 24, 92, 151645], "meta_info": {"id": "780eac9e315b463ba09fc813a694882f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.4007320404052734, "response_sent_to_client_ts": 1773877222.2873664}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "50", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\n1 is not prime: 1\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n9 is not prime: 9\nS(15559) = 1 + 25 + 25 + 25 + 9 = 85\n\n\\boxed{85}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 50, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 24, 284, 220, 23, 20, 271, 59, 79075, 90, 23, 20, 92, 151645], "meta_info": {"id": "71947b6bce5149ae8113e9dfa051ed8b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.6763112545013428, "response_sent_to_client_ts": 1773877222.5629172}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\n1 is not prime: 1\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n9 is not prime: 9\nT(15559) = 1 + 25 + 25 + 25 + 9 = 85\n\n\\boxed{85}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 51, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 24, 284, 220, 23, 20, 271, 59, 79075, 90, 23, 20, 92, 151645], "meta_info": {"id": "f174753008684ff594df9401d2463205", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.6763203144073486, "response_sent_to_client_ts": 1773877222.5629241}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "54331", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 13453 is \"13453\".\nRotations: 13453, 34531, 45313, 53134, 31345\nQ(13453) = min(13453, 34531, 45313, 53134, 31345) = 13453\n\n\\boxed{13453}", "output_ids": [785, 15723, 914, 315, 220, 16, 18, 19, 20, 18, 374, 330, 16, 18, 19, 20, 18, 22956, 36936, 804, 25, 220, 16, 18, 19, 20, 18, 11, 220, 18, 19, 20, 18, 16, 11, 220, 19, 20, 18, 16, 18, 11, 220, 20, 18, 16, 18, 19, 11, 220, 18, 16, 18, 19, 20, 198, 48, 7, 16, 18, 19, 20, 18, 8, 284, 1308, 7, 16, 18, 19, 20, 18, 11, 220, 18, 19, 20, 18, 16, 11, 220, 19, 20, 18, 16, 18, 11, 220, 20, 18, 16, 18, 19, 11, 220, 18, 16, 18, 19, 20, 8, 284, 220, 16, 18, 19, 20, 18, 271, 59, 79075, 90, 16, 18, 19, 20, 18, 92, 151645], "meta_info": {"id": "ffb26199a41f492db20c7c2956f93938", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.691993236541748, "response_sent_to_client_ts": 1773877222.5786195}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "10803", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 30801 is \"30801\".\nRotations: 30801, 8013, 80130, 1308, 13080\nI(30801) = min(30801, 8013, 80130, 1308, 13080) = 1308\n\n\\boxed{1308}", "output_ids": [785, 15723, 914, 315, 220, 18, 15, 23, 15, 16, 374, 330, 18, 15, 23, 15, 16, 22956, 36936, 804, 25, 220, 18, 15, 23, 15, 16, 11, 220, 23, 15, 16, 18, 11, 220, 23, 15, 16, 18, 15, 11, 220, 16, 18, 15, 23, 11, 220, 16, 18, 15, 23, 15, 198, 40, 7, 18, 15, 23, 15, 16, 8, 284, 1308, 7, 18, 15, 23, 15, 16, 11, 220, 23, 15, 16, 18, 11, 220, 23, 15, 16, 18, 15, 11, 220, 16, 18, 15, 23, 11, 220, 16, 18, 15, 23, 15, 8, 284, 220, 16, 18, 15, 23, 271, 59, 79075, 90, 16, 18, 15, 23, 92, 151645], "meta_info": {"id": "45ab2a9e78dd43638ec2ef40e2de68b7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 113, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.5937561988830566, "response_sent_to_client_ts": 1773877222.480357}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "64421", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 41426 is \"41426\".\nRotations: 41426, 14264, 42641, 26414, 64142\nQ(41426) = min(41426, 14264, 42641, 26414, 64142) = 14264\n\n\\boxed{14264}", "output_ids": [785, 15723, 914, 315, 220, 19, 16, 19, 17, 21, 374, 330, 19, 16, 19, 17, 21, 22956, 36936, 804, 25, 220, 19, 16, 19, 17, 21, 11, 220, 16, 19, 17, 21, 19, 11, 220, 19, 17, 21, 19, 16, 11, 220, 17, 21, 19, 16, 19, 11, 220, 21, 19, 16, 19, 17, 198, 48, 7, 19, 16, 19, 17, 21, 8, 284, 1308, 7, 19, 16, 19, 17, 21, 11, 220, 16, 19, 17, 21, 19, 11, 220, 19, 17, 21, 19, 16, 11, 220, 17, 21, 19, 16, 19, 11, 220, 21, 19, 16, 19, 17, 8, 284, 220, 16, 19, 17, 21, 19, 271, 59, 79075, 90, 16, 19, 17, 21, 19, 92, 151645], "meta_info": {"id": "ef2c340a3ce34245b2417e2be8f8bdab", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.692006826400757, "response_sent_to_client_ts": 1773877222.5786283}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\n9 is not prime: 9\nE(52879) = 25 + 4 + 8 + 49 + 9 = 95\n\n\\boxed{95}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 36, 7, 20, 17, 23, 22, 24, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 284, 220, 24, 20, 271, 59, 79075, 90, 24, 20, 92, 151645], "meta_info": {"id": "4f60fdde24a84c0c80478cbe7c2c664b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.6587531566619873, "response_sent_to_client_ts": 1773877222.5453453}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "74", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nO(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 46, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "2e6b68109dda4546b6a7196d3cd9de56", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 2.9574291706085205, "response_sent_to_client_ts": 1773877222.844022}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nAlternating sum of squares = 5^2 - 8^2 + 2^2 - 2^2 + 0^2 = 25 - 64 + 4 - 4 + 0 = -39\nD(58220) = |-39| = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 17, 61, 17, 481, 220, 17, 61, 17, 488, 220, 15, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 481, 220, 19, 488, 220, 15, 284, 481, 18, 24, 198, 35, 7, 20, 23, 17, 17, 15, 8, 284, 44561, 18, 24, 91, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "371336d6ad724684b4d397255f5d45da", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3561553955078125, "response_sent_to_client_ts": 1773877222.242741}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "48", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\n6 is not prime: 6\n6 is not prime: 6\n4 is not prime: 4\n4 is not prime: 4\n4 is not prime: 4\nS(66444) = 6 + 6 + 4 + 4 + 4 = 24\n\n\\boxed{24}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 50, 7, 21, 21, 19, 19, 19, 8, 284, 220, 21, 488, 220, 21, 488, 220, 19, 488, 220, 19, 488, 220, 19, 284, 220, 17, 19, 271, 59, 79075, 90, 17, 19, 92, 151645], "meta_info": {"id": "7acf4ae4c3064d2b975162e792974320", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 100, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.3156111240386963, "response_sent_to_client_ts": 1773877222.2028046}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nAlternating sum of squares = 7^2 - 5^2 + 1^2 - 0^2 + 8^2 = 49 - 25 + 1 - 0 + 64 = 89\nG(75108) = |89| = 89\n\n\\boxed{89}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 20, 61, 17, 488, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 284, 220, 19, 24, 481, 220, 17, 20, 488, 220, 16, 481, 220, 15, 488, 220, 21, 19, 284, 220, 23, 24, 198, 38, 7, 22, 20, 16, 15, 23, 8, 284, 760, 23, 24, 91, 284, 220, 23, 24, 271, 59, 79075, 90, 23, 24, 92, 151645], "meta_info": {"id": "43ac0b861b13466eb11793c1a262d47e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.3779802322387695, "response_sent_to_client_ts": 1773877222.264569}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nJ(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 41, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "0e91ce31916d4f93b2dda321cd4d0c50", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.987180709838867, "response_sent_to_client_ts": 1773877222.8737898}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "66444", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 66444 is \"66444\".\nRotations: 66444, 64446, 44466, 44664, 46644\nQ(66444) = min(66444, 64446, 44466, 44664, 46644) = 44466\n\n\\boxed{44466}", "output_ids": [785, 15723, 914, 315, 220, 21, 21, 19, 19, 19, 374, 330, 21, 21, 19, 19, 19, 22956, 36936, 804, 25, 220, 21, 21, 19, 19, 19, 11, 220, 21, 19, 19, 19, 21, 11, 220, 19, 19, 19, 21, 21, 11, 220, 19, 19, 21, 21, 19, 11, 220, 19, 21, 21, 19, 19, 198, 48, 7, 21, 21, 19, 19, 19, 8, 284, 1308, 7, 21, 21, 19, 19, 19, 11, 220, 21, 19, 19, 19, 21, 11, 220, 19, 19, 19, 21, 21, 11, 220, 19, 19, 21, 21, 19, 11, 220, 19, 21, 21, 19, 19, 8, 284, 220, 19, 19, 19, 21, 21, 271, 59, 79075, 90, 19, 19, 19, 21, 21, 92, 151645], "meta_info": {"id": "1dac023f47134cfeba80fa8a7185ecd7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6920154094696045, "response_sent_to_client_ts": 1773877222.5786347}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3456", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nB(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 33, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "6ffbd9e1449043e0977afd68ddbbbfc4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.1893391609191895, "response_sent_to_client_ts": 1773877223.0759692}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nE(58733) = 25 + 8 + 49 + 9 + 9 = 90\n\n\\boxed{90}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 36, 7, 20, 23, 22, 18, 18, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 488, 220, 24, 284, 220, 24, 15, 271, 59, 79075, 90, 24, 15, 92, 151645], "meta_info": {"id": "ba41e970a25d48f6bf0d4786af10d285", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 120, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.70637845993042, "response_sent_to_client_ts": 1773877222.5929706}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "33356", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 65333 is \"65333\".\nRotations: 65333, 53336, 33365, 33653, 36533\nI(65333) = min(65333, 53336, 33365, 33653, 36533) = 33365\n\n\\boxed{33365}", "output_ids": [785, 15723, 914, 315, 220, 21, 20, 18, 18, 18, 374, 330, 21, 20, 18, 18, 18, 22956, 36936, 804, 25, 220, 21, 20, 18, 18, 18, 11, 220, 20, 18, 18, 18, 21, 11, 220, 18, 18, 18, 21, 20, 11, 220, 18, 18, 21, 20, 18, 11, 220, 18, 21, 20, 18, 18, 198, 40, 7, 21, 20, 18, 18, 18, 8, 284, 1308, 7, 21, 20, 18, 18, 18, 11, 220, 20, 18, 18, 18, 21, 11, 220, 18, 18, 18, 21, 20, 11, 220, 18, 18, 21, 20, 18, 11, 220, 18, 21, 20, 18, 18, 8, 284, 220, 18, 18, 18, 21, 20, 271, 59, 79075, 90, 18, 18, 18, 21, 20, 92, 151645], "meta_info": {"id": "80154ef6b17c4dbc9aa780901587dd6f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.692023277282715, "response_sent_to_client_ts": 1773877222.5786405}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "10", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nJ(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 41, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "ddab1b692b2341bab25694b44bf472ec", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 195, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 2.7211709022521973, "response_sent_to_client_ts": 1773877222.6077518}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "95551", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 15559 is \"15559\".\nRotations: 15559, 55591, 55915, 59155, 91555\nI(15559) = min(15559, 55591, 55915, 59155, 91555) = 15559\n\n\\boxed{15559}", "output_ids": [785, 15723, 914, 315, 220, 16, 20, 20, 20, 24, 374, 330, 16, 20, 20, 20, 24, 22956, 36936, 804, 25, 220, 16, 20, 20, 20, 24, 11, 220, 20, 20, 20, 24, 16, 11, 220, 20, 20, 24, 16, 20, 11, 220, 20, 24, 16, 20, 20, 11, 220, 24, 16, 20, 20, 20, 198, 40, 7, 16, 20, 20, 20, 24, 8, 284, 1308, 7, 16, 20, 20, 20, 24, 11, 220, 20, 20, 20, 24, 16, 11, 220, 20, 20, 24, 16, 20, 11, 220, 20, 24, 16, 20, 20, 11, 220, 24, 16, 20, 20, 20, 8, 284, 220, 16, 20, 20, 20, 24, 271, 59, 79075, 90, 16, 20, 20, 20, 24, 92, 151645], "meta_info": {"id": "15b32e6ed425430fb40d423e73849a98", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.692030668258667, "response_sent_to_client_ts": 1773877222.5786455}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nC(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 34, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "b025e5a4fb004001bfe1d75a36469d67", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.016874313354492, "response_sent_to_client_ts": 1773877222.9035106}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\n6 is not prime: 6\n6 is not prime: 6\n4 is not prime: 4\n4 is not prime: 4\n4 is not prime: 4\nT(66444) = 6 + 6 + 4 + 4 + 4 = 24\n\n\\boxed{24}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 51, 7, 21, 21, 19, 19, 19, 8, 284, 220, 21, 488, 220, 21, 488, 220, 19, 488, 220, 19, 488, 220, 19, 284, 220, 17, 19, 271, 59, 79075, 90, 17, 19, 92, 151645], "meta_info": {"id": "2e2b53aaf4c049ef8c9d6e03e8f2bbcc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 100, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.3156838417053223, "response_sent_to_client_ts": 1773877222.2028954}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nAlternating sum of squares = 4^2 - 6^2 + 9^2 - 6^2 = 16 - 36 + 81 - 36 = 25\nF(4696) = |25| = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 21, 61, 17, 488, 220, 24, 61, 17, 481, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 18, 21, 488, 220, 23, 16, 481, 220, 18, 21, 284, 220, 17, 20, 198, 37, 7, 19, 21, 24, 21, 8, 284, 760, 17, 20, 91, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "22357c8000b0411a8abe211f7427a1ee", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.1171064376831055, "response_sent_to_client_ts": 1773877222.0036995}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nAlternating sum of squares = 3^2 - 0^2 + 8^2 - 0^2 + 1^2 = 9 - 0 + 64 - 0 + 1 = 74\nF(30801) = |74| = 74\n\n\\boxed{74}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 18, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 284, 220, 24, 481, 220, 15, 488, 220, 21, 19, 481, 220, 15, 488, 220, 16, 284, 220, 22, 19, 198, 37, 7, 18, 15, 23, 15, 16, 8, 284, 760, 22, 19, 91, 284, 220, 22, 19, 271, 59, 79075, 90, 22, 19, 92, 151645], "meta_info": {"id": "d9e2045231994002bbda443eb271b091", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 101, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.334386110305786, "response_sent_to_client_ts": 1773877222.2209795}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "10", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nJ(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 41, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "aaf743bd166445318b059edf0a60ab5c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0574748516082764, "response_sent_to_client_ts": 1773877222.9440632}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "83100", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 30801 is \"30801\".\nRotations: 30801, 8013, 80130, 1308, 13080\nQ(30801) = min(30801, 8013, 80130, 1308, 13080) = 1308\n\n\\boxed{1308}", "output_ids": [785, 15723, 914, 315, 220, 18, 15, 23, 15, 16, 374, 330, 18, 15, 23, 15, 16, 22956, 36936, 804, 25, 220, 18, 15, 23, 15, 16, 11, 220, 23, 15, 16, 18, 11, 220, 23, 15, 16, 18, 15, 11, 220, 16, 18, 15, 23, 11, 220, 16, 18, 15, 23, 15, 198, 48, 7, 18, 15, 23, 15, 16, 8, 284, 1308, 7, 18, 15, 23, 15, 16, 11, 220, 23, 15, 16, 18, 11, 220, 23, 15, 16, 18, 15, 11, 220, 16, 18, 15, 23, 11, 220, 16, 18, 15, 23, 15, 8, 284, 220, 16, 18, 15, 23, 271, 59, 79075, 90, 16, 18, 15, 23, 92, 151645], "meta_info": {"id": "7317b25b753349339d838a7b216983e2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 113, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.593770980834961, "response_sent_to_client_ts": 1773877222.480367}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "18", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n9 is not prime: 9\nT(2329) = 4 + 9 + 4 + 9 = 26\n\n\\boxed{26}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 51, 7, 17, 18, 17, 24, 8, 284, 220, 19, 488, 220, 24, 488, 220, 19, 488, 220, 24, 284, 220, 17, 21, 271, 59, 79075, 90, 17, 21, 92, 151645], "meta_info": {"id": "0a13aafe79c74dbf901d66f2ff3f51aa", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.224799394607544, "response_sent_to_client_ts": 1773877222.1114166}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\n4 is not prime: 4\n1 is not prime: 1\n4 is not prime: 4\n2 is prime: 2^2 = 4\n6 is not prime: 6\nT(41426) = 4 + 1 + 4 + 4 + 6 = 19\n\n\\boxed{19}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 51, 7, 19, 16, 19, 17, 21, 8, 284, 220, 19, 488, 220, 16, 488, 220, 19, 488, 220, 19, 488, 220, 21, 284, 220, 16, 24, 271, 59, 79075, 90, 16, 24, 92, 151645], "meta_info": {"id": "45fc001512a24ac2a6c3dff4e459f5ed", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.4007394313812256, "response_sent_to_client_ts": 1773877222.2873719}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "32", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\n1 is not prime: 1\n1 is not prime: 1\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n6 is not prime: 6\nS(11536) = 1 + 1 + 25 + 9 + 6 = 42\n\n\\boxed{42}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 50, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 17, 20, 488, 220, 24, 488, 220, 21, 284, 220, 19, 17, 271, 59, 79075, 90, 19, 17, 92, 151645], "meta_info": {"id": "5b49cc177cbe43ab8ad9d46065d4e011", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.527989625930786, "response_sent_to_client_ts": 1773877222.414607}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n9 is not prime: 9\nE(2329) = 4 + 9 + 4 + 9 = 26\n\n\\boxed{26}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 36, 7, 17, 18, 17, 24, 8, 284, 220, 19, 488, 220, 24, 488, 220, 19, 488, 220, 24, 284, 220, 17, 21, 271, 59, 79075, 90, 17, 21, 92, 151645], "meta_info": {"id": "6309858a73a64de8bebbee9619b9be8d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.224808931350708, "response_sent_to_client_ts": 1773877222.1114225}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nL(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 43, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "342c8708f29d4c409db464c3dafcaeaf", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.9313125610351562, "response_sent_to_client_ts": 1773877226.0098503}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nR(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 49, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "3453e38d2dd14dab965dc5dfe49c50d4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.993100166320801, "response_sent_to_client_ts": 1773877226.0717113}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\n3 is prime: 3^2 = 9\n0 is not prime: 0\n8 is not prime: 8\n0 is not prime: 0\n1 is not prime: 1\nE(30801) = 9 + 0 + 8 + 0 + 1 = 18\n\n\\boxed{18}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 36, 7, 18, 15, 23, 15, 16, 8, 284, 220, 24, 488, 220, 15, 488, 220, 23, 488, 220, 15, 488, 220, 16, 284, 220, 16, 23, 271, 59, 79075, 90, 16, 23, 92, 151645], "meta_info": {"id": "180fda277cfc4fff9e53ad7eaada7438", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.38081431388855, "response_sent_to_client_ts": 1773877225.4593909}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\n0 is not prime: 0\nK(58220) = 25 + 8 + 4 + 4 + 0 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 42, 7, 20, 23, 17, 17, 15, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 488, 220, 19, 488, 220, 15, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "0208247b40b24473b840f766ec9cf001", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.5944271087646484, "response_sent_to_client_ts": 1773877225.6729717}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nAlternating sum of squares = 1^2 - 0^2 + 3^2 - 3^2 + 2^2 = 1 - 0 + 9 - 9 + 4 = 5\nG(10332) = |5| = 5\n\n\\boxed{5}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 284, 220, 16, 481, 220, 15, 488, 220, 24, 481, 220, 24, 488, 220, 19, 284, 220, 20, 198, 38, 7, 16, 15, 18, 18, 17, 8, 284, 760, 20, 91, 284, 220, 20, 271, 59, 79075, 90, 20, 92, 151645], "meta_info": {"id": "d556ca9fe13848f68cdccdb44c7f049a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.208085536956787, "response_sent_to_client_ts": 1773877225.2866287}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "33356", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nP(65333) = 6 + 25 + 9 + 9 + 9 = 58\n\n\\boxed{58}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 47, 7, 21, 20, 18, 18, 18, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 488, 220, 24, 284, 220, 20, 23, 271, 59, 79075, 90, 20, 23, 92, 151645], "meta_info": {"id": "cfa9213e372844f1ac0e8576fa72b010", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.681346893310547, "response_sent_to_client_ts": 1773877225.759891}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "108", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nB(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 33, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "77a2f85cd2064241a7afa224422449f6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 205, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 2.616536855697632, "response_sent_to_client_ts": 1773877225.6950848}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n1 is not prime: 1\n0 is not prime: 0\n8 is not prime: 8\nK(75108) = 49 + 25 + 1 + 0 + 8 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 42, 7, 22, 20, 16, 15, 23, 8, 284, 220, 19, 24, 488, 220, 17, 20, 488, 220, 16, 488, 220, 15, 488, 220, 23, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "cc42e36f2aa04132ade707ad2d9b06dd", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.550262928009033, "response_sent_to_client_ts": 1773877225.628778}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5040", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nB(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 33, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "bb6bce7f2f3c4e2592d740c45c5defec", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 182, "cached_tokens_details": null, "e2e_latency": 3.0907223224639893, "response_sent_to_client_ts": 1773877226.169261}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "95551", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 15559 is \"15559\".