diff --git "a/data/math_operations/compositional_sft_n_steps_2/test_alpaca.jsonl" "b/data/math_operations/compositional_sft_n_steps_2/test_alpaca.jsonl"
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@@ -1,200 +0,0 @@
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(6599) + 97645)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6599 are [6, 5, 9, 9].\nSum of digits = 6 + 5 + 9 + 9 = 29\nMax digit = 9\nA(6599) = 29 * 9 = 261\n\n261 + 97645 = 97906\n\nThe digits of 97906 are [9, 7, 9, 0, 6].\nRunning max: 9, 9, 9, 9, 9\nF(97906) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(F(66444) + 80255)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 66444 are [6, 6, 4, 4, 4].\nRunning max: 6, 6, 6, 6, 6\nF(66444) = 6 + 6 + 6 + 6 + 6 = 30\n\n30 + 80255 = 80285\n\nThe digits of 80285 are [8, 0, 2, 8, 5].\nMin digit = 0\n(8 - 0)^2 = 64\n(0 - 0)^2 = 0\n(2 - 0)^2 = 4\n(8 - 0)^2 = 64\n(5 - 0)^2 = 25\nB(80285) = 64 + 0 + 4 + 64 + 25 = 157\n\n\\boxed{157}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(D(29190) + 49234)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\n23 + 49234 = 49257\n\nThe digits of 49257 are [4, 9, 2, 5, 7].\nSum of digits = 4 + 9 + 2 + 5 + 7 = 27\nMax digit = 9\nA(49257) = 27 * 9 = 243\n\n\\boxed{243}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(72154) + 54018)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\n83 + 54018 = 54101\n\nThe digits of 54101 are [5, 4, 1, 0, 1].\nReversed: [1, 0, 1, 4, 5]\n5*1 + 4*0 + 1*1 + 0*4 + 1*5 = 5 + 0 + 1 + 0 + 5 = 11\nE(54101) = 11\n\n\\boxed{11}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(49628) + 10261)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nD(49628) = 4 + 9 + 6 + 4 + 8 = 31\n\n31 + 10261 = 10292\n\nThe digits of 10292 are [1, 0, 2, 9, 2].\nReversed: [2, 9, 2, 0, 1]\n1*2 + 0*9 + 2*2 + 9*0 + 2*1 = 2 + 0 + 4 + 0 + 2 = 8\nE(10292) = 8\n\n\\boxed{8}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(52858) + 12339)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 52858 are [5, 2, 8, 5, 8].\nRunning max: 5, 5, 8, 8, 8\nF(52858) = 5 + 5 + 8 + 8 + 8 = 34\n\n34 + 12339 = 12373\n\nThe digits of 12373 are [1, 2, 3, 7, 3].\nAlternating sum of squares = 1^2 - 2^2 + 3^2 - 7^2 + 3^2 = 1 - 4 + 9 - 49 + 9 = -34\nC(12373) = |-34| = 34\n\n\\boxed{34}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(30801) + 54857)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nC(30801) = |74| = 74\n\n74 + 54857 = 54931\n\nThe digits of 54931 are [5, 4, 9, 3, 1].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(1) = 1*2/2 = 1\nG(54931) = 15 + 10 + 45 + 6 + 1 = 77\n\n\\boxed{77}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(D(10332) + 35115)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nD(10332) = 1 + 0 + 9 + 9 + 4 = 23\n\n23 + 35115 = 35138\n\nThe digits of 35138 are [3, 5, 1, 3, 8].\nSum of digits = 3 + 5 + 1 + 3 + 8 = 20\nMax digit = 8\nA(35138) = 20 * 8 = 160\n\n\\boxed{160}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(B(60174) + 77429)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 60174 are [6, 0, 1, 7, 4].\nMin digit = 0\n(6 - 0)^2 = 36\n(0 - 0)^2 = 0\n(1 - 0)^2 = 1\n(7 - 0)^2 = 49\n(4 - 0)^2 = 16\nB(60174) = 36 + 0 + 1 + 49 + 16 = 102\n\n102 + 77429 = 77531\n\nThe digit string of 77531 is \"77531\".\nRotations: 77531, 75317, 53177, 31775, 17753\nH(77531) = min(77531, 75317, 53177, 31775, 17753) = 17753\n\n\\boxed{17753}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(58220) + 13730)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nG(58220) = 15 + 36 + 3 + 3 + 0 = 57\n\n57 + 13730 = 13787\n\nThe digit string of 13787 is \"13787\".\nRotations: 13787, 37871, 78713, 87137, 71378\nH(13787) = min(13787, 37871, 78713, 87137, 71378) = 13787\n\n\\boxed{13787}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(75108) + 20811)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\n83 + 20811 = 20894\n\nThe digits of 20894 are [2, 0, 8, 9, 4].\nReversed: [4, 9, 8, 0, 2]\n2*4 + 0*9 + 8*8 + 9*0 + 4*2 = 8 + 0 + 64 + 0 + 8 = 80\nE(20894) = 80\n\n\\boxed{80}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(58733) + 45756)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 58733 are [5, 8, 7, 3, 3].\nRunning max: 5, 8, 8, 8, 8\nF(58733) = 5 + 8 + 8 + 8 + 8 = 37\n\n37 + 45756 = 45793\n\nThe digits of 45793 are [4, 5, 7, 9, 3].