\nRotations: 15559, 55591, 55915, 59155, 91555\nQ(15559) = min(15559, 55591, 55915, 59155, 91555) = 15559\n\n\\boxed{15559}", "output_ids": [785, 15723, 914, 315, 220, 16, 20, 20, 20, 24, 374, 330, 16, 20, 20, 20, 24, 22956, 36936, 804, 25, 220, 16, 20, 20, 20, 24, 11, 220, 20, 20, 20, 24, 16, 11, 220, 20, 20, 24, 16, 20, 11, 220, 20, 24, 16, 20, 20, 11, 220, 24, 16, 20, 20, 20, 198, 48, 7, 16, 20, 20, 20, 24, 8, 284, 1308, 7, 16, 20, 20, 20, 24, 11, 220, 20, 20, 20, 24, 16, 11, 220, 20, 20, 24, 16, 20, 11, 220, 20, 24, 16, 20, 20, 11, 220, 24, 16, 20, 20, 20, 8, 284, 220, 16, 20, 20, 20, 24, 271, 59, 79075, 90, 16, 20, 20, 20, 24, 92, 151645], "meta_info": {"id": "aed861f6f5b54e5c862280fb08c348f8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.7022650241851807, "response_sent_to_client_ts": 1773877225.780787}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "38", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n5 is prime: 5^2 = 25\n4 is not prime: 4\nS(72154) = 49 + 4 + 1 + 25 + 4 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 50, 7, 22, 17, 16, 20, 19, 8, 284, 220, 19, 24, 488, 220, 19, 488, 220, 16, 488, 220, 17, 20, 488, 220, 19, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "26f3a1beab46443aa85ebf797ebb6804", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.638357162475586, "response_sent_to_client_ts": 1773877225.7169023}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "156", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nO(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 46, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "b813bdfa472e404c92220f60c2af8e4e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 3.0219953060150146, "response_sent_to_client_ts": 1773877226.100579}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1299", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\n2 is prime: 2^2 = 4\n9 is not prime: 9\n1 is not prime: 1\n9 is not prime: 9\n0 is not prime: 0\nP(29190) = 4 + 9 + 1 + 9 + 0 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 47, 7, 17, 24, 16, 24, 15, 8, 284, 220, 19, 488, 220, 24, 488, 220, 16, 488, 220, 24, 488, 220, 15, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "7f70916796374efcaae54d5afc71c42a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.3808298110961914, "response_sent_to_client_ts": 1773877225.459403}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "16", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nA(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 32, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "ad40f4d87e4f46a3a934c86c2b9ff28b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.993116855621338, "response_sent_to_client_ts": 1773877226.0717213}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nAlternating sum of squares = 4^2 - 9^2 + 6^2 - 2^2 + 8^2 = 16 - 81 + 36 - 4 + 64 = 31\nG(49628) = |31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 24, 61, 17, 488, 220, 21, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 284, 220, 16, 21, 481, 220, 23, 16, 488, 220, 18, 21, 481, 220, 19, 488, 220, 21, 19, 284, 220, 18, 16, 198, 38, 7, 19, 24, 21, 17, 23, 8, 284, 760, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "1ca824b7c0994f359ce267c78a9001c9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.380838632583618, "response_sent_to_client_ts": 1773877225.4594092}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nN(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 45, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "d277edb1364146189077f15e80602687", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.04882550239563, "response_sent_to_client_ts": 1773877226.1273315}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\n0 is not prime: 0\nE(58220) = 25 + 8 + 4 + 4 + 0 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 36, 7, 20, 23, 17, 17, 15, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 488, 220, 19, 488, 220, 15, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "a516d22caa4646c09ca61ecab5e6f276", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.5944488048553467, "response_sent_to_client_ts": 1773877225.6729827}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "296", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nO(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 46, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "1a40b707b1ea4d5a99fd17f1d33dd49a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 3.1303188800811768, "response_sent_to_client_ts": 1773877226.2088244}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nC(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 34, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "3bd885350d9c423a9c231e2e044120cc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0220108032226562, "response_sent_to_client_ts": 1773877226.100588}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nJ(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 41, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "e18e4978f28e4db499ef24e2f3a7c24c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.993126153945923, "response_sent_to_client_ts": 1773877226.0717273}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n5 is prime: 5^2 = 25\n8 is not prime: 8\nK(52858) = 25 + 4 + 8 + 25 + 8 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 42, 7, 20, 17, 23, 20, 23, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 17, 20, 488, 220, 23, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "3cb6d3305fc64a638ea8ec9838993f91", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.638376235961914, "response_sent_to_client_ts": 1773877225.716914}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "42037", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 73024 is \"73024\".\nRotations: 73024, 30247, 2473, 24730, 47302\nI(73024) = min(73024, 30247, 2473, 24730, 47302) = 2473\n\n\\boxed{2473}", "output_ids": [785, 15723, 914, 315, 220, 22, 18, 15, 17, 19, 374, 330, 22, 18, 15, 17, 19, 22956, 36936, 804, 25, 220, 22, 18, 15, 17, 19, 11, 220, 18, 15, 17, 19, 22, 11, 220, 17, 19, 22, 18, 11, 220, 17, 19, 22, 18, 15, 11, 220, 19, 22, 18, 15, 17, 198, 40, 7, 22, 18, 15, 17, 19, 8, 284, 1308, 7, 22, 18, 15, 17, 19, 11, 220, 18, 15, 17, 19, 22, 11, 220, 17, 19, 22, 18, 11, 220, 17, 19, 22, 18, 15, 11, 220, 19, 22, 18, 15, 17, 8, 284, 220, 17, 19, 22, 18, 271, 59, 79075, 90, 17, 19, 22, 18, 92, 151645], "meta_info": {"id": "48c60af3528844208da6fcf9253ce6ad", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6165528297424316, "response_sent_to_client_ts": 1773877225.6950953}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nM(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 44, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "23bc55e023cb4858af4a41a7ee3070c1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.022019624710083, "response_sent_to_client_ts": 1773877226.1005943}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "88", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nO(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 46, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "5f849e0121bb46e78b8d1d4b547c32ca", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 2.9931352138519287, "response_sent_to_client_ts": 1773877226.071733}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nAlternating sum of squares = 2^2 - 3^2 + 2^2 - 9^2 = 4 - 9 + 4 - 81 = -82\nG(2329) = |-82| = 82\n\n\\boxed{82}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 481, 220, 24, 61, 17, 284, 220, 19, 481, 220, 24, 488, 220, 19, 481, 220, 23, 16, 284, 481, 23, 17, 198, 38, 7, 17, 18, 17, 24, 8, 284, 44561, 23, 17, 91, 284, 220, 23, 17, 271, 59, 79075, 90, 23, 17, 92, 151645], "meta_info": {"id": "f99f30c5f3f846eda4f0fbe62c5674eb", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 88, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.0370254516601562, "response_sent_to_client_ts": 1773877225.1155522}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\n6 is not prime: 6\n6 is not prime: 6\n4 is not prime: 4\n4 is not prime: 4\n4 is not prime: 4\nE(66444) = 6 + 6 + 4 + 4 + 4 = 24\n\n\\boxed{24}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 36, 7, 21, 21, 19, 19, 19, 8, 284, 220, 21, 488, 220, 21, 488, 220, 19, 488, 220, 19, 488, 220, 19, 284, 220, 17, 19, 271, 59, 79075, 90, 17, 19, 92, 151645], "meta_info": {"id": "1493094455234727bb08c82fb35c0229", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 100, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.296816349029541, "response_sent_to_client_ts": 1773877225.3759303}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nM(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 44, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "80ac6b6e6a7044eab69232982b9274c3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9931442737579346, "response_sent_to_client_ts": 1773877226.0717387}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "169", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nO(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 46, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "fa39134de0884ec48cac9503efdf566f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 203, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 2.7197258472442627, "response_sent_to_client_ts": 1773877225.7982447}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nN(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 45, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "dd9965a10af44d9abbbc58396d80d697", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9313297271728516, "response_sent_to_client_ts": 1773877226.0098612}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nN(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 45, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "7b82525343b647119e88ce363ce59d1a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0220274925231934, "response_sent_to_client_ts": 1773877226.1006}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "97", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nO(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 46, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "c8057196ddd04fd6bdda2837b20337c0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 2.993152141571045, "response_sent_to_client_ts": 1773877226.0717442}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nAlternating sum of squares = 2^2 - 3^2 + 2^2 - 9^2 = 4 - 9 + 4 - 81 = -82\nD(2329) = |-82| = 82\n\n\\boxed{82}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 481, 220, 24, 61, 17, 284, 220, 19, 481, 220, 24, 488, 220, 19, 481, 220, 23, 16, 284, 481, 23, 17, 198, 35, 7, 17, 18, 17, 24, 8, 284, 44561, 23, 17, 91, 284, 220, 23, 17, 271, 59, 79075, 90, 23, 17, 92, 151645], "meta_info": {"id": "9810efd73f434377b5db07dd4bc1663c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 88, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.0370426177978516, "response_sent_to_client_ts": 1773877225.1155632}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nL(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 43, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "d239ea95f78a4b339fadbb5cd8c38e96", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9931607246398926, "response_sent_to_client_ts": 1773877226.0717492}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "15", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nJ(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 41, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "25d4f60018df4e848fdc9f6f74f94e6d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.022035837173462, "response_sent_to_client_ts": 1773877226.100605}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nC(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 34, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "9539801add99429f977fc475b74e59c0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.993168830871582, "response_sent_to_client_ts": 1773877226.0717537}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nC(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 34, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "a413c2957b394d7ea2cb45bca19439cd", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 3.076389789581299, "response_sent_to_client_ts": 1773877226.1549106}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\n4 is not prime: 4\n6 is not prime: 6\n9 is not prime: 9\n6 is not prime: 6\nK(4696) = 4 + 6 + 9 + 6 = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 42, 7, 19, 21, 24, 21, 8, 284, 220, 19, 488, 220, 21, 488, 220, 24, 488, 220, 21, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "0407590fb32a4015bb92b6921d12cd63", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 84, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 1.9522109031677246, "response_sent_to_client_ts": 1773877225.0307462}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "98642", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 49628 is \"49628\".\nRotations: 49628, 96284, 62849, 28496, 84962\nQ(49628) = min(49628, 96284, 62849, 28496, 84962) = 28496\n\n\\boxed{28496}", "output_ids": [785, 15723, 914, 315, 220, 19, 24, 21, 17, 23, 374, 330, 19, 24, 21, 17, 23, 22956, 36936, 804, 25, 220, 19, 24, 21, 17, 23, 11, 220, 24, 21, 17, 23, 19, 11, 220, 21, 17, 23, 19, 24, 11, 220, 17, 23, 19, 24, 21, 11, 220, 23, 19, 24, 21, 17, 198, 48, 7, 19, 24, 21, 17, 23, 8, 284, 1308, 7, 19, 24, 21, 17, 23, 11, 220, 24, 21, 17, 23, 19, 11, 220, 21, 17, 23, 19, 24, 11, 220, 17, 23, 19, 24, 21, 11, 220, 23, 19, 24, 21, 17, 8, 284, 220, 17, 23, 19, 24, 21, 271, 59, 79075, 90, 17, 23, 19, 24, 21, 92, 151645], "meta_info": {"id": "84fb966ad06d4fe685589d1eb617d950", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.702280044555664, "response_sent_to_client_ts": 1773877225.7807975}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "12", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nJ(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 41, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "d4d3a797e3ff4e6ebdec48ff8f7e335f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0907368659973145, "response_sent_to_client_ts": 1773877226.1692696}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "280", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nB(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 33, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "9ef46554467c467ebffd82c565d83271", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 3.0220446586608887, "response_sent_to_client_ts": 1773877226.1006103}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "65440", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 54046 is \"54046\".\nRotations: 54046, 40465, 4654, 46540, 65404\nQ(54046) = min(54046, 40465, 4654, 46540, 65404) = 4654\n\n\\boxed{4654}", "output_ids": [785, 15723, 914, 315, 220, 20, 19, 15, 19, 21, 374, 330, 20, 19, 15, 19, 21, 22956, 36936, 804, 25, 220, 20, 19, 15, 19, 21, 11, 220, 19, 15, 19, 21, 20, 11, 220, 19, 21, 20, 19, 11, 220, 19, 21, 20, 19, 15, 11, 220, 21, 20, 19, 15, 19, 198, 48, 7, 20, 19, 15, 19, 21, 8, 284, 1308, 7, 20, 19, 15, 19, 21, 11, 220, 19, 15, 19, 21, 20, 11, 220, 19, 21, 20, 19, 11, 220, 19, 21, 20, 19, 15, 11, 220, 21, 20, 19, 15, 19, 8, 284, 220, 19, 21, 20, 19, 271, 59, 79075, 90, 19, 21, 20, 19, 92, 151645], "meta_info": {"id": "911df2a8304449c59842febc6f103cff", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.616562604904175, "response_sent_to_client_ts": 1773877225.6951015}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "15559", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\n1 is not prime: 1\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n9 is not prime: 9\nP(15559) = 1 + 25 + 25 + 25 + 9 = 85\n\n\\boxed{85}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 47, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 24, 284, 220, 23, 20, 271, 59, 79075, 90, 23, 20, 92, 151645], "meta_info": {"id": "49408473f78c4b798c20963cb771b10f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.681363105773926, "response_sent_to_client_ts": 1773877225.7599025}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\n4 is not prime: 4\n9 is not prime: 9\n6 is not prime: 6\n2 is prime: 2^2 = 4\n8 is not prime: 8\nE(49628) = 4 + 9 + 6 + 4 + 8 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 36, 7, 19, 24, 21, 17, 23, 8, 284, 220, 19, 488, 220, 24, 488, 220, 21, 488, 220, 19, 488, 220, 23, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "6b19fa6e58f74ef0a94116672e4c2212", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.3808469772338867, "response_sent_to_client_ts": 1773877225.4594147}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2520", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nB(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 33, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "ac3a4e4e71f7468cb4a4f4f53d552463", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.022052764892578, "response_sent_to_client_ts": 1773877226.100616}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\n4 is not prime: 4\n6 is not prime: 6\n9 is not prime: 9\n6 is not prime: 6\nE(4696) = 4 + 6 + 9 + 6 = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 36, 7, 19, 21, 24, 21, 8, 284, 220, 19, 488, 220, 21, 488, 220, 24, 488, 220, 21, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "1eadefe03c7c4d4da5401cd9102bbab6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 84, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 1.9522309303283691, "response_sent_to_client_ts": 1773877225.0307589}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nAlternating sum of squares = 2^2 - 9^2 + 1^2 - 9^2 + 0^2 = 4 - 81 + 1 - 81 + 0 = -117\nG(29190) = |-117| = 117\n\n\\boxed{117}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 24, 61, 17, 488, 220, 16, 61, 17, 481, 220, 24, 61, 17, 488, 220, 15, 61, 17, 284, 220, 19, 481, 220, 23, 16, 488, 220, 16, 481, 220, 23, 16, 488, 220, 15, 284, 481, 16, 16, 22, 198, 38, 7, 17, 24, 16, 24, 15, 8, 284, 44561, 16, 16, 22, 91, 284, 220, 16, 16, 22, 271, 59, 79075, 90, 16, 16, 22, 92, 151645], "meta_info": {"id": "db92efd4114a49dcbf2971861e52ea12", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.4238343238830566, "response_sent_to_client_ts": 1773877225.502341}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "223", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nO(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 46, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "82a33ba09dd74145a6812a32a276c2f5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.090745210647583, "response_sent_to_client_ts": 1773877226.1692762}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nN(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 45, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "c8006445ec9b444da492e27059c6509c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 3.0907533168792725, "response_sent_to_client_ts": 1773877226.1692817}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "16", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nA(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 32, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "a26b62275b4e4b29a20b6aa2d214ea17", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.6165709495544434, "response_sent_to_client_ts": 1773877225.6951072}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\n1 is not prime: 1\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n9 is not prime: 9\nK(15559) = 1 + 25 + 25 + 25 + 9 = 85\n\n\\boxed{85}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 42, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 17, 20, 488, 220, 24, 284, 220, 23, 20, 271, 59, 79075, 90, 23, 20, 92, 151645], "meta_info": {"id": "6286e0ff957d425481071bb796b04744", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.6813721656799316, "response_sent_to_client_ts": 1773877225.7599087}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nAlternating sum of squares = 5^2 - 8^2 + 2^2 - 2^2 + 0^2 = 25 - 64 + 4 - 4 + 0 = -39\nG(58220) = |-39| = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 17, 61, 17, 481, 220, 17, 61, 17, 488, 220, 15, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 481, 220, 19, 488, 220, 15, 284, 481, 18, 24, 198, 38, 7, 20, 23, 17, 17, 15, 8, 284, 44561, 18, 24, 91, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "ecc7082c45994989ab6b2003ffe3eaf4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.336336374282837, "response_sent_to_client_ts": 1773877225.414849}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nM(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 44, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "526ca525a61b49ecadc758a04b793291", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.9931769371032715, "response_sent_to_client_ts": 1773877226.0717585}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "25", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nA(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 32, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "382b90e6341f4080b798143ad6c4d111", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.0626018047332764, "response_sent_to_client_ts": 1773877226.141107}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\n3 is prime: 3^2 = 9\n0 is not prime: 0\n8 is not prime: 8\n0 is not prime: 0\n1 is not prime: 1\nK(30801) = 9 + 0 + 8 + 0 + 1 = 18\n\n\\boxed{18}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 42, 7, 18, 15, 23, 15, 16, 8, 284, 220, 24, 488, 220, 15, 488, 220, 23, 488, 220, 15, 488, 220, 16, 284, 220, 16, 23, 271, 59, 79075, 90, 16, 23, 92, 151645], "meta_info": {"id": "6a25b89f86f44a5da3b5d5d43dba56ff", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.380854368209839, "response_sent_to_client_ts": 1773877225.4594204}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nL(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 43, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "2f4b0a64eb2140a4ae242dcc5690b7f5", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.993185043334961, "response_sent_to_client_ts": 1773877226.071764}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\n2 is prime: 2^2 = 4\n9 is not prime: 9\n1 is not prime: 1\n9 is not prime: 9\n0 is not prime: 0\nD(29190) = 4 + 9 + 1 + 9 + 0 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 35, 7, 17, 24, 16, 24, 15, 8, 284, 220, 19, 488, 220, 24, 488, 220, 16, 488, 220, 24, 488, 220, 15, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "421a11b7dbae40b68d04d6f55f596308", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.380862236022949, "response_sent_to_client_ts": 1773877225.4594257}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nAlternating sum of squares = 4^2 - 1^2 + 4^2 - 2^2 + 6^2 = 16 - 1 + 16 - 4 + 36 = 63\nH(41426) = |63| = 63\n\n\\boxed{63}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 16, 61, 17, 488, 220, 19, 61, 17, 481, 220, 17, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 16, 488, 220, 16, 21, 481, 220, 19, 488, 220, 18, 21, 284, 220, 21, 18, 198, 39, 7, 19, 16, 19, 17, 21, 8, 284, 760, 21, 18, 91, 284, 220, 21, 18, 271, 59, 79075, 90, 21, 18, 92, 151645], "meta_info": {"id": "40f17517816049809eb0592eda0b17c2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.358065128326416, "response_sent_to_client_ts": 1773877225.4365716}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nN(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 45, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "302f140e84c24937bdc8af161422c8b6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.719740390777588, "response_sent_to_client_ts": 1773877225.7982543}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "58", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\n4 is not prime: 4\n9 is not prime: 9\n6 is not prime: 6\n2 is prime: 2^2 = 4\n8 is not prime: 8\nS(49628) = 4 + 9 + 6 + 4 + 8 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 50, 7, 19, 24, 21, 17, 23, 8, 284, 220, 19, 488, 220, 24, 488, 220, 21, 488, 220, 19, 488, 220, 23, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "0f96080a7ac347bfbbdedcfd68fd9cb8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.3808693885803223, "response_sent_to_client_ts": 1773877225.4594312}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2347", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n0 is not prime: 0\n2 is prime: 2^2 = 4\n4 is not prime: 4\nP(73024) = 49 + 9 + 0 + 4 + 4 = 66\n\n\\boxed{66}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 47, 7, 22, 18, 15, 17, 19, 8, 284, 220, 19, 24, 488, 220, 24, 488, 220, 15, 488, 220, 19, 488, 220, 19, 284, 220, 21, 21, 271, 59, 79075, 90, 21, 21, 92, 151645], "meta_info": {"id": "4d45b02770ff4d679714e028062a4c64", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.5944581031799316, "response_sent_to_client_ts": 1773877225.6729894}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nM(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 44, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "2ce6933b408c457887e10ee133ca3b6d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9313387870788574, "response_sent_to_client_ts": 1773877226.009867}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nAlternating sum of squares = 6^2 - 6^2 + 4^2 - 4^2 + 4^2 = 36 - 36 + 16 - 16 + 16 = 36\nG(66444) = |36| = 36\n\n\\boxed{36}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 21, 61, 17, 488, 220, 19, 61, 17, 481, 220, 19, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 18, 21, 488, 220, 16, 21, 481, 220, 16, 21, 488, 220, 16, 21, 284, 220, 18, 21, 198, 38, 7, 21, 21, 19, 19, 19, 8, 284, 760, 18, 21, 91, 284, 220, 18, 21, 271, 59, 79075, 90, 18, 21, 92, 151645], "meta_info": {"id": "82d90eded1a84675931fe0e8cc17f75c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.4023842811584473, "response_sent_to_client_ts": 1773877225.480902}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nC(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 34, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "9f490c1a4e064968adbb26c9bf83ff59", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0220608711242676, "response_sent_to_client_ts": 1773877226.1006212}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n9 is not prime: 9\nK(2329) = 4 + 9 + 4 + 9 = 26\n\n\\boxed{26}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 42, 7, 17, 18, 17, 24, 8, 284, 220, 19, 488, 220, 24, 488, 220, 19, 488, 220, 24, 284, 220, 17, 21, 271, 59, 79075, 90, 17, 21, 92, 151645], "meta_info": {"id": "1b58a674c77447cbb9c6f3dbd582efd3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.2081053256988525, "response_sent_to_client_ts": 1773877225.286641}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\n4 is not prime: 4\n1 is not prime: 1\n4 is not prime: 4\n2 is prime: 2^2 = 4\n6 is not prime: 6\nD(41426) = 4 + 1 + 4 + 4 + 6 = 19\n\n\\boxed{19}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 35, 7, 19, 16, 19, 17, 21, 8, 284, 220, 19, 488, 220, 16, 488, 220, 19, 488, 220, 19, 488, 220, 21, 284, 220, 16, 24, 271, 59, 79075, 90, 16, 24, 92, 151645], "meta_info": {"id": "77f5c4fe17b5402f85af01b8d1ac8665", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.390082359313965, "response_sent_to_client_ts": 1773877228.6013753}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nK(65333) = 6 + 25 + 9 + 9 + 9 = 58\n\n\\boxed{58}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 42, 7, 21, 20, 18, 18, 18, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 488, 220, 24, 284, 220, 20, 23, 271, 59, 79075, 90, 20, 23, 92, 151645], "meta_info": {"id": "e9e1c96bf7734046af777ae34714dc58", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.6903865337371826, "response_sent_to_client_ts": 1773877228.9016402}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nR(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 49, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "8c995cd884db43c886057837851ac1bc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 3.102212905883789, "response_sent_to_client_ts": 1773877229.313506}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "16", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nA(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 32, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "df1e2619c09041cf884a0506d3a70ac6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.0006906986236572, "response_sent_to_client_ts": 1773877229.2120283}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "32", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n9 is not prime: 9\nS(2329) = 4 + 9 + 4 + 9 = 26\n\n\\boxed{26}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 50, 7, 17, 18, 17, 24, 8, 284, 220, 19, 488, 220, 24, 488, 220, 19, 488, 220, 24, 284, 220, 17, 21, 271, 59, 79075, 90, 17, 21, 92, 151645], "meta_info": {"id": "d16191a87e4342ccbd784c66669eb46a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 199, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.216419219970703, "response_sent_to_client_ts": 1773877228.4276729}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 7^2 + 9^2 = 25 - 4 + 64 - 49 + 81 = 97\nD(52879) = |97| = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 24, 22, 198, 35, 7, 20, 17, 23, 22, 24, 8, 284, 760, 24, 22, 91, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "b7273459abea4379b4ad42ea4a56cc7c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 2.3901002407073975, "response_sent_to_client_ts": 1773877228.6013858}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6964", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 4696 is \"4696\".\nRotations: 4696, 6964, 9646, 6469\nI(4696) = min(4696, 6964, 9646, 6469) = 4696\n\n\\boxed{4696}", "output_ids": [785, 15723, 914, 315, 220, 19, 21, 24, 21, 374, 330, 19, 21, 24, 21, 22956, 36936, 804, 25, 220, 19, 21, 24, 21, 11, 220, 21, 24, 21, 19, 11, 220, 24, 21, 19, 21, 11, 220, 21, 19, 21, 24, 198, 40, 7, 19, 21, 24, 21, 8, 284, 1308, 7, 19, 21, 24, 21, 11, 220, 21, 24, 21, 19, 11, 220, 24, 21, 19, 21, 11, 220, 21, 19, 21, 24, 8, 284, 220, 19, 21, 24, 21, 271, 59, 79075, 90, 19, 21, 24, 21, 92, 151645], "meta_info": {"id": "0d90739800464238b36a87bbe35d2458", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 92, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.130910873413086, "response_sent_to_client_ts": 1773877228.3421714}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nR(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 49, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "10e351281a5547acb30fc494ea283982", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0007169246673584, "response_sent_to_client_ts": 1773877229.2120388}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "32", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\n4 is not prime: 4\n9 is not prime: 9\n6 is not prime: 6\n2 is prime: 2^2 = 4\n8 is not prime: 8\nT(49628) = 4 + 9 + 6 + 4 + 8 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 51, 7, 19, 24, 21, 17, 23, 8, 284, 220, 19, 488, 220, 24, 488, 220, 21, 488, 220, 19, 488, 220, 23, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "775c8389593e4fbebc58a6e74b1579e0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.3901102542877197, "response_sent_to_client_ts": 1773877228.601392}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "62", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\n9 is not prime: 9\nS(52879) = 25 + 4 + 8 + 49 + 9 = 95\n\n\\boxed{95}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 50, 7, 20, 17, 23, 22, 24, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 284, 220, 24, 20, 271, 59, 79075, 90, 24, 20, 92, 151645], "meta_info": {"id": "fd1be952701d4bc4b94ff501cb7529d1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.649172782897949, "response_sent_to_client_ts": 1773877228.860461}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nN(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 45, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "5a27c951aa184a93bdd52015260ee48b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.0879361629486084, "response_sent_to_client_ts": 1773877229.2992227}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "87533", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 58733 is \"58733\".\nRotations: 58733, 87335, 73358, 33587, 35873\nQ(58733) = min(58733, 87335, 73358, 33587, 35873) = 33587\n\n\\boxed{33587}", "output_ids": [785, 15723, 914, 315, 220, 20, 23, 22, 18, 18, 374, 330, 20, 23, 22, 18, 18, 22956, 36936, 804, 25, 220, 20, 23, 22, 18, 18, 11, 220, 23, 22, 18, 18, 20, 11, 220, 22, 18, 18, 20, 23, 11, 220, 18, 18, 20, 23, 22, 11, 220, 18, 20, 23, 22, 18, 198, 48, 7, 20, 23, 22, 18, 18, 8, 284, 1308, 7, 20, 23, 22, 18, 18, 11, 220, 23, 22, 18, 18, 20, 11, 220, 22, 18, 18, 20, 23, 11, 220, 18, 18, 20, 23, 22, 11, 220, 18, 20, 23, 22, 18, 8, 284, 220, 18, 18, 20, 23, 22, 271, 59, 79075, 90, 18, 18, 20, 23, 22, 92, 151645], "meta_info": {"id": "173f489001784bcbb9bac69c2f18c48d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.7120893001556396, "response_sent_to_client_ts": 1773877228.9233932}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nR(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 49, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "3ba98395af2649f5a113eb2507b10830", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.030003547668457, "response_sent_to_client_ts": 1773877229.2413023}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nC(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 34, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "95f065454f31439d9864a7e3de6dabe2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.129070520401001, "response_sent_to_client_ts": 1773877229.3403566}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "31", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nA(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 32, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "f2d92451df4643f1a3dd5769c87e5fc2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 3.1022298336029053, "response_sent_to_client_ts": 1773877229.3135164}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nL(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 43, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "a2bdf8dca410414eb0618f09d4502797", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.12909197807312, "response_sent_to_client_ts": 1773877229.3403676}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nAlternating sum of squares = 8^2 - 5^2 + 6^2 - 3^2 + 8^2 = 64 - 25 + 36 - 9 + 64 = 130\nF(85638) = |130| = 130\n\n\\boxed{130}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 21, 61, 17, 481, 220, 18, 61, 17, 488, 220, 23, 61, 17, 284, 220, 21, 19, 481, 220, 17, 20, 488, 220, 18, 21, 481, 220, 24, 488, 220, 21, 19, 284, 220, 16, 18, 15, 198, 37, 7, 23, 20, 21, 18, 23, 8, 284, 760, 16, 18, 15, 91, 284, 220, 16, 18, 15, 271, 59, 79075, 90, 16, 18, 15, 92, 151645], "meta_info": {"id": "2b55bc129bb045c4be89cd20e9e4bd17", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.476268768310547, "response_sent_to_client_ts": 1773877228.6875196}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n9 is not prime: 9\n9 is not prime: 9\nK(6599) = 6 + 25 + 9 + 9 = 49\n\n\\boxed{49}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 42, 7, 21, 20, 24, 24, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 284, 220, 19, 24, 271, 59, 79075, 90, 19, 24, 92, 151645], "meta_info": {"id": "daf432c30aee48b39cbba066cf6f77a2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 90, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.086822986602783, "response_sent_to_client_ts": 1773877228.2980745}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "13", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nJ(52858) = 15 + 3 + 36 + 15 + 36 = 105\n\n\\boxed{105}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 41, 7, 20, 17, 23, 20, 23, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 18, 21, 284, 220, 16, 15, 20, 271, 59, 79075, 90, 16, 15, 20, 92, 151645], "meta_info": {"id": "887a5f5bba07484296565f1ddb172e5e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 3.0879571437835693, "response_sent_to_client_ts": 1773877229.2992325}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "98752", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 52879 is \"52879\".\nRotations: 52879, 28795, 87952, 79528, 95287\nQ(52879) = min(52879, 28795, 87952, 79528, 95287) = 28795\n\n\\boxed{28795}", "output_ids": [785, 15723, 914, 315, 220, 20, 17, 23, 22, 24, 374, 330, 20, 17, 23, 22, 24, 22956, 36936, 804, 25, 220, 20, 17, 23, 22, 24, 11, 220, 17, 23, 22, 24, 20, 11, 220, 23, 22, 24, 20, 17, 11, 220, 22, 24, 20, 17, 23, 11, 220, 24, 20, 17, 23, 22, 198, 48, 7, 20, 17, 23, 22, 24, 8, 284, 1308, 7, 20, 17, 23, 22, 24, 11, 220, 17, 23, 22, 24, 20, 11, 220, 23, 22, 24, 20, 17, 11, 220, 22, 24, 20, 17, 23, 11, 220, 24, 20, 17, 23, 22, 8, 284, 220, 17, 23, 22, 24, 20, 271, 59, 79075, 90, 17, 23, 22, 24, 20, 92, 151645], "meta_info": {"id": "1a0cd81075d548faba54c8e0546e4587", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.7121076583862305, "response_sent_to_client_ts": 1773877228.923404}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nAlternating sum of squares = 6^2 - 5^2 + 9^2 - 9^2 = 36 - 25 + 81 - 81 = 11\nH(6599) = |11| = 11\n\n\\boxed{11}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 481, 220, 24, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 23, 16, 481, 220, 23, 16, 284, 220, 16, 16, 198, 39, 7, 21, 20, 24, 24, 8, 284, 760, 16, 16, 91, 284, 220, 16, 16, 271, 59, 79075, 90, 16, 16, 92, 151645], "meta_info": {"id": "012dcf8cea3049c4af3e0178428c6818", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.10897159576416, "response_sent_to_client_ts": 1773877228.3202448}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nAlternating sum of squares = 4^2 - 6^2 + 9^2 - 6^2 = 16 - 36 + 81 - 36 = 25\nH(4696) = |25| = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 21, 61, 17, 488, 220, 24, 61, 17, 481, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 18, 21, 488, 220, 23, 16, 481, 220, 18, 21, 284, 220, 17, 20, 198, 39, 7, 19, 21, 24, 21, 8, 284, 760, 17, 20, 91, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "e81f13cd824149a0ab970a1da654be77", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.1089937686920166, "response_sent_to_client_ts": 1773877228.3202558}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "162", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nB(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 33, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "d4d300e4add841b2bc8f7f1ddeca790d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.0300209522247314, "response_sent_to_client_ts": 1773877229.2413135}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\nT(5) = 5*6/2 = 15\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nM(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n\\boxed{127}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 44, 7, 20, 17, 23, 22, 24, 8, 284, 220, 16, 20, 488, 220, 18, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 17, 22, 271, 59, 79075, 90, 16, 17, 22, 92, 151645], "meta_info": {"id": "ea4bdc3cb3a64ed1b568728444eb19df", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 3.102240800857544, "response_sent_to_client_ts": 1773877229.313522}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\n6 is not prime: 6\n0 is not prime: 0\n1 is not prime: 1\n7 is prime: 7^2 = 49\n4 is not prime: 4\nT(60174) = 6 + 0 + 1 + 49 + 4 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 51, 7, 21, 15, 16, 22, 19, 8, 284, 220, 21, 488, 220, 15, 488, 220, 16, 488, 220, 19, 24, 488, 220, 19, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "d12ff9ef320b417295b0fb72c44fb9c1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.4336328506469727, "response_sent_to_client_ts": 1773877228.6449163}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "70", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n5 is prime: 5^2 = 25\n9 is not prime: 9\n8 is not prime: 8\nS(58598) = 25 + 8 + 25 + 9 + 8 = 75\n\n\\boxed{75}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 50, 7, 20, 23, 20, 24, 23, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 17, 20, 488, 220, 24, 488, 220, 23, 284, 220, 22, 20, 271, 59, 79075, 90, 22, 20, 92, 151645], "meta_info": {"id": "5ffca2bbb6b24b768d56d445b60cf05f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 175, "cached_tokens_details": null, "e2e_latency": 2.5623104572296143, "response_sent_to_client_ts": 1773877228.7735772}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nR(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 49, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "5752141a0cef4137ab37a7461a9449b7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.030032157897949, "response_sent_to_client_ts": 1773877229.24132}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n6 is not prime: 6\n3 is prime: 3^2 = 9\n8 is not prime: 8\nD(85638) = 8 + 25 + 6 + 9 + 8 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 35, 7, 23, 20, 21, 18, 23, 8, 284, 220, 23, 488, 220, 17, 20, 488, 220, 21, 488, 220, 24, 488, 220, 23, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "d35f6f8f51d04179a303b2c3246ad340", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.5193097591400146, "response_sent_to_client_ts": 1773877228.7305794}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nC(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 34, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "251852e463c341dda07b6ff8f8881a66", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.000727653503418, "response_sent_to_client_ts": 1773877229.212046}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "16", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nA(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 32, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "cba0314a40d8459eb504f2bdb92c466a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 3.000737428665161, "response_sent_to_client_ts": 1773877229.2120516}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "24", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nB(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 33, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "fb1ece7d928c425e9e940f84a05a6d89", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 2.969289779663086, "response_sent_to_client_ts": 1773877229.1805422}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\n6 is not prime: 6\n6 is not prime: 6\n4 is not prime: 4\n4 is not prime: 4\n4 is not prime: 4\nK(66444) = 6 + 6 + 4 + 4 + 4 = 24\n\n\\boxed{24}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 42, 7, 21, 21, 19, 19, 19, 8, 284, 220, 21, 488, 220, 21, 488, 220, 19, 488, 220, 19, 488, 220, 19, 284, 220, 17, 19, 271, 59, 79075, 90, 17, 19, 92, 151645], "meta_info": {"id": "007f029a5b184736a1d02de783e2dc3d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 100, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.305957555770874, "response_sent_to_client_ts": 1773877228.5178592}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\n1 is not prime: 1\n3 is prime: 3^2 = 9\n4 is not prime: 4\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\nK(13453) = 1 + 9 + 4 + 25 + 9 = 48\n\n\\boxed{48}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 42, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 24, 488, 220, 19, 488, 220, 17, 20, 488, 220, 24, 284, 220, 19, 23, 271, 59, 79075, 90, 19, 23, 92, 151645], "meta_info": {"id": "11fcccac48b54525a2eb3c96acb33381", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.605227470397949, "response_sent_to_client_ts": 1773877228.816494}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nC(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 34, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "b1e278b31be14cc482e8ba1c566d3080", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.774034261703491, "response_sent_to_client_ts": 1773877228.985284}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "12457", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n5 is prime: 5^2 = 25\n4 is not prime: 4\nP(72154) = 49 + 4 + 1 + 25 + 4 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 47, 7, 22, 17, 16, 20, 19, 8, 284, 220, 19, 24, 488, 220, 19, 488, 220, 16, 488, 220, 17, 20, 488, 220, 19, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "60d9a88693d04706946b37e72a55b4b1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.64919114112854, "response_sent_to_client_ts": 1773877228.8604715}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nR(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 49, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "d65b0a957ced4f309ba7b286da4ef834", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.087968111038208, "response_sent_to_client_ts": 1773877229.299239}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "33785", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 58733 is \"58733\".\nRotations: 58733, 87335, 73358, 33587, 35873\nI(58733) = min(58733, 87335, 73358, 33587, 35873) = 33587\n\n\\boxed{33587}", "output_ids": [785, 15723, 914, 315, 220, 20, 23, 22, 18, 18, 374, 330, 20, 23, 22, 18, 18, 22956, 36936, 804, 25, 220, 20, 23, 22, 18, 18, 11, 220, 23, 22, 18, 18, 20, 11, 220, 22, 18, 18, 20, 23, 11, 220, 18, 18, 20, 23, 22, 11, 220, 18, 20, 23, 22, 18, 198, 40, 7, 20, 23, 22, 18, 18, 8, 284, 1308, 7, 20, 23, 22, 18, 18, 11, 220, 23, 22, 18, 18, 20, 11, 220, 22, 18, 18, 20, 23, 11, 220, 18, 18, 20, 23, 22, 11, 220, 18, 20, 23, 22, 18, 8, 284, 220, 18, 18, 20, 23, 22, 271, 59, 79075, 90, 18, 18, 20, 23, 22, 92, 151645], "meta_info": {"id": "e22ceeb9cbd84f7ab43ee8711cdea7c1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.712118148803711, "response_sent_to_client_ts": 1773877228.9234102}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nL(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 43, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "0d9cf2cde3d746ad88a189cff7142a2b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.1022493839263916, "response_sent_to_client_ts": 1773877229.3135276}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "23301", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 10332 is \"10332\".\nRotations: 10332, 3321, 33210, 32103, 21033\nI(10332) = min(10332, 3321, 33210, 32103, 21033) = 3321\n\n\\boxed{3321}", "output_ids": [785, 15723, 914, 315, 220, 16, 15, 18, 18, 17, 374, 330, 16, 15, 18, 18, 17, 22956, 36936, 804, 25, 220, 16, 15, 18, 18, 17, 11, 220, 18, 18, 17, 16, 11, 220, 18, 18, 17, 16, 15, 11, 220, 18, 17, 16, 15, 18, 11, 220, 17, 16, 15, 18, 18, 198, 40, 7, 16, 15, 18, 18, 17, 8, 284, 1308, 7, 16, 15, 18, 18, 17, 11, 220, 18, 18, 17, 16, 11, 220, 18, 18, 17, 16, 15, 11, 220, 18, 17, 16, 15, 18, 11, 220, 17, 16, 15, 18, 18, 8, 284, 220, 18, 18, 17, 16, 271, 59, 79075, 90, 18, 18, 17, 16, 92, 151645], "meta_info": {"id": "af486344feeb4b83882bfd37d9b04c2a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6269900798797607, "response_sent_to_client_ts": 1773877228.838257}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nL(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 43, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "0cbac0c7371341c4994493d0840c91b3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0007479190826416, "response_sent_to_client_ts": 1773877229.2120574}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nAlternating sum of squares = 2^2 - 3^2 + 2^2 - 9^2 = 4 - 9 + 4 - 81 = -82\nF(2329) = |-82| = 82\n\n\\boxed{82}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 17, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 481, 220, 24, 61, 17, 284, 220, 19, 481, 220, 24, 488, 220, 19, 481, 220, 23, 16, 284, 481, 23, 17, 198, 37, 7, 17, 18, 17, 24, 8, 284, 44561, 23, 17, 91, 284, 220, 23, 17, 271, 59, 79075, 90, 23, 17, 92, 151645], "meta_info": {"id": "8500022710a64c2c8b90ade6d470b8ed", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 88, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.0438308715820312, "response_sent_to_client_ts": 1773877228.2550895}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nL(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 43, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "2f746ed76ae54810bf36a6ef53da6b38", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.072819709777832, "response_sent_to_client_ts": 1773877229.2840612}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "32", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n0 is not prime: 0\n2 is prime: 2^2 = 4\n4 is not prime: 4\nS(73024) = 49 + 9 + 0 + 4 + 4 = 66\n\n\\boxed{66}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 50, 7, 22, 18, 15, 17, 19, 8, 284, 220, 19, 24, 488, 220, 24, 488, 220, 15, 488, 220, 19, 488, 220, 19, 284, 220, 21, 21, 271, 59, 79075, 90, 21, 21, 92, 151645], "meta_info": {"id": "66ffbfdd9491404daae9529d59021092", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.6052474975585938, "response_sent_to_client_ts": 1773877228.8165054}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nAlternating sum of squares = 1^2 - 1^2 + 5^2 - 3^2 + 6^2 = 1 - 1 + 25 - 9 + 36 = 52\nF(11536) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 16, 61, 17, 488, 220, 20, 61, 17, 481, 220, 18, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 481, 220, 16, 488, 220, 17, 20, 481, 220, 24, 488, 220, 18, 21, 284, 220, 20, 17, 198, 37, 7, 16, 16, 20, 18, 21, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "86e87c7d5d124ec39817d9ca554a48da", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.346054792404175, "response_sent_to_client_ts": 1773877228.5573072}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "30", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\n5 is prime: 5^2 = 25\n4 is not prime: 4\n0 is not prime: 0\n4 is not prime: 4\n6 is not prime: 6\nT(54046) = 25 + 4 + 0 + 4 + 6 = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 51, 7, 20, 19, 15, 19, 21, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 15, 488, 220, 19, 488, 220, 21, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "892eef5d41f645c2888f12185d39188d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.433650016784668, "response_sent_to_client_ts": 1773877228.644927}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nR(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 49, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "0a4bd170146646319420859156e56402", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0300424098968506, "response_sent_to_client_ts": 1773877229.2413263}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nC(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 34, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "0d9afb81e4cc468ea14ec8dd92e5b119", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.1022582054138184, "response_sent_to_client_ts": 1773877229.3135324}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "11", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nJ(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 41, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "fc99c987182a4e0bb38743c16a8b40dc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 195, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 169, "cached_tokens_details": null, "e2e_latency": 2.6270089149475098, "response_sent_to_client_ts": 1773877228.8382695}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nN(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 45, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "9154b6492a704fc8b9e845e92e343b93", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.0300521850585938, "response_sent_to_client_ts": 1773877229.2413323}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "44466", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 66444 is \"66444\".\nRotations: 66444, 64446, 44466, 44664, 46644\nI(66444) = min(66444, 64446, 44466, 44664, 46644) = 44466\n\n\\boxed{44466}", "output_ids": [785, 15723, 914, 315, 220, 21, 21, 19, 19, 19, 374, 330, 21, 21, 19, 19, 19, 22956, 36936, 804, 25, 220, 21, 21, 19, 19, 19, 11, 220, 21, 19, 19, 19, 21, 11, 220, 19, 19, 19, 21, 21, 11, 220, 19, 19, 21, 21, 19, 11, 220, 19, 21, 21, 19, 19, 198, 40, 7, 21, 21, 19, 19, 19, 8, 284, 1308, 7, 21, 21, 19, 19, 19, 11, 220, 21, 19, 19, 19, 21, 11, 220, 19, 19, 19, 21, 21, 11, 220, 19, 19, 21, 21, 19, 11, 220, 19, 21, 21, 19, 19, 8, 284, 220, 19, 19, 19, 21, 21, 271, 59, 79075, 90, 19, 19, 19, 21, 21, 92, 151645], "meta_info": {"id": "8e243fe9854d4c10acef361a1babdf06", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.7121286392211914, "response_sent_to_client_ts": 1773877228.923416}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\n9 is not prime: 9\nK(52879) = 25 + 4 + 8 + 49 + 9 = 95\n\n\\boxed{95}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 42, 7, 20, 17, 23, 22, 24, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 284, 220, 24, 20, 271, 59, 79075, 90, 24, 20, 92, 151645], "meta_info": {"id": "cfb641276aeb44a1a8e949d0379a5269", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 2.6492011547088623, "response_sent_to_client_ts": 1773877228.8604774}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nN(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 45, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "8e42f539e1c84b0190df2698afb01767", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0007588863372803, "response_sent_to_client_ts": 1773877229.2120628}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "11356", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\n1 is not prime: 1\n1 is not prime: 1\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n6 is not prime: 6\nP(11536) = 1 + 1 + 25 + 9 + 6 = 42\n\n\\boxed{42}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 47, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 17, 20, 488, 220, 24, 488, 220, 21, 284, 220, 19, 17, 271, 59, 79075, 90, 19, 17, 92, 151645], "meta_info": {"id": "c31c8bc03b724ed39f9b658231587941", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.519327402114868, "response_sent_to_client_ts": 1773877228.7305913}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "25789", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\n9 is not prime: 9\nP(52879) = 25 + 4 + 8 + 49 + 9 = 95\n\n\\boxed{95}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 47, 7, 20, 17, 23, 22, 24, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 284, 220, 24, 20, 271, 59, 79075, 90, 24, 20, 92, 151645], "meta_info": {"id": "e12c7bac2d0f464b8af5138c6e10cae0", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 188, "cached_tokens_details": null, "e2e_latency": 2.6492104530334473, "response_sent_to_client_ts": 1773877228.8604834}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "93", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nO(54046) = 15 + 10 + 0 + 10 + 21 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 46, 7, 20, 19, 15, 19, 21, 8, 284, 220, 16, 20, 488, 220, 16, 15, 488, 220, 15, 488, 220, 16, 15, 488, 220, 17, 16, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "15cabda7be5147559cc6d3337fcaad4e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 143, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.058370590209961, "response_sent_to_client_ts": 1773877229.2696168}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nL(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 43, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "5053779d1e514ab5bbe80cf09cddc902", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0007693767547607, "response_sent_to_client_ts": 1773877229.2120678}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n5 is prime: 5^2 = 25\n9 is not prime: 9\n8 is not prime: 8\nE(58598) = 25 + 8 + 25 + 9 + 8 = 65\n\n\\boxed{65}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 36, 7, 20, 23, 20, 24, 23, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 17, 20, 488, 220, 24, 488, 220, 23, 284, 220, 21, 20, 271, 59, 79075, 90, 21, 20, 92, 151645], "meta_info": {"id": "e59a61a341a544a389896b3c28bc971a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.5623276233673096, "response_sent_to_client_ts": 1773877228.7735884}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "14400", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nB(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 33, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "308a689c21d143559a92d56ace028996", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 181, "cached_tokens_details": null, "e2e_latency": 3.1291022300720215, "response_sent_to_client_ts": 1773877229.3403738}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nAlternating sum of squares = 6^2 - 0^2 + 1^2 - 7^2 + 4^2 = 36 - 0 + 1 - 49 + 16 = 4\nF(60174) = |4| = 4\n\n\\boxed{4}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 481, 220, 22, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 15, 488, 220, 16, 481, 220, 19, 24, 488, 220, 16, 21, 284, 220, 19, 198, 37, 7, 21, 15, 16, 22, 19, 8, 284, 760, 19, 91, 284, 220, 19, 271, 59, 79075, 90, 19, 92, 151645], "meta_info": {"id": "1fc5ba9d04c849e68ad9acd3fb447bf2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 99, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.2804691791534424, "response_sent_to_client_ts": 1773877228.4917243}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "97825", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 52879 is \"52879\".\nRotations: 52879, 28795, 87952, 79528, 95287\nI(52879) = min(52879, 28795, 87952, 79528, 95287) = 28795\n\n\\boxed{28795}", "output_ids": [785, 15723, 914, 315, 220, 20, 17, 23, 22, 24, 374, 330, 20, 17, 23, 22, 24, 22956, 36936, 804, 25, 220, 20, 17, 23, 22, 24, 11, 220, 17, 23, 22, 24, 20, 11, 220, 23, 22, 24, 20, 17, 11, 220, 22, 24, 20, 17, 23, 11, 220, 24, 20, 17, 23, 22, 198, 40, 7, 20, 17, 23, 22, 24, 8, 284, 1308, 7, 20, 17, 23, 22, 24, 11, 220, 17, 23, 22, 24, 20, 11, 220, 23, 22, 24, 20, 17, 11, 220, 22, 24, 20, 17, 23, 11, 220, 24, 20, 17, 23, 22, 8, 284, 220, 17, 23, 22, 24, 20, 271, 59, 79075, 90, 17, 23, 22, 24, 20, 92, 151645], "meta_info": {"id": "4448d981bb684de98335768150b99a4d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.712139129638672, "response_sent_to_client_ts": 1773877228.923422}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nAlternating sum of squares = 7^2 - 2^2 + 1^2 - 5^2 + 4^2 = 49 - 4 + 1 - 25 + 16 = 37\nG(72154) = |37| = 37\n\n\\boxed{37}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 17, 61, 17, 488, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 19, 61, 17, 284, 220, 19, 24, 481, 220, 19, 488, 220, 16, 481, 220, 17, 20, 488, 220, 16, 21, 284, 220, 18, 22, 198, 38, 7, 22, 17, 16, 20, 19, 8, 284, 760, 18, 22, 91, 284, 220, 18, 22, 271, 59, 79075, 90, 18, 22, 92, 151645], "meta_info": {"id": "410022cd96ca4608b0910fbc63b066df", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.367725372314453, "response_sent_to_client_ts": 1773877228.5789723}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\n2 is prime: 2^2 = 4\n9 is not prime: 9\n1 is not prime: 1\n9 is not prime: 9\n0 is not prime: 0\nT(29190) = 4 + 9 + 1 + 9 + 0 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 51, 7, 17, 24, 16, 24, 15, 8, 284, 220, 19, 488, 220, 24, 488, 220, 16, 488, 220, 24, 488, 220, 15, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "661f778449de46439a4d481e3391eb79", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.3901185989379883, "response_sent_to_client_ts": 1773877228.6013975}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\n5 is prime: 5^2 = 25\n4 is not prime: 4\n0 is not prime: 0\n4 is not prime: 4\n6 is not prime: 6\nE(54046) = 25 + 4 + 0 + 4 + 6 = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 36, 7, 20, 19, 15, 19, 21, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 15, 488, 220, 19, 488, 220, 21, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "2f24ea0a5f0f4342a5ee66f6a98186b2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.433659076690674, "response_sent_to_client_ts": 1773877228.6449327}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5760", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nB(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 33, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "caaab9772c9d4d5c81bc23bc3d8784a6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 179, "cached_tokens_details": null, "e2e_latency": 3.087977170944214, "response_sent_to_client_ts": 1773877229.2992454}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nAlternating sum of squares = 4^2 - 1^2 + 4^2 - 2^2 + 6^2 = 16 - 1 + 16 - 4 + 36 = 63\nG(41426) = |63| = 63\n\n\\boxed{63}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 16, 61, 17, 488, 220, 19, 61, 17, 481, 220, 17, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 16, 488, 220, 16, 21, 481, 220, 19, 488, 220, 18, 21, 284, 220, 21, 18, 198, 38, 7, 19, 16, 19, 17, 21, 8, 284, 760, 21, 18, 91, 284, 220, 21, 18, 271, 59, 79075, 90, 21, 18, 92, 151645], "meta_info": {"id": "fdf1a29ba05f4560b8595aa8c4b338bc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.359556198120117, "response_sent_to_client_ts": 1773877231.7027235}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "157", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nO(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 46, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "f4ebc60a9d8c439cb1935f32c7bb0c4a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.0600531101226807, "response_sent_to_client_ts": 1773877232.4032047}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "38", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\n5 is prime: 5^2 = 25\n4 is not prime: 4\n0 is not prime: 0\n4 is not prime: 4\n6 is not prime: 6\nS(54046) = 25 + 4 + 0 + 4 + 6 = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 50, 7, 20, 19, 15, 19, 21, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 15, 488, 220, 19, 488, 220, 21, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "ad920ece2b674668b5371bf32fa818e7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.4258549213409424, "response_sent_to_client_ts": 1773877231.7689908}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nL(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 43, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "13d95669604a42efa4191162ad6d4360", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.989622116088867, "response_sent_to_client_ts": 1773877232.3328516}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "120", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nO(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 46, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "c63b0060aa584c05b57d818c3526f5e2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.073537826538086, "response_sent_to_client_ts": 1773877232.4166672}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "28", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n0 is not prime: 0\n2 is prime: 2^2 = 4\n4 is not prime: 4\nT(73024) = 49 + 9 + 0 + 4 + 4 = 66\n\n\\boxed{66}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 51, 7, 22, 18, 15, 17, 19, 8, 284, 220, 19, 24, 488, 220, 24, 488, 220, 15, 488, 220, 19, 488, 220, 19, 284, 220, 21, 21, 271, 59, 79075, 90, 21, 21, 92, 151645], "meta_info": {"id": "07efcd91cd664acd9d0b1b0f4a90bbba", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.5972142219543457, "response_sent_to_client_ts": 1773877231.9403813}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nAlternating sum of squares = 9^2 - 7^2 + 6^2 - 7^2 + 9^2 = 81 - 49 + 36 - 49 + 81 = 60\nF(97679) = |60| = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 24, 61, 17, 481, 220, 22, 61, 17, 488, 220, 21, 61, 17, 481, 220, 22, 61, 17, 488, 220, 24, 61, 17, 284, 220, 23, 16, 481, 220, 19, 24, 488, 220, 18, 21, 481, 220, 19, 24, 488, 220, 23, 16, 284, 220, 21, 15, 198, 37, 7, 24, 22, 21, 22, 24, 8, 284, 760, 21, 15, 91, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "1062e25538ac40cb89a15554e676c5a4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.4042608737945557, "response_sent_to_client_ts": 1773877231.7474384}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "76", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\n9 is not prime: 9\n7 is prime: 7^2 = 49\n6 is not prime: 6\n7 is prime: 7^2 = 49\n9 is not prime: 9\nS(97679) = 9 + 49 + 6 + 49 + 9 = 122\n\n\\boxed{122}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 24, 374, 537, 10250, 25, 220, 24, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 50, 7, 24, 22, 21, 22, 24, 8, 284, 220, 24, 488, 220, 19, 24, 488, 220, 21, 488, 220, 19, 24, 488, 220, 24, 284, 220, 16, 17, 17, 271, 59, 79075, 90, 16, 17, 17, 92, 151645], "meta_info": {"id": "dfad0874f0134d29a0e9d91534fa6de6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.597229480743408, "response_sent_to_client_ts": 1773877231.9403925}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "11", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nJ(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 41, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "5f890cbc128146e8b294256bcb598e13", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.01863431930542, "response_sent_to_client_ts": 1773877232.361832}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9322", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 2329 is \"2329\".\nRotations: 2329, 3292, 2923, 9232\nQ(2329) = min(2329, 3292, 2923, 9232) = 2329\n\n\\boxed{2329}", "output_ids": [785, 15723, 914, 315, 220, 17, 18, 17, 24, 374, 330, 17, 18, 17, 24, 22956, 36936, 804, 25, 220, 17, 18, 17, 24, 11, 220, 18, 17, 24, 17, 11, 220, 17, 24, 17, 18, 11, 220, 24, 17, 18, 17, 198, 48, 7, 17, 18, 17, 24, 8, 284, 1308, 7, 17, 18, 17, 24, 11, 220, 18, 17, 24, 17, 11, 220, 17, 24, 17, 18, 11, 220, 24, 17, 18, 17, 8, 284, 220, 17, 18, 17, 24, 271, 59, 79075, 90, 17, 18, 17, 24, 92, 151645], "meta_info": {"id": "cd57390143634c0e8e386ff1e6a204c1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 92, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.1246469020843506, "response_sent_to_client_ts": 1773877231.4677868}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\n1 is not prime: 1\n0 is not prime: 0\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\nT(10332) = 1 + 0 + 9 + 9 + 4 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 51, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 24, 488, 220, 24, 488, 220, 19, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "d370ebbf97cd472084b81b9393f4ed49", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.554307222366333, "response_sent_to_client_ts": 1773877231.8974452}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nR(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 49, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "33923ce2580a4bb49c94a03e9f6d1dfe", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1282267570495605, "response_sent_to_client_ts": 1773877232.4713838}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\n4 is not prime: 4\n9 is not prime: 9\n6 is not prime: 6\n2 is prime: 2^2 = 4\n8 is not prime: 8\nK(49628) = 4 + 9 + 6 + 4 + 8 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 42, 7, 19, 24, 21, 17, 23, 8, 284, 220, 19, 488, 220, 24, 488, 220, 21, 488, 220, 19, 488, 220, 23, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "aba3c6ed33b14a46b489b56377640093", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.382162094116211, "response_sent_to_client_ts": 1773877231.7253501}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nAlternating sum of squares = 6^2 - 0^2 + 1^2 - 7^2 + 4^2 = 36 - 0 + 1 - 49 + 16 = 4\nD(60174) = |4| = 4\n\n\\boxed{4}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 15, 61, 17, 488, 220, 16, 61, 17, 481, 220, 22, 61, 17, 488, 220, 19, 61, 17, 284, 220, 18, 21, 481, 220, 15, 488, 220, 16, 481, 220, 19, 24, 488, 220, 16, 21, 284, 220, 19, 198, 35, 7, 21, 15, 16, 22, 19, 8, 284, 760, 19, 91, 284, 220, 19, 271, 59, 79075, 90, 19, 92, 151645], "meta_info": {"id": "c77bbca0b2b04a21b7c378f95cd72363", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 99, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.2734057903289795, "response_sent_to_client_ts": 1773877231.6165442}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "75421", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 72154 is \"72154\".\nRotations: 72154, 21547, 15472, 54721, 47215\nQ(72154) = min(72154, 21547, 15472, 54721, 47215) = 15472\n\n\\boxed{15472}", "output_ids": [785, 15723, 914, 315, 220, 22, 17, 16, 20, 19, 374, 330, 22, 17, 16, 20, 19, 22956, 36936, 804, 25, 220, 22, 17, 16, 20, 19, 11, 220, 17, 16, 20, 19, 22, 11, 220, 16, 20, 19, 22, 17, 11, 220, 20, 19, 22, 17, 16, 11, 220, 19, 22, 17, 16, 20, 198, 48, 7, 22, 17, 16, 20, 19, 8, 284, 1308, 7, 22, 17, 16, 20, 19, 11, 220, 17, 16, 20, 19, 22, 11, 220, 16, 20, 19, 22, 17, 11, 220, 20, 19, 22, 17, 16, 11, 220, 19, 22, 17, 16, 20, 8, 284, 220, 16, 20, 19, 22, 17, 271, 59, 79075, 90, 16, 20, 19, 22, 17, 92, 151645], "meta_info": {"id": "35e192e253f9447abc54b69e0dffd286", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.7000837326049805, "response_sent_to_client_ts": 1773877232.0432372}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nM(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 44, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "7562e99ccc1a48c0a713ff6c28190b4b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.018648624420166, "response_sent_to_client_ts": 1773877232.3618417}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "280", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nB(72154) = 28 + 3 + 1 + 15 + 10 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 33, 7, 22, 17, 16, 20, 19, 8, 284, 220, 17, 23, 488, 220, 18, 488, 220, 16, 488, 220, 16, 20, 488, 220, 16, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "2de8db8ae6774e6f977c16d8d022ad04", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 3.018657684326172, "response_sent_to_client_ts": 1773877232.361848}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nN(65333) = 21 + 15 + 6 + 6 + 6 = 54\n\n\\boxed{54}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 45, 7, 21, 20, 18, 18, 18, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 21, 488, 220, 21, 284, 220, 20, 19, 271, 59, 79075, 90, 20, 19, 92, 151645], "meta_info": {"id": "a3c7e6e36ced4d57a0a4bc775c5659c7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.989637851715088, "response_sent_to_client_ts": 1773877232.3328617}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nN(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 45, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "4d0675ac0c12426990764c43c4f2d750", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.989647388458252, "response_sent_to_client_ts": 1773877232.3328679}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "58", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n9 is not prime: 9\n9 is not prime: 9\nS(6599) = 6 + 25 + 9 + 9 = 49\n\n\\boxed{49}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 50, 7, 21, 20, 24, 24, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 284, 220, 19, 24, 271, 59, 79075, 90, 19, 24, 92, 151645], "meta_info": {"id": "d91550bf7d5543d2be7c7dc0ec40ab45", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 199, "weight_version": "default", "total_retractions": 0, "completion_tokens": 90, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.0824663639068604, "response_sent_to_client_ts": 1773877231.425633}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nAlternating sum of squares = 7^2 - 2^2 + 1^2 - 5^2 + 4^2 = 49 - 4 + 1 - 25 + 16 = 37\nF(72154) = |37| = 37\n\n\\boxed{37}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 17, 61, 17, 488, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 19, 61, 17, 284, 220, 19, 24, 481, 220, 19, 488, 220, 16, 481, 220, 17, 20, 488, 220, 16, 21, 284, 220, 18, 22, 198, 37, 7, 22, 17, 16, 20, 19, 8, 284, 760, 18, 22, 91, 284, 220, 18, 22, 271, 59, 79075, 90, 18, 22, 92, 151645], "meta_info": {"id": "85dec95c9ab24c2bb8523e5e0bea7b5a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.359570264816284, "response_sent_to_client_ts": 1773877231.7027323}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nN(75108) = 28 + 15 + 1 + 0 + 36 = 80\n\n\\boxed{80}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 45, 7, 22, 20, 16, 15, 23, 8, 284, 220, 17, 23, 488, 220, 16, 20, 488, 220, 16, 488, 220, 15, 488, 220, 18, 21, 284, 220, 23, 15, 271, 59, 79075, 90, 23, 15, 92, 151645], "meta_info": {"id": "790f99034fd041f881dadb2cedd566ea", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0186657905578613, "response_sent_to_client_ts": 1773877232.361853}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\n2 is prime: 2^2 = 4\n9 is not prime: 9\n1 is not prime: 1\n9 is not prime: 9\n0 is not prime: 0\nE(29190) = 4 + 9 + 1 + 9 + 0 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 36, 7, 17, 24, 16, 24, 15, 8, 284, 220, 19, 488, 220, 24, 488, 220, 16, 488, 220, 24, 488, 220, 15, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "4ae59a61d48846999e2ba28389d7a258", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.382176160812378, "response_sent_to_client_ts": 1773877231.7253597}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nAlternating sum of squares = 6^2 - 5^2 + 3^2 - 3^2 + 3^2 = 36 - 25 + 9 - 9 + 9 = 20\nH(65333) = |20| = 20\n\n\\boxed{20}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 24, 481, 220, 24, 488, 220, 24, 284, 220, 17, 15, 198, 39, 7, 21, 20, 18, 18, 18, 8, 284, 760, 17, 15, 91, 284, 220, 17, 15, 271, 59, 79075, 90, 17, 15, 92, 151645], "meta_info": {"id": "4ba151aa5ef040b6b9a670c4859bdb01", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.337620258331299, "response_sent_to_client_ts": 1773877231.6807704}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\nAlternating sum of squares = 5^2 - 2^2 + 8^2 - 5^2 + 8^2 = 25 - 4 + 64 - 25 + 64 = 124\nH(52858) = |124| = 124\n\n\\boxed{124}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 481, 220, 20, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 19, 488, 220, 21, 19, 481, 220, 17, 20, 488, 220, 21, 19, 284, 220, 16, 17, 19, 198, 39, 7, 20, 17, 23, 20, 23, 8, 284, 760, 16, 17, 19, 91, 284, 220, 16, 17, 19, 271, 59, 79075, 90, 16, 17, 19, 92, 151645], "meta_info": {"id": "57880787ff2845db8300c712f3242615", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 108, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 2.468651533126831, "response_sent_to_client_ts": 1773877231.8117878}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nAlternating sum of squares = 5^2 - 8^2 + 5^2 - 9^2 + 8^2 = 25 - 64 + 25 - 81 + 64 = -31\nD(58598) = |-31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 20, 61, 17, 481, 220, 24, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 17, 20, 481, 220, 23, 16, 488, 220, 21, 19, 284, 481, 18, 16, 198, 35, 7, 20, 23, 20, 24, 23, 8, 284, 44561, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "cfab096fed2441ff85fe2033ce73a188", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.40427827835083, "response_sent_to_client_ts": 1773877231.7474499}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\nAlternating sum of squares = 7^2 - 2^2 + 1^2 - 5^2 + 4^2 = 49 - 4 + 1 - 25 + 16 = 37\nH(72154) = |37| = 37\n\n\\boxed{37}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 17, 61, 17, 488, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 19, 61, 17, 284, 220, 19, 24, 481, 220, 19, 488, 220, 16, 481, 220, 17, 20, 488, 220, 16, 21, 284, 220, 18, 22, 198, 39, 7, 22, 17, 16, 20, 19, 8, 284, 760, 18, 22, 91, 284, 220, 18, 22, 271, 59, 79075, 90, 18, 22, 92, 151645], "meta_info": {"id": "1deac69288af4e4e9df1eaf6c3128717", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3595778942108154, "response_sent_to_client_ts": 1773877231.7027376}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "7", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nN(15559) = 1 + 15 + 15 + 15 + 45 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 45, 7, 16, 20, 20, 20, 24, 8, 284, 220, 16, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 16, 20, 488, 220, 19, 20, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "cb1f705ccf2e448ea73722d95bf5ce3e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 144, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0600697994232178, "response_sent_to_client_ts": 1773877232.4032154}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nJ(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 41, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "6c27787784064c79b57fe421180c595c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0186729431152344, "response_sent_to_client_ts": 1773877232.361858}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "52", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nS(58733) = 25 + 8 + 49 + 9 + 9 = 100\n\n\\boxed{100}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 50, 7, 20, 23, 22, 18, 18, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 488, 220, 24, 284, 220, 16, 15, 15, 271, 59, 79075, 90, 16, 15, 15, 92, 151645], "meta_info": {"id": "d1bb358d15bb4bcbb9c824a5576d8f85", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 122, "cached_tokens": 175, "cached_tokens_details": null, "e2e_latency": 2.732407569885254, "response_sent_to_client_ts": 1773877232.0755377}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nR(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 49, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "94152e741c404d659b6a084cba91229b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.717562437057495, "response_sent_to_client_ts": 1773877232.060711}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nC(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 34, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "29c50a93280f4997bea4ac95700058a3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.989657163619995, "response_sent_to_client_ts": 1773877232.332873}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "64", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n6 is not prime: 6\n3 is prime: 3^2 = 9\n8 is not prime: 8\nT(85638) = 8 + 25 + 6 + 9 + 8 = 56\n\n\\boxed{56}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 51, 7, 23, 20, 21, 18, 23, 8, 284, 220, 23, 488, 220, 17, 20, 488, 220, 21, 488, 220, 24, 488, 220, 23, 284, 220, 20, 21, 271, 59, 79075, 90, 20, 21, 92, 151645], "meta_info": {"id": "ad68059745a14112b02453f6855a7e88", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.511596918106079, "response_sent_to_client_ts": 1773877231.8547344}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nR(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 49, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "24fe139e5f1f4c4c9acbb45b273bd14a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9277801513671875, "response_sent_to_client_ts": 1773877232.2709215}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nAlternating sum of squares = 4^2 - 9^2 + 6^2 - 2^2 + 8^2 = 16 - 81 + 36 - 4 + 64 = 31\nF(49628) = |31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 24, 61, 17, 488, 220, 21, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 284, 220, 16, 21, 481, 220, 23, 16, 488, 220, 18, 21, 481, 220, 19, 488, 220, 21, 19, 284, 220, 18, 16, 198, 37, 7, 19, 24, 21, 17, 23, 8, 284, 760, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "a1bdc95e63454f338e96eac61cd48818", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.382185459136963, "response_sent_to_client_ts": 1773877231.7253647}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5699", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n9 is not prime: 9\n9 is not prime: 9\nP(6599) = 6 + 25 + 9 + 9 = 49\n\n\\boxed{49}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 47, 7, 21, 20, 24, 24, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 284, 220, 19, 24, 271, 59, 79075, 90, 19, 24, 92, 151645], "meta_info": {"id": "e6872269fb04431d9594dfee746ed080", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 211, "weight_version": "default", "total_retractions": 0, "completion_tokens": 90, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.082487106323242, "response_sent_to_client_ts": 1773877231.4256468}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\n4 is not prime: 4\n1 is not prime: 1\n4 is not prime: 4\n2 is prime: 2^2 = 4\n6 is not prime: 6\nE(41426) = 4 + 1 + 4 + 4 + 6 = 19\n\n\\boxed{19}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 19, 374, 537, 10250, 25, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 36, 7, 19, 16, 19, 17, 21, 8, 284, 220, 19, 488, 220, 16, 488, 220, 19, 488, 220, 19, 488, 220, 21, 284, 220, 16, 24, 271, 59, 79075, 90, 16, 24, 92, 151645], "meta_info": {"id": "685d9eaee9464bbf9f7e8f329aad6879", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.382192850112915, "response_sent_to_client_ts": 1773877231.72537}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nN(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 45, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "7a32e3e1c7994a4a9994d2c340f2f3a6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1282436847686768, "response_sent_to_client_ts": 1773877232.4713929}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "29", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nA(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 32, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "5ad9d069cd094f8e822bbdc8430b5472", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.087573289871216, "response_sent_to_client_ts": 1773877232.430719}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "180", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nB(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 33, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "6a8ff328d506498c952bbb82ecb8ecfc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 2.9896652698516846, "response_sent_to_client_ts": 1773877232.3328836}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "60", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nO(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 46, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "2171b303ec6e4b1cb59da7af28df41e3", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 2.989673376083374, "response_sent_to_client_ts": 1773877232.3328884}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nAlternating sum of squares = 4^2 - 9^2 + 6^2 - 2^2 + 8^2 = 16 - 81 + 36 - 4 + 64 = 31\nD(49628) = |31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 24, 61, 17, 488, 220, 21, 61, 17, 481, 220, 17, 61, 17, 488, 220, 23, 61, 17, 284, 220, 16, 21, 481, 220, 23, 16, 488, 220, 18, 21, 481, 220, 19, 488, 220, 21, 19, 284, 220, 18, 16, 198, 35, 7, 19, 24, 21, 17, 23, 8, 284, 760, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "7c4775318f554995bf6d3c297d3f8270", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3822004795074463, "response_sent_to_client_ts": 1773877231.7253752}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nL(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 43, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "3e9df893ed3e4f79a97e001ac049b702", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.7624330520629883, "response_sent_to_client_ts": 1773877232.105563}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nAlternating sum of squares = 1^2 - 3^2 + 4^2 - 5^2 + 3^2 = 1 - 9 + 16 - 25 + 9 = -8\nH(13453) = |-8| = 8\n\n\\boxed{8}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 18, 61, 17, 488, 220, 19, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 284, 220, 16, 481, 220, 24, 488, 220, 16, 21, 481, 220, 17, 20, 488, 220, 24, 284, 481, 23, 198, 39, 7, 16, 18, 19, 20, 18, 8, 284, 44561, 23, 91, 284, 220, 23, 271, 59, 79075, 90, 23, 92, 151645], "meta_info": {"id": "ba844f1ec46b4f39822656f380362d01", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 98, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.252002000808716, "response_sent_to_client_ts": 1773877231.5951536}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nM(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 44, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "ccaba3878ff649a1a105cd6ead314b69", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.0186798572540283, "response_sent_to_client_ts": 1773877232.3618627}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nM(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 44, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "d24e548c992e41d5809e1e25453184c4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.957897424697876, "response_sent_to_client_ts": 1773877232.3010283}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "74320", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 73024 is \"73024\".\nRotations: 73024, 30247, 2473, 24730, 47302\nQ(73024) = min(73024, 30247, 2473, 24730, 47302) = 2473\n\n\\boxed{2473}", "output_ids": [785, 15723, 914, 315, 220, 22, 18, 15, 17, 19, 374, 330, 22, 18, 15, 17, 19, 22956, 36936, 804, 25, 220, 22, 18, 15, 17, 19, 11, 220, 18, 15, 17, 19, 22, 11, 220, 17, 19, 22, 18, 11, 220, 17, 19, 22, 18, 15, 11, 220, 19, 22, 18, 15, 17, 198, 48, 7, 22, 18, 15, 17, 19, 8, 284, 1308, 7, 22, 18, 15, 17, 19, 11, 220, 18, 15, 17, 19, 22, 11, 220, 17, 19, 22, 18, 11, 220, 17, 19, 22, 18, 15, 11, 220, 19, 22, 18, 15, 17, 8, 284, 220, 17, 19, 22, 18, 271, 59, 79075, 90, 17, 19, 22, 18, 92, 151645], "meta_info": {"id": "c10f570e5ebc47729615ec932e9e06e2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6183571815490723, "response_sent_to_client_ts": 1773877231.9615052}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "9", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nAlternating sum of squares = 1^2 - 5^2 + 5^2 - 5^2 + 9^2 = 1 - 25 + 25 - 25 + 81 = 57\nG(15559) = |57| = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 20, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 284, 220, 16, 481, 220, 17, 20, 488, 220, 17, 20, 481, 220, 17, 20, 488, 220, 23, 16, 284, 220, 20, 22, 198, 38, 7, 16, 20, 20, 20, 24, 8, 284, 760, 20, 22, 91, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "adefa118314947f58bab6dba74bcb7ec", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3822073936462402, "response_sent_to_client_ts": 1773877231.7253792}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nL(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 43, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "dc02f3a8e37c4368acdfa31100f58292", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 3.018688440322876, "response_sent_to_client_ts": 1773877232.3618672}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "160", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nB(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 33, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "1b1fa2651c834f1b91a0edefbd2ade62", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 181, "cached_tokens_details": null, "e2e_latency": 2.989680528640747, "response_sent_to_client_ts": 1773877232.3328936}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(75108)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 75108 are [7, 5, 1, 0, 8].\nAlternating sum of squares = 7^2 - 5^2 + 1^2 - 0^2 + 8^2 = 49 - 25 + 1 - 0 + 64 = 89\nH(75108) = |89| = 89\n\n\\boxed{89}", "output_ids": [785, 18509, 315, 220, 22, 20, 16, 15, 23, 525, 508, 22, 11, 220, 20, 11, 220, 16, 11, 220, 15, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 20, 61, 17, 488, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 23, 61, 17, 284, 220, 19, 24, 481, 220, 17, 20, 488, 220, 16, 481, 220, 15, 488, 220, 21, 19, 284, 220, 23, 24, 198, 39, 7, 22, 20, 16, 15, 23, 8, 284, 760, 23, 24, 91, 284, 220, 23, 24, 271, 59, 79075, 90, 23, 24, 92, 151645], "meta_info": {"id": "b10897e2802a4c249931424e40b8d300", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.359585762023926, "response_sent_to_client_ts": 1773877231.7027426}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nC(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 34, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "20dfd3ce68494465ab4e1552d2595c72", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 3.1282529830932617, "response_sent_to_client_ts": 1773877232.471399}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n0 is not prime: 0\n2 is prime: 2^2 = 4\n4 is not prime: 4\nK(73024) = 49 + 9 + 0 + 4 + 4 = 66\n\n\\boxed{66}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 42, 7, 22, 18, 15, 17, 19, 8, 284, 220, 19, 24, 488, 220, 24, 488, 220, 15, 488, 220, 19, 488, 220, 19, 284, 220, 21, 21, 271, 59, 79075, 90, 21, 21, 92, 151645], "meta_info": {"id": "f844669c8a844072aa4824a13c1e53ff", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.5972423553466797, "response_sent_to_client_ts": 1773877231.9403992}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nJ(13453) = 1 + 6 + 10 + 15 + 6 = 38\n\n\\boxed{38}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 41, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 21, 488, 220, 16, 15, 488, 220, 16, 20, 488, 220, 21, 284, 220, 18, 23, 271, 59, 79075, 90, 18, 23, 92, 151645], "meta_info": {"id": "a4c34983d38e48f9994dd65059330ab2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 2.989691972732544, "response_sent_to_client_ts": 1773877232.3328989}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "201", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(49628)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 49628 are [4, 9, 6, 2, 8].\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(8) = 8*9/2 = 36\nO(49628) = 10 + 45 + 21 + 3 + 36 = 115\n\n\\boxed{115}", "output_ids": [785, 18509, 315, 220, 19, 24, 21, 17, 23, 525, 508, 19, 11, 220, 24, 11, 220, 21, 11, 220, 17, 11, 220, 23, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 46, 7, 19, 24, 21, 17, 23, 8, 284, 220, 16, 15, 488, 220, 19, 20, 488, 220, 17, 16, 488, 220, 18, 488, 220, 18, 21, 284, 220, 16, 16, 20, 271, 59, 79075, 90, 16, 16, 20, 92, 151645], "meta_info": {"id": "7e9b70f96fd24ce88899fe866ccfbea7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 146, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 3.0875892639160156, "response_sent_to_client_ts": 1773877232.430729}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "25", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nA(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 32, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "26a925b485dc44109821a2814bb9189f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 2.717578411102295, "response_sent_to_client_ts": 1773877232.0607216}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "99776", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 97679 is \"97679\".\nRotations: 97679, 76799, 67997, 79976, 99767\nQ(97679) = min(97679, 76799, 67997, 79976, 99767) = 67997\n\n\\boxed{67997}", "output_ids": [785, 15723, 914, 315, 220, 24, 22, 21, 22, 24, 374, 330, 24, 22, 21, 22, 24, 22956, 36936, 804, 25, 220, 24, 22, 21, 22, 24, 11, 220, 22, 21, 22, 24, 24, 11, 220, 21, 22, 24, 24, 22, 11, 220, 22, 24, 24, 22, 21, 11, 220, 24, 24, 22, 21, 22, 198, 48, 7, 24, 22, 21, 22, 24, 8, 284, 1308, 7, 24, 22, 21, 22, 24, 11, 220, 22, 21, 22, 24, 24, 11, 220, 21, 22, 24, 24, 22, 11, 220, 22, 24, 24, 22, 21, 11, 220, 24, 24, 22, 21, 22, 8, 284, 220, 21, 22, 24, 24, 22, 271, 59, 79075, 90, 21, 22, 24, 24, 22, 92, 151645], "meta_info": {"id": "74da6038db2842da95bf906b1e9b6bf9", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.700101375579834, "response_sent_to_client_ts": 1773877232.0432472}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\nAlternating sum of squares = 1^2 - 3^2 + 4^2 - 5^2 + 3^2 = 1 - 9 + 16 - 25 + 9 = -8\nF(13453) = |-8| = 8\n\n\\boxed{8}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 18, 61, 17, 488, 220, 19, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 284, 220, 16, 481, 220, 24, 488, 220, 16, 21, 481, 220, 17, 20, 488, 220, 24, 284, 481, 23, 198, 37, 7, 16, 18, 19, 20, 18, 8, 284, 44561, 23, 91, 284, 220, 23, 271, 59, 79075, 90, 23, 92, 151645], "meta_info": {"id": "6bc7a3bacf6f4b54951593873556282e", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 98, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.252018451690674, "response_sent_to_client_ts": 1773877231.5951633}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nM(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 44, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "c73e69e06df346b09af83e6f6f8ab220", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.6183714866638184, "response_sent_to_client_ts": 1773877231.9615152}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nAlternating sum of squares = 1^2 - 1^2 + 5^2 - 3^2 + 6^2 = 1 - 1 + 25 - 9 + 36 = 52\nH(11536) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 16, 61, 17, 488, 220, 20, 61, 17, 481, 220, 18, 61, 17, 488, 220, 21, 61, 17, 284, 220, 16, 481, 220, 16, 488, 220, 17, 20, 481, 220, 24, 488, 220, 18, 21, 284, 220, 20, 17, 198, 39, 7, 16, 16, 20, 18, 21, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "1327cd4a46e241ef9cb925c364c44115", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3376364707946777, "response_sent_to_client_ts": 1773877231.6807802}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nR(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 49, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "4007b4f4f84a48d8b79eff803bcca391", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.1142537593841553, "response_sent_to_client_ts": 1773877232.4573853}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nAlternating sum of squares = 5^2 - 8^2 + 5^2 - 9^2 + 8^2 = 25 - 64 + 25 - 81 + 64 = -31\nH(58598) = |-31| = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 20, 61, 17, 481, 220, 24, 61, 17, 488, 220, 23, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 17, 20, 481, 220, 23, 16, 488, 220, 21, 19, 284, 481, 18, 16, 198, 39, 7, 20, 23, 20, 24, 23, 8, 284, 44561, 18, 16, 91, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "9faa237083794294bc072f0a1ed3c870", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 105, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.404287576675415, "response_sent_to_client_ts": 1773877231.7474563}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "168", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nB(73024) = 28 + 6 + 0 + 3 + 10 = 47\n\n\\boxed{47}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 33, 7, 22, 18, 15, 17, 19, 8, 284, 220, 17, 23, 488, 220, 21, 488, 220, 15, 488, 220, 18, 488, 220, 16, 15, 284, 220, 19, 22, 271, 59, 79075, 90, 19, 22, 92, 151645], "meta_info": {"id": "99880c138ac347d7961b412b058e4e2c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 2.9896998405456543, "response_sent_to_client_ts": 1773877232.332904}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function h. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 6\n\nInput: 41\nOutput: 3\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 6\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 6\n\nInput: 21395\nOutput: 8\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 7\n\nQuestion:\nWhat is the output of h(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nAlternating sum of squares = 1^2 - 0^2 + 3^2 - 3^2 + 2^2 = 1 - 0 + 9 - 9 + 4 = 5\nH(10332) = |5| = 5\n\n\\boxed{5}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 15, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 17, 61, 17, 284, 220, 16, 481, 220, 15, 488, 220, 24, 481, 220, 24, 488, 220, 19, 284, 220, 20, 198, 39, 7, 16, 15, 18, 18, 17, 8, 284, 760, 20, 91, 284, 220, 20, 271, 59, 79075, 90, 20, 92, 151645], "meta_info": {"id": "986abf99c43a48f390c97fe1d493e744", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 96, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.2093584537506104, "response_sent_to_client_ts": 1773877231.5525}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "45", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(52879)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52879 are [5, 2, 8, 7, 9].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\n9 is not prime: 9\nT(52879) = 25 + 4 + 8 + 49 + 9 = 95\n\n\\boxed{95}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 22, 24, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 22, 11, 220, 24, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 51, 7, 20, 17, 23, 22, 24, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 284, 220, 24, 20, 271, 59, 79075, 90, 24, 20, 92, 151645], "meta_info": {"id": "3bc0dc2b85674a4dbc56e9c93a581c39", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 174, "cached_tokens_details": null, "e2e_latency": 2.5744502544403076, "response_sent_to_client_ts": 1773877235.048474}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\n0 is not prime: 0\nT(58220) = 25 + 8 + 4 + 4 + 0 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 51, 7, 20, 23, 17, 17, 15, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 488, 220, 19, 488, 220, 15, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "d97826d013934c7ba6a75714ac60c25d", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.5498573780059814, "response_sent_to_client_ts": 1773877235.0238845}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nAlternating sum of squares = 4^2 - 6^2 + 9^2 - 6^2 = 16 - 36 + 81 - 36 = 25\nG(4696) = |25| = 25\n\n\\boxed{25}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 19, 61, 17, 481, 220, 21, 61, 17, 488, 220, 24, 61, 17, 481, 220, 21, 61, 17, 284, 220, 16, 21, 481, 220, 18, 21, 488, 220, 23, 16, 481, 220, 18, 21, 284, 220, 17, 20, 198, 38, 7, 19, 21, 24, 21, 8, 284, 760, 17, 20, 91, 284, 220, 17, 20, 271, 59, 79075, 90, 17, 20, 92, 151645], "meta_info": {"id": "3d15d44737dc438b8bd32336d051eb71", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 91, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.0582382678985596, "response_sent_to_client_ts": 1773877234.5322518}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2258", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\n0 is not prime: 0\nP(58220) = 25 + 8 + 4 + 4 + 0 = 31\n\n\\boxed{31}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 47, 7, 20, 23, 17, 17, 15, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 488, 220, 19, 488, 220, 15, 284, 220, 18, 16, 271, 59, 79075, 90, 18, 16, 92, 151645], "meta_info": {"id": "1f79c8a98ea449eea7f1f5cf5f37fb28", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.549872636795044, "response_sent_to_client_ts": 1773877235.0238962}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(13453)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 13453 are [1, 3, 4, 5, 3].\n1 is not prime: 1\n3 is prime: 3^2 = 9\n4 is not prime: 4\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\nE(13453) = 1 + 9 + 4 + 25 + 9 = 48\n\n\\boxed{48}", "output_ids": [785, 18509, 315, 220, 16, 18, 19, 20, 18, 525, 508, 16, 11, 220, 18, 11, 220, 19, 11, 220, 20, 11, 220, 18, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 36, 7, 16, 18, 19, 20, 18, 8, 284, 220, 16, 488, 220, 24, 488, 220, 19, 488, 220, 17, 20, 488, 220, 24, 284, 220, 19, 23, 271, 59, 79075, 90, 19, 23, 92, 151645], "meta_info": {"id": "4e23766bfe514c1dace20faf1b6e8502", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.549882173538208, "response_sent_to_client_ts": 1773877235.023903}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nAlternating sum of squares = 5^2 - 8^2 + 7^2 - 3^2 + 3^2 = 25 - 64 + 49 - 9 + 9 = 10\nD(58733) = |10| = 10\n\n\\boxed{10}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 24, 481, 220, 24, 488, 220, 24, 284, 220, 16, 15, 198, 35, 7, 20, 23, 22, 18, 18, 8, 284, 760, 16, 15, 91, 284, 220, 16, 15, 271, 59, 79075, 90, 16, 15, 92, 151645], "meta_info": {"id": "9d3484b7ee61428cb3e79fa8df06e06f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 103, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.313847064971924, "response_sent_to_client_ts": 1773877234.7878265}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "56", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n5 is prime: 5^2 = 25\n8 is not prime: 8\nS(52858) = 25 + 4 + 8 + 25 + 8 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 50, 7, 20, 17, 23, 20, 23, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 17, 20, 488, 220, 23, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "f8f97bcc578e4a4baf553f63b32b1919", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 176, "cached_tokens_details": null, "e2e_latency": 2.574463129043579, "response_sent_to_client_ts": 1773877235.0484843}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function g. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of g(73024)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 73024 are [7, 3, 0, 2, 4].\nAlternating sum of squares = 7^2 - 3^2 + 0^2 - 2^2 + 4^2 = 49 - 9 + 0 - 4 + 16 = 52\nG(73024) = |52| = 52\n\n\\boxed{52}", "output_ids": [785, 18509, 315, 220, 22, 18, 15, 17, 19, 525, 508, 22, 11, 220, 18, 11, 220, 15, 11, 220, 17, 11, 220, 19, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 22, 61, 17, 481, 220, 18, 61, 17, 488, 220, 15, 61, 17, 481, 220, 17, 61, 17, 488, 220, 19, 61, 17, 284, 220, 19, 24, 481, 220, 24, 488, 220, 15, 481, 220, 19, 488, 220, 16, 21, 284, 220, 20, 17, 198, 38, 7, 22, 18, 15, 17, 19, 8, 284, 760, 20, 17, 91, 284, 220, 20, 17, 271, 59, 79075, 90, 20, 17, 92, 151645], "meta_info": {"id": "ea9ddf6554cb46c7a38fad9db6300643", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.292416572570801, "response_sent_to_client_ts": 1773877234.766429}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "40", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n5 is prime: 5^2 = 25\n9 is not prime: 9\n8 is not prime: 8\nT(58598) = 25 + 8 + 25 + 9 + 8 = 75\n\n\\boxed{75}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 51, 7, 20, 23, 20, 24, 23, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 17, 20, 488, 220, 24, 488, 220, 23, 284, 220, 22, 20, 271, 59, 79075, 90, 22, 20, 92, 151645], "meta_info": {"id": "914f1f1cc54d4244b1395590d7eec51c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 173, "cached_tokens_details": null, "e2e_latency": 2.5064775943756104, "response_sent_to_client_ts": 1773877234.9804864}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "167", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nO(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 46, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "d416dfa810e748caad821ba5c2fedade", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 2.944737434387207, "response_sent_to_client_ts": 1773877235.418817}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function d. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 8\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 5\n\nInput: 87397\nOutput: 9\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 9\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9\n\nQuestion:\nWhat is the output of d(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\nAlternating sum of squares = 6^2 - 5^2 + 3^2 - 3^2 + 3^2 = 36 - 25 + 9 - 9 + 9 = 20\nD(65333) = |20| = 20\n\n\\boxed{20}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 21, 61, 17, 481, 220, 20, 61, 17, 488, 220, 18, 61, 17, 481, 220, 18, 61, 17, 488, 220, 18, 61, 17, 284, 220, 18, 21, 481, 220, 17, 20, 488, 220, 24, 481, 220, 24, 488, 220, 24, 284, 220, 17, 15, 198, 35, 7, 21, 20, 18, 18, 18, 8, 284, 760, 17, 15, 91, 284, 220, 17, 15, 271, 59, 79075, 90, 17, 15, 92, 151645], "meta_info": {"id": "78429c74684c436fbf86ca362e818445", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.292433738708496, "response_sent_to_client_ts": 1773877234.76644}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "76410", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 60174 is \"60174\".\nRotations: 60174, 1746, 17460, 74601, 46017\nQ(60174) = min(60174, 1746, 17460, 74601, 46017) = 1746\n\n\\boxed{1746}", "output_ids": [785, 15723, 914, 315, 220, 21, 15, 16, 22, 19, 374, 330, 21, 15, 16, 22, 19, 22956, 36936, 804, 25, 220, 21, 15, 16, 22, 19, 11, 220, 16, 22, 19, 21, 11, 220, 16, 22, 19, 21, 15, 11, 220, 22, 19, 21, 15, 16, 11, 220, 19, 21, 15, 16, 22, 198, 48, 7, 21, 15, 16, 22, 19, 8, 284, 1308, 7, 21, 15, 16, 22, 19, 11, 220, 16, 22, 19, 21, 11, 220, 16, 22, 19, 21, 15, 11, 220, 22, 19, 21, 15, 16, 11, 220, 19, 21, 15, 16, 22, 8, 284, 220, 16, 22, 19, 21, 271, 59, 79075, 90, 16, 22, 19, 21, 92, 151645], "meta_info": {"id": "c8d834e073994760bd34e9b3abeabf93", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.571446418762207, "response_sent_to_client_ts": 1773877235.0454457}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "67799", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\n9 is not prime: 9\n7 is prime: 7^2 = 49\n6 is not prime: 6\n7 is prime: 7^2 = 49\n9 is not prime: 9\nP(97679) = 9 + 49 + 6 + 49 + 9 = 122\n\n\\boxed{122}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 24, 374, 537, 10250, 25, 220, 24, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 47, 7, 24, 22, 21, 22, 24, 8, 284, 220, 24, 488, 220, 19, 24, 488, 220, 21, 488, 220, 19, 24, 488, 220, 24, 284, 220, 16, 17, 17, 271, 59, 79075, 90, 16, 17, 17, 92, 151645], "meta_info": {"id": "d069496056eb4f0c8fa433dfc7d03531", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 114, "cached_tokens": 185, "cached_tokens_details": null, "e2e_latency": 2.5498902797698975, "response_sent_to_client_ts": 1773877235.0239089}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "30", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(85638)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 85638 are [8, 5, 6, 3, 8].\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nA(85638) = 36 + 15 + 21 + 6 + 36 = 114\n\n\\boxed{114}", "output_ids": [785, 18509, 315, 220, 23, 20, 21, 18, 23, 525, 508, 23, 11, 220, 20, 11, 220, 21, 11, 220, 18, 11, 220, 23, 26126, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 32, 7, 23, 20, 21, 18, 23, 8, 284, 220, 18, 21, 488, 220, 16, 20, 488, 220, 17, 16, 488, 220, 21, 488, 220, 18, 21, 284, 220, 16, 16, 19, 271, 59, 79075, 90, 16, 16, 19, 92, 151645], "meta_info": {"id": "17e223e9aec3431a9d3120b7cdd0fb01", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 2.9991402626037598, "response_sent_to_client_ts": 1773877235.4731748}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function r. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 0\n\nInput: 41\nOutput: 0\n\nInput: 45\nOutput: 0\n\nInput: 87397\nOutput: 0\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 0\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 0\n\nQuestion:\nWhat is the output of r(6599)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 6599 are [6, 5, 9, 9].\nT(6) = 6*7/2 = 21\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nR(6599) = 21 + 15 + 45 + 45 = 126\n\n\\boxed{126}", "output_ids": [785, 18509, 315, 220, 21, 20, 24, 24, 525, 508, 21, 11, 220, 20, 11, 220, 24, 11, 220, 24, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 49, 7, 21, 20, 24, 24, 8, 284, 220, 17, 16, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 19, 20, 284, 220, 16, 17, 21, 271, 59, 79075, 90, 16, 17, 21, 92, 151645], "meta_info": {"id": "8d02e6b27b574448bd7c2ad8b1c7dcb7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 191, "weight_version": "default", "total_retractions": 0, "completion_tokens": 124, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.6930887699127197, "response_sent_to_client_ts": 1773877235.1670682}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "88552", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function q. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 832\n\nInput: 41\nOutput: 41\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 98773\n\nInput: 242\nOutput: 422\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9953\n\nInput: 21395\nOutput: 95321\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of q(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 52858 is \"52858\".\nRotations: 52858, 28585, 85852, 58528, 85285\nQ(52858) = min(52858, 28585, 85852, 58528, 85285) = 28585\n\n\\boxed{28585}", "output_ids": [785, 15723, 914, 315, 220, 20, 17, 23, 20, 23, 374, 330, 20, 17, 23, 20, 23, 22956, 36936, 804, 25, 220, 20, 17, 23, 20, 23, 11, 220, 17, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 17, 11, 220, 20, 23, 20, 17, 23, 11, 220, 23, 20, 17, 23, 20, 198, 48, 7, 20, 17, 23, 20, 23, 8, 284, 1308, 7, 20, 17, 23, 20, 23, 11, 220, 17, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 17, 11, 220, 20, 23, 20, 17, 23, 11, 220, 23, 20, 17, 23, 20, 8, 284, 220, 17, 23, 20, 23, 20, 271, 59, 79075, 90, 17, 23, 20, 23, 20, 92, 151645], "meta_info": {"id": "e7d4cbbea0ee43989366eccb22d77222", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 188, "cached_tokens_details": null, "e2e_latency": 2.619011640548706, "response_sent_to_client_ts": 1773877235.093014}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(54046)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 54046 are [5, 4, 0, 4, 6].\nAlternating sum of squares = 5^2 - 4^2 + 0^2 - 4^2 + 6^2 = 25 - 16 + 0 - 16 + 36 = 29\nF(54046) = |29| = 29\n\n\\boxed{29}", "output_ids": [785, 18509, 315, 220, 20, 19, 15, 19, 21, 525, 508, 20, 11, 220, 19, 11, 220, 15, 11, 220, 19, 11, 220, 21, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 19, 61, 17, 488, 220, 15, 61, 17, 481, 220, 19, 61, 17, 488, 220, 21, 61, 17, 284, 220, 17, 20, 481, 220, 16, 21, 488, 220, 15, 481, 220, 16, 21, 488, 220, 18, 21, 284, 220, 17, 24, 198, 37, 7, 20, 19, 15, 19, 21, 8, 284, 760, 17, 24, 91, 284, 220, 17, 24, 271, 59, 79075, 90, 17, 24, 92, 151645], "meta_info": {"id": "18fd1ce5fd7e485a93a2f85e14345171", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.335726499557495, "response_sent_to_client_ts": 1773877234.8097303}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nM(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n\\boxed{44}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 44, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 16, 20, 488, 220, 21, 488, 220, 17, 16, 284, 220, 19, 19, 271, 59, 79075, 90, 19, 19, 92, 151645], "meta_info": {"id": "e9ff5315acd44311937d9f34eb62cf8a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9142086505889893, "response_sent_to_client_ts": 1773877235.3882089}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "8", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function j. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 11\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 15\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 14\n\nInput: 21395\nOutput: 7\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 11\n\nQuestion:\nWhat is the output of j(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nJ(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 41, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "e1eae5d83fec4baa80de48ab472bb52a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 196, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.944753646850586, "response_sent_to_client_ts": 1773877235.4188278}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\n6 is not prime: 6\n0 is not prime: 0\n1 is not prime: 1\n7 is prime: 7^2 = 49\n4 is not prime: 4\nE(60174) = 6 + 0 + 1 + 49 + 4 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 36, 7, 21, 15, 16, 22, 19, 8, 284, 220, 21, 488, 220, 15, 488, 220, 16, 488, 220, 19, 24, 488, 220, 19, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "bbed8ac9e4694c13ad91f62e39d265ce", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 106, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.378411293029785, "response_sent_to_client_ts": 1773877234.8523953}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "85825", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 52858 is \"52858\".\nRotations: 52858, 28585, 85852, 58528, 85285\nI(52858) = min(52858, 28585, 85852, 58528, 85285) = 28585\n\n\\boxed{28585}", "output_ids": [785, 15723, 914, 315, 220, 20, 17, 23, 20, 23, 374, 330, 20, 17, 23, 20, 23, 22956, 36936, 804, 25, 220, 20, 17, 23, 20, 23, 11, 220, 17, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 17, 11, 220, 20, 23, 20, 17, 23, 11, 220, 23, 20, 17, 23, 20, 198, 40, 7, 20, 17, 23, 20, 23, 8, 284, 1308, 7, 20, 17, 23, 20, 23, 11, 220, 17, 23, 20, 23, 20, 11, 220, 23, 20, 23, 20, 17, 11, 220, 20, 23, 20, 17, 23, 11, 220, 23, 20, 17, 23, 20, 8, 284, 220, 17, 23, 20, 23, 20, 271, 59, 79075, 90, 17, 23, 20, 23, 20, 92, 151645], "meta_info": {"id": "122e86b77c454a2e8a58f0f2c60ae0dc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 188, "cached_tokens_details": null, "e2e_latency": 2.619025707244873, "response_sent_to_client_ts": 1773877235.0930235}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "28", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n5 is prime: 5^2 = 25\n4 is not prime: 4\nT(72154) = 49 + 4 + 1 + 25 + 4 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 51, 7, 22, 17, 16, 20, 19, 8, 284, 220, 19, 24, 488, 220, 19, 488, 220, 16, 488, 220, 17, 20, 488, 220, 19, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "47e3e3951a584b9d8b6c68a68b8475af", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.5744714736938477, "response_sent_to_client_ts": 1773877235.0484905}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "98", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(2329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 2329 are [2, 3, 2, 9].\nT(2) = 2*3/2 = 3\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nO(2329) = 3 + 6 + 3 + 45 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 17, 18, 17, 24, 525, 508, 17, 11, 220, 18, 11, 220, 17, 11, 220, 24, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 46, 7, 17, 18, 17, 24, 8, 284, 220, 18, 488, 220, 21, 488, 220, 18, 488, 220, 19, 20, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "619279cd917b41128fc86c2221eed21f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 203, "weight_version": "default", "total_retractions": 0, "completion_tokens": 115, "cached_tokens": 177, "cached_tokens_details": null, "e2e_latency": 2.5714609622955322, "response_sent_to_client_ts": 1773877235.0454562}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nN(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 45, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "8f67e00a3ea04d06b51466edee92e0e8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9447622299194336, "response_sent_to_client_ts": 1773877235.418834}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "73", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function o. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 77\n\nInput: 41\nOutput: 17\n\nInput: 45\nOutput: 41\n\nInput: 87397\nOutput: 252\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 196\n\nInput: 21395\nOutput: 120\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 170\n\nQuestion:\nWhat is the output of o(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nO(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 46, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "5c214ffbf94f40b5b2ad2aa0db497f5b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 204, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 178, "cached_tokens_details": null, "e2e_latency": 2.944769859313965, "response_sent_to_client_ts": 1773877235.4188392}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(11536)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 11536 are [1, 1, 5, 3, 6].\n1 is not prime: 1\n1 is not prime: 1\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n6 is not prime: 6\nE(11536) = 1 + 1 + 25 + 9 + 6 = 42\n\n\\boxed{42}", "output_ids": [785, 18509, 315, 220, 16, 16, 20, 18, 21, 525, 508, 16, 11, 220, 16, 11, 220, 20, 11, 220, 18, 11, 220, 21, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 36, 7, 16, 16, 20, 18, 21, 8, 284, 220, 16, 488, 220, 16, 488, 220, 17, 20, 488, 220, 24, 488, 220, 21, 284, 220, 19, 17, 271, 59, 79075, 90, 19, 17, 92, 151645], "meta_info": {"id": "651ccb7233c44f3cac60cacc337a806a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 110, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.4633140563964844, "response_sent_to_client_ts": 1773877234.9372985}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nL(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 43, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "1aba21cded5147e58bdce84cb517858c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.944777488708496, "response_sent_to_client_ts": 1773877235.418845}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "38", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(97679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 97679 are [9, 7, 6, 7, 9].\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nA(97679) = 45 + 28 + 21 + 28 + 45 = 167\n\n\\boxed{167}", "output_ids": [785, 18509, 315, 220, 24, 22, 21, 22, 24, 525, 508, 24, 11, 220, 22, 11, 220, 21, 11, 220, 22, 11, 220, 24, 26126, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 32, 7, 24, 22, 21, 22, 24, 8, 284, 220, 19, 20, 488, 220, 17, 23, 488, 220, 17, 16, 488, 220, 17, 23, 488, 220, 19, 20, 284, 220, 16, 21, 22, 271, 59, 79075, 90, 16, 21, 22, 92, 151645], "meta_info": {"id": "04b6f9da80374bbea2f369153e9264d8", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 149, "cached_tokens": 170, "cached_tokens_details": null, "e2e_latency": 3.0518951416015625, "response_sent_to_client_ts": 1773877235.5258808}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nM(58598) = 15 + 36 + 15 + 45 + 36 = 147\n\n\\boxed{147}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 44, 7, 20, 23, 20, 24, 23, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 16, 20, 488, 220, 19, 20, 488, 220, 18, 21, 284, 220, 16, 19, 22, 271, 59, 79075, 90, 16, 19, 22, 92, 151645], "meta_info": {"id": "1004b440f9254655b810a3a2b5bf8a23", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 148, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 3.038684129714966, "response_sent_to_client_ts": 1773877235.5126746}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function k. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 1\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 0\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of k(58598)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58598 are [5, 8, 5, 9, 8].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n5 is prime: 5^2 = 25\n9 is not prime: 9\n8 is not prime: 8\nK(58598) = 25 + 8 + 25 + 9 + 8 = 65\n\n\\boxed{65}", "output_ids": [785, 18509, 315, 220, 20, 23, 20, 24, 23, 525, 508, 20, 11, 220, 23, 11, 220, 20, 11, 220, 24, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 24, 374, 537, 10250, 25, 220, 24, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 42, 7, 20, 23, 20, 24, 23, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 17, 20, 488, 220, 24, 488, 220, 23, 284, 220, 21, 20, 271, 59, 79075, 90, 21, 20, 92, 151645], "meta_info": {"id": "9d7d20e57aa842de95b51a5e6a22742b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.506493330001831, "response_sent_to_client_ts": 1773877234.9804971}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "0", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\n1 is not prime: 1\n0 is not prime: 0\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\nE(10332) = 1 + 0 + 9 + 9 + 4 = 23\n\n\\boxed{23}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 16, 374, 537, 10250, 25, 220, 16, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 36, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 24, 488, 220, 24, 488, 220, 19, 284, 220, 17, 18, 271, 59, 79075, 90, 17, 18, 92, 151645], "meta_info": {"id": "1695eb31915e470884cfb3da4a6aa88c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 112, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.5065016746520996, "response_sent_to_client_ts": 1773877234.9805043}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(72154)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 72154 are [7, 2, 1, 5, 4].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n1 is not prime: 1\n5 is prime: 5^2 = 25\n4 is not prime: 4\nE(72154) = 49 + 4 + 1 + 25 + 4 = 83\n\n\\boxed{83}", "output_ids": [785, 18509, 315, 220, 22, 17, 16, 20, 19, 525, 508, 22, 11, 220, 17, 11, 220, 16, 11, 220, 20, 11, 220, 19, 26126, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 36, 7, 22, 17, 16, 20, 19, 8, 284, 220, 19, 24, 488, 220, 19, 488, 220, 16, 488, 220, 17, 20, 488, 220, 19, 284, 220, 23, 18, 271, 59, 79075, 90, 23, 18, 92, 151645], "meta_info": {"id": "bc37f89a1a8c46ba874fa2dca34898a1", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.574479103088379, "response_sent_to_client_ts": 1773877235.0484958}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1296", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(4696)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 4696 are [4, 6, 9, 6].\nT(4) = 4*5/2 = 10\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nB(4696) = 10 + 21 + 45 + 21 = 97\n\n\\boxed{97}", "output_ids": [785, 18509, 315, 220, 19, 21, 24, 21, 525, 508, 19, 11, 220, 21, 11, 220, 24, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 33, 7, 19, 21, 24, 21, 8, 284, 220, 16, 15, 488, 220, 17, 16, 488, 220, 19, 20, 488, 220, 17, 16, 284, 220, 24, 22, 271, 59, 79075, 90, 24, 22, 92, 151645], "meta_info": {"id": "a4f2b6f44d5f4699b68bf5333cbb56dd", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 205, "weight_version": "default", "total_retractions": 0, "completion_tokens": 121, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 2.6484711170196533, "response_sent_to_client_ts": 1773877235.1224499}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "17", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nA(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 32, 7, 20, 23, 17, 17, 15, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 18, 488, 220, 18, 488, 220, 15, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "53bfacf46314427ea7e9963bff48e3b2", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 139, "cached_tokens": 172, "cached_tokens_details": null, "e2e_latency": 2.914224147796631, "response_sent_to_client_ts": 1773877235.3882196}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "17", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 41426 are [4, 1, 4, 2, 6].\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nA(41426) = 10 + 1 + 10 + 3 + 21 = 45\n\n\\boxed{45}", "output_ids": [785, 18509, 315, 220, 19, 16, 19, 17, 21, 525, 508, 19, 11, 220, 16, 11, 220, 19, 11, 220, 17, 11, 220, 21, 26126, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 32, 7, 19, 16, 19, 17, 21, 8, 284, 220, 16, 15, 488, 220, 16, 488, 220, 16, 15, 488, 220, 18, 488, 220, 17, 16, 284, 220, 19, 20, 271, 59, 79075, 90, 19, 20, 92, 151645], "meta_info": {"id": "b5f9e7ef667243f58086b484e3dbd92f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.944786310195923, "response_sent_to_client_ts": 1773877235.4188507}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "62414", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function i. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 823\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 54\n\nInput: 87397\nOutput: 79378\n\nInput: 242\nOutput: 242\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 5399\n\nInput: 21395\nOutput: 59312\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 9762\n\nQuestion:\nWhat is the output of i(41426)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digit string of 41426 is \"41426\".\nRotations: 41426, 14264, 42641, 26414, 64142\nI(41426) = min(41426, 14264, 42641, 26414, 64142) = 14264\n\n\\boxed{14264}", "output_ids": [785, 15723, 914, 315, 220, 19, 16, 19, 17, 21, 374, 330, 19, 16, 19, 17, 21, 22956, 36936, 804, 25, 220, 19, 16, 19, 17, 21, 11, 220, 16, 19, 17, 21, 19, 11, 220, 19, 17, 21, 19, 16, 11, 220, 17, 21, 19, 16, 19, 11, 220, 21, 19, 16, 19, 17, 198, 40, 7, 19, 16, 19, 17, 21, 8, 284, 1308, 7, 19, 16, 19, 17, 21, 11, 220, 16, 19, 17, 21, 19, 11, 220, 19, 17, 21, 19, 16, 11, 220, 17, 21, 19, 16, 19, 11, 220, 21, 19, 16, 19, 17, 8, 284, 220, 16, 19, 17, 21, 19, 271, 59, 79075, 90, 16, 19, 17, 21, 19, 92, 151645], "meta_info": {"id": "0fe949660db8405ba4f7e16a7e7fbbb6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 119, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.6190335750579834, "response_sent_to_client_ts": 1773877235.0930297}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function m. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of m(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nM(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 44, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "a9eac80dafd549068777e9e00bfec53f", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.999159336090088, "response_sent_to_client_ts": 1773877235.473188}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "18", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function b. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 48\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 10584\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 1215\n\nInput: 21395\nOutput: 270\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 756\n\nQuestion:\nWhat is the output of b(10332)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 10332 are [1, 0, 3, 3, 2].\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nB(10332) = 1 + 0 + 6 + 6 + 3 = 16\n\n\\boxed{16}", "output_ids": [785, 18509, 315, 220, 16, 15, 18, 18, 17, 525, 508, 16, 11, 220, 15, 11, 220, 18, 11, 220, 18, 11, 220, 17, 26126, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 33, 7, 16, 15, 18, 18, 17, 8, 284, 220, 16, 488, 220, 15, 488, 220, 21, 488, 220, 21, 488, 220, 18, 284, 220, 16, 21, 271, 59, 79075, 90, 16, 21, 92, 151645], "meta_info": {"id": "b5c409379ae242d4a8753e0be9fa8822", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 206, "weight_version": "default", "total_retractions": 0, "completion_tokens": 135, "cached_tokens": 180, "cached_tokens_details": null, "e2e_latency": 2.8551974296569824, "response_sent_to_client_ts": 1773877235.3291879}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "4", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function l. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 1\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 4\n\nInput: 242\nOutput: 0\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 4\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of l(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nL(58733) = 15 + 36 + 28 + 6 + 6 = 91\n\n\\boxed{91}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 51, 7, 20, 8, 284, 220, 20, 9, 21, 14, 17, 284, 220, 16, 20, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 43, 7, 20, 23, 22, 18, 18, 8, 284, 220, 16, 20, 488, 220, 18, 21, 488, 220, 17, 23, 488, 220, 21, 488, 220, 21, 284, 220, 24, 16, 271, 59, 79075, 90, 24, 16, 92, 151645], "meta_info": {"id": "92a5177c1f9f40cd80d5034ad5e11de4", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.944794178009033, "response_sent_to_client_ts": 1773877235.4188561}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "40", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function s. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 26\n\nInput: 41\nOutput: 10\n\nInput: 45\nOutput: 18\n\nInput: 87397\nOutput: 68\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 2\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 40\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 48\n\nQuestion:\nWhat is the output of s(65333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 65333 are [6, 5, 3, 3, 3].\n6 is not prime: 6\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nS(65333) = 6 + 25 + 9 + 9 + 9 = 58\n\n\\boxed{58}", "output_ids": [785, 18509, 315, 220, 21, 20, 18, 18, 18, 525, 508, 21, 11, 220, 20, 11, 220, 18, 11, 220, 18, 11, 220, 18, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 50, 7, 21, 20, 18, 18, 18, 8, 284, 220, 21, 488, 220, 17, 20, 488, 220, 24, 488, 220, 24, 488, 220, 24, 284, 220, 20, 23, 271, 59, 79075, 90, 20, 23, 92, 151645], "meta_info": {"id": "1df3e2a6e03541219ccf957daf1866fc", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 200, "weight_version": "default", "total_retractions": 0, "completion_tokens": 118, "cached_tokens": 175, "cached_tokens_details": null, "e2e_latency": 2.60355281829834, "response_sent_to_client_ts": 1773877235.0775313}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function t. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 24\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 20\n\nInput: 87397\nOutput: 56\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 45\n\nInput: 21395\nOutput: 10\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 18\n\nQuestion:\nWhat is the output of t(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\n3 is prime: 3^2 = 9\n0 is not prime: 0\n8 is not prime: 8\n0 is not prime: 0\n1 is not prime: 1\nT(30801) = 9 + 0 + 8 + 0 + 1 = 18\n\n\\boxed{18}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 15, 374, 537, 10250, 25, 220, 15, 198, 16, 374, 537, 10250, 25, 220, 16, 198, 51, 7, 18, 15, 23, 15, 16, 8, 284, 220, 24, 488, 220, 15, 488, 220, 23, 488, 220, 15, 488, 220, 16, 284, 220, 16, 23, 271, 59, 79075, 90, 16, 23, 92, 151645], "meta_info": {"id": "32035aa97bac413cb5e4eb403b41b024", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 198, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.335740089416504, "response_sent_to_client_ts": 1773877234.8097396}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "3", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nN(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 45, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "649f3b2a36d94ef5b397b452da5de44b", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.8847744464874268, "response_sent_to_client_ts": 1773877235.35877}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nC(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 34, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "91107178f3594ae69f646f64a8254cb6", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.9991683959960938, "response_sent_to_client_ts": 1773877235.4731948}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "44466", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\n6 is not prime: 6\n6 is not prime: 6\n4 is not prime: 4\n4 is not prime: 4\n4 is not prime: 4\nP(66444) = 6 + 6 + 4 + 4 + 4 = 24\n\n\\boxed{24}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 21, 374, 537, 10250, 25, 220, 21, 198, 21, 374, 537, 10250, 25, 220, 21, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 19, 374, 537, 10250, 25, 220, 19, 198, 47, 7, 21, 21, 19, 19, 19, 8, 284, 220, 21, 488, 220, 21, 488, 220, 19, 488, 220, 19, 488, 220, 19, 284, 220, 17, 19, 271, 59, 79075, 90, 17, 19, 92, 151645], "meta_info": {"id": "537191c5fe5942ecac96d4f28b465303", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 100, "cached_tokens": 186, "cached_tokens_details": null, "e2e_latency": 2.2523140907287598, "response_sent_to_client_ts": 1773877234.7268524}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(30801)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 30801 are [3, 0, 8, 0, 1].\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nC(30801) = 6 + 0 + 36 + 0 + 1 = 43\n\n\\boxed{43}", "output_ids": [785, 18509, 315, 220, 18, 15, 23, 15, 16, 525, 508, 18, 11, 220, 15, 11, 220, 23, 11, 220, 15, 11, 220, 16, 26126, 51, 7, 18, 8, 284, 220, 18, 9, 19, 14, 17, 284, 220, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 23, 8, 284, 220, 23, 9, 24, 14, 17, 284, 220, 18, 21, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 34, 7, 18, 15, 23, 15, 16, 8, 284, 220, 21, 488, 220, 15, 488, 220, 18, 21, 488, 220, 15, 488, 220, 16, 284, 220, 19, 18, 271, 59, 79075, 90, 19, 18, 92, 151645], "meta_info": {"id": "373eee6f833e4f729a7d0dbcca5d43c7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 137, "cached_tokens": 165, "cached_tokens_details": null, "e2e_latency": 2.8847906589508057, "response_sent_to_client_ts": 1773877235.35878}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "2", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function e. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 2\n\nInput: 41\nOutput: 1\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 3\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3\n\nInput: 21395\nOutput: 1\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of e(52858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 52858 are [5, 2, 8, 5, 8].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n5 is prime: 5^2 = 25\n8 is not prime: 8\nE(52858) = 25 + 4 + 8 + 25 + 8 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 20, 17, 23, 20, 23, 525, 508, 20, 11, 220, 17, 11, 220, 23, 11, 220, 20, 11, 220, 23, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 17, 374, 10250, 25, 220, 17, 61, 17, 284, 220, 19, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 36, 7, 20, 17, 23, 20, 23, 8, 284, 220, 17, 20, 488, 220, 19, 488, 220, 23, 488, 220, 17, 20, 488, 220, 23, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "9e9c95ad88964e0fa8f0653120ae58ae", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 116, "cached_tokens": 168, "cached_tokens_details": null, "e2e_latency": 2.5744869709014893, "response_sent_to_client_ts": 1773877235.0485013}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "1", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(15559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 15559 are [1, 5, 5, 5, 9].\nAlternating sum of squares = 1^2 - 5^2 + 5^2 - 5^2 + 9^2 = 1 - 25 + 25 - 25 + 81 = 57\nF(15559) = |57| = 57\n\n\\boxed{57}", "output_ids": [785, 18509, 315, 220, 16, 20, 20, 20, 24, 525, 508, 16, 11, 220, 20, 11, 220, 20, 11, 220, 20, 11, 220, 24, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 16, 61, 17, 481, 220, 20, 61, 17, 488, 220, 20, 61, 17, 481, 220, 20, 61, 17, 488, 220, 24, 61, 17, 284, 220, 16, 481, 220, 17, 20, 488, 220, 17, 20, 481, 220, 17, 20, 488, 220, 23, 16, 284, 220, 20, 22, 198, 37, 7, 16, 20, 20, 20, 24, 8, 284, 760, 20, 22, 91, 284, 220, 20, 22, 271, 59, 79075, 90, 20, 22, 92, 151645], "meta_info": {"id": "925389bb682c4e7384595a69147e6fec", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 104, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.3357481956481934, "response_sent_to_client_ts": 1773877234.8097453}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function f. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 4\n\nInput: 45\nOutput: 4\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 2\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 9\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2\n\nQuestion:\nWhat is the output of f(58220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58220 are [5, 8, 2, 2, 0].\nAlternating sum of squares = 5^2 - 8^2 + 2^2 - 2^2 + 0^2 = 25 - 64 + 4 - 4 + 0 = -39\nF(58220) = |-39| = 39\n\n\\boxed{39}", "output_ids": [785, 18509, 315, 220, 20, 23, 17, 17, 15, 525, 508, 20, 11, 220, 23, 11, 220, 17, 11, 220, 17, 11, 220, 15, 26126, 34543, 1095, 2629, 315, 31340, 284, 220, 20, 61, 17, 481, 220, 23, 61, 17, 488, 220, 17, 61, 17, 481, 220, 17, 61, 17, 488, 220, 15, 61, 17, 284, 220, 17, 20, 481, 220, 21, 19, 488, 220, 19, 481, 220, 19, 488, 220, 15, 284, 481, 18, 24, 198, 37, 7, 20, 23, 17, 17, 15, 8, 284, 44561, 18, 24, 91, 284, 220, 18, 24, 271, 59, 79075, 90, 18, 24, 92, 151645], "meta_info": {"id": "ba7b9bb77a104df1a1a17f5ae70d215a", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 102, "cached_tokens": 167, "cached_tokens_details": null, "e2e_latency": 2.2924413681030273, "response_sent_to_client_ts": 1773877234.7664459}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "33578", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function p. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 238\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 37789\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 12359\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of p(58733)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 58733 are [5, 8, 7, 3, 3].\n5 is prime: 5^2 = 25\n8 is not prime: 8\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nP(58733) = 25 + 8 + 49 + 9 + 9 = 100\n\n\\boxed{100}", "output_ids": [785, 18509, 315, 220, 20, 23, 22, 18, 18, 525, 508, 20, 11, 220, 23, 11, 220, 22, 11, 220, 18, 11, 220, 18, 26126, 20, 374, 10250, 25, 220, 20, 61, 17, 284, 220, 17, 20, 198, 23, 374, 537, 10250, 25, 220, 23, 198, 22, 374, 10250, 25, 220, 22, 61, 17, 284, 220, 19, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 18, 374, 10250, 25, 220, 18, 61, 17, 284, 220, 24, 198, 47, 7, 20, 23, 22, 18, 18, 8, 284, 220, 17, 20, 488, 220, 23, 488, 220, 19, 24, 488, 220, 24, 488, 220, 24, 284, 220, 16, 15, 15, 271, 59, 79075, 90, 16, 15, 15, 92, 151645], "meta_info": {"id": "3aa15694376a41bf98962c730af7cda7", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 212, "weight_version": "default", "total_retractions": 0, "completion_tokens": 122, "cached_tokens": 187, "cached_tokens_details": null, "e2e_latency": 2.6634409427642822, "response_sent_to_client_ts": 1773877235.13742}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "18", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function a. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 13\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 34\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 26\n\nInput: 21395\nOutput: 20\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nQuestion:\nWhat is the output of a(60174)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 60174 are [6, 0, 1, 7, 4].\nT(6) = 6*7/2 = 21\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nA(60174) = 21 + 0 + 1 + 28 + 10 = 60\n\n\\boxed{60}", "output_ids": [785, 18509, 315, 220, 21, 15, 16, 22, 19, 525, 508, 21, 11, 220, 15, 11, 220, 16, 11, 220, 22, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 22, 8, 284, 220, 22, 9, 23, 14, 17, 284, 220, 17, 23, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 32, 7, 21, 15, 16, 22, 19, 8, 284, 220, 17, 16, 488, 220, 15, 488, 220, 16, 488, 220, 17, 23, 488, 220, 16, 15, 284, 220, 21, 15, 271, 59, 79075, 90, 21, 15, 92, 151645], "meta_info": {"id": "0ade219a321a4370af15a11a712cb613", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 197, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 171, "cached_tokens_details": null, "e2e_latency": 2.9448018074035645, "response_sent_to_client_ts": 1773877235.4188619}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "5", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function c. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 3\n\nInput: 41\nOutput: 2\n\nInput: 45\nOutput: 2\n\nInput: 87397\nOutput: 5\n\nInput: 242\nOutput: 3\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 4\n\nInput: 21395\nOutput: 5\n\nInput: 2\nOutput: 1\n\nInput: 2679\nOutput: 4\n\nQuestion:\nWhat is the output of c(29190)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 29190 are [2, 9, 1, 9, 0].\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nC(29190) = 3 + 45 + 1 + 45 + 0 = 94\n\n\\boxed{94}", "output_ids": [785, 18509, 315, 220, 17, 24, 16, 24, 15, 525, 508, 17, 11, 220, 24, 11, 220, 16, 11, 220, 24, 11, 220, 15, 26126, 51, 7, 17, 8, 284, 220, 17, 9, 18, 14, 17, 284, 220, 18, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 16, 8, 284, 220, 16, 9, 17, 14, 17, 284, 220, 16, 198, 51, 7, 24, 8, 284, 220, 24, 9, 16, 15, 14, 17, 284, 220, 19, 20, 198, 51, 7, 15, 8, 284, 220, 15, 9, 16, 14, 17, 284, 220, 15, 198, 34, 7, 17, 24, 16, 24, 15, 8, 284, 220, 18, 488, 220, 19, 20, 488, 220, 16, 488, 220, 19, 20, 488, 220, 15, 284, 220, 24, 19, 271, 59, 79075, 90, 24, 19, 92, 151645], "meta_info": {"id": "f365a3aa5338468d959c3aaeceff9d3c", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 141, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.944809913635254, "response_sent_to_client_ts": 1773877235.4188664}}} +{"prompt": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "ground_truth_answer": "6", "instruction": "Based on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "chat_prompt": "<|im_start|>user\nBased on the input\u2013output examples below, infer the rule implemented by function n. Then apply the same rule to determine the output for the given input.\n\nExamples:\nInput: 328\nOutput: 4\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 7\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 8\n\nInput: 21395\nOutput: 2\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 6\n\nQuestion:\nWhat is the output of n(66444)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end|>\n<|im_start|>assistant\n", "output": {"text": "The digits of 66444 are [6, 6, 4, 4, 4].\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nN(66444) = 21 + 21 + 10 + 10 + 10 = 72\n\n\\boxed{72}", "output_ids": [785, 18509, 315, 220, 21, 21, 19, 19, 19, 525, 508, 21, 11, 220, 21, 11, 220, 19, 11, 220, 19, 11, 220, 19, 26126, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 21, 8, 284, 220, 21, 9, 22, 14, 17, 284, 220, 17, 16, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 51, 7, 19, 8, 284, 220, 19, 9, 20, 14, 17, 284, 220, 16, 15, 198, 45, 7, 21, 21, 19, 19, 19, 8, 284, 220, 17, 16, 488, 220, 17, 16, 488, 220, 16, 15, 488, 220, 16, 15, 488, 220, 16, 15, 284, 220, 22, 17, 271, 59, 79075, 90, 22, 17, 92, 151645], "meta_info": {"id": "c171e8bd8b114ca397a3510988eaa241", "finish_reason": {"type": "stop", "matched": 151645}, "prompt_tokens": 192, "weight_version": "default", "total_retractions": 0, "completion_tokens": 145, "cached_tokens": 166, "cached_tokens_details": null, "e2e_latency": 2.999178409576416, "response_sent_to_client_ts": 1773877235.4732018}}} diff --git a/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/eval_results.csv b/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/eval_results.csv new file mode 100644 index 0000000000000000000000000000000000000000..78ec5bc805876878c049ca7e65fe03c4e07d44af --- /dev/null +++ b/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/eval_results.csv @@ -0,0 +1,2 @@ +category,filename,total,correct,accuracy,format_found,format_accuracy,errors_count +math_operations,balanced_test_alpaca_results,500,3,0.60,500,100.00,497 diff --git a/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/eval_summary.json b/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/eval_summary.json new file mode 100644 index 0000000000000000000000000000000000000000..ad43b7bb6e4adf45ff16178fb96a9cb62393904a --- /dev/null +++ b/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/eval_summary.json @@ -0,0 +1,133 @@ +{ + "overall": { + "total": 500, + "correct": 3, + "accuracy": 0.6, + "format_found": 500, + "format_accuracy": 100.0 + }, + "per_operation": { + "a": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "b": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "c": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "d": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "e": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "f": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "g": { + "total": 25, + "correct": 1, + "accuracy": 4.0, + "format_found": 25 + }, + "h": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "i": { + "total": 25, + "correct": 1, + "accuracy": 4.0, + "format_found": 25 + }, + "j": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "k": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "l": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "m": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "n": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "o": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "p": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "q": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "r": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "s": { + "total": 25, + "correct": 0, + "accuracy": 0.0, + "format_found": 25 + }, + "t": { + "total": 25, + "correct": 1, + "accuracy": 4.0, + "format_found": 25 + } + }, + "n_errors": 497, + "results_file": "/home/jiaruil5/math_rl/mix_teachers/r3lit_rl/mix_teachers/checkpoints/math_operations/primitive_atomic_full_sft_50k_lr1e4_t20260308/eval_results_easy_ops/balanced_test_alpaca_results.jsonl" +} \ No newline at end of file