\nAlternating sum of squares = 4^2 - 5^2 + 7^2 - 9^2 + 3^2 = 16 - 25 + 49 - 81 + 9 = -32\nC(45793) = |-32| = 32\n\n\\boxed{32}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(11536) + 75055)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nG(11536) = 1 + 1 + 15 + 6 + 21 = 44\n\n44 + 75055 = 75099\n\nThe digit string of 75099 is \"75099\".\nRotations: 75099, 50997, 9975, 99750, 97509\nH(75099) = min(75099, 50997, 9975, 99750, 97509) = 9975\n\n\\boxed{9975}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(65333) + 8202)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nC(65333) = |20| = 20\n\n20 + 8202 = 8222\n\nThe digits of 8222 are [8, 2, 2, 2].\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nG(8222) = 36 + 3 + 3 + 3 = 45\n\n\\boxed{45}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(D(58598) + 69281)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nD(58598) = 25 + 8 + 25 + 9 + 8 = 75\n\n75 + 69281 = 69356\n\nThe digits of 69356 are [6, 9, 3, 5, 6].\nT(6) = 6*7/2 = 21\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nG(69356) = 21 + 45 + 6 + 15 + 21 = 108\n\n\\boxed{108}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(41426) + 70656)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nC(41426) = |63| = 63\n\n63 + 70656 = 70719\n\nThe digits of 70719 are [7, 0, 7, 1, 9].\nReversed: [9, 1, 7, 0, 7]\n7*9 + 0*1 + 7*7 + 1*0 + 9*7 = 63 + 0 + 49 + 0 + 63 = 175\nE(70719) = 175\n\n\\boxed{175}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(15559) + 25581)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nD(15559) = 1 + 25 + 25 + 25 + 9 = 85\n\n85 + 25581 = 25666\n\nThe digits of 25666 are [2, 5, 6, 6, 6].\nAlternating sum of squares = 2^2 - 5^2 + 6^2 - 6^2 + 6^2 = 4 - 25 + 36 - 36 + 36 = 15\nC(25666) = |15| = 15\n\n\\boxed{15}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(D(97679) + 63451)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nD(97679) = 9 + 49 + 6 + 49 + 9 = 122\n\n122 + 63451 = 63573\n\nThe digits of 63573 are [6, 3, 5, 7, 3].\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(5) = 5*6/2 = 15\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nG(63573) = 21 + 6 + 15 + 28 + 6 = 76\n\n\\boxed{76}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(C(85638) + 60781)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nC(85638) = |130| = 130\n\n130 + 60781 = 60911\n\nThe digits of 60911 are [6, 0, 9, 1, 1].\nRunning max: 6, 6, 9, 9, 9\nF(60911) = 6 + 6 + 9 + 9 + 9 = 39\n\n\\boxed{39}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(2329) + 60047)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nD(2329) = 4 + 9 + 4 + 9 = 26\n\n26 + 60047 = 60073\n\nThe digits of 60073 are [6, 0, 0, 7, 3].\nReversed: [3, 7, 0, 0, 6]\n6*3 + 0*7 + 0*0 + 7*0 + 3*6 = 18 + 0 + 0 + 0 + 18 = 36\nE(60073) = 36\n\n\\boxed{36}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(13453) + 91829)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13453 are [1, 3, 4, 5, 3].\nReversed: [3, 5, 4, 3, 1]\n1*3 + 3*5 + 4*4 + 5*3 + 3*1 = 3 + 15 + 16 + 15 + 3 = 52\nE(13453) = 52\n\n52 + 91829 = 91881\n\nThe digits of 91881 are [9, 1, 8, 8, 1].\n9 is not prime: 9\n1 is not prime: 1\n8 is not prime: 8\n8 is not prime: 8\n1 is not prime: 1\nD(91881) = 9 + 1 + 8 + 8 + 1 = 27\n\n\\boxed{27}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(52879) + 59023)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "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\nG(52879) = 15 + 3 + 36 + 28 + 45 = 127\n\n127 + 59023 = 59150\n\nThe digits of 59150 are [5, 9, 1, 5, 0].\nReversed: [0, 5, 1, 9, 5]\n5*0 + 9*5 + 1*1 + 5*9 + 0*5 = 0 + 45 + 1 + 45 + 0 = 91\nE(59150) = 91\n\n\\boxed{91}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(A(54046) + 81969)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 54046 are [5, 4, 0, 4, 6].\nSum of digits = 5 + 4 + 0 + 4 + 6 = 19\nMax digit = 6\nA(54046) = 19 * 6 = 114\n\n114 + 81969 = 82083\n\nThe digits of 82083 are [8, 2, 0, 8, 3].\nMin digit = 0\n(8 - 0)^2 = 64\n(2 - 0)^2 = 4\n(0 - 0)^2 = 0\n(8 - 0)^2 = 64\n(3 - 0)^2 = 9\nB(82083) = 64 + 4 + 0 + 64 + 9 = 141\n\n\\boxed{141}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(4696) + 65581)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 4696 is \"4696\".\nRotations: 4696, 6964, 9646, 6469\nH(4696) = min(4696, 6964, 9646, 6469) = 4696\n\n4696 + 65581 = 70277\n\nThe digits of 70277 are [7, 0, 2, 7, 7].\n7 is prime: 7^2 = 49\n0 is not prime: 0\n2 is prime: 2^2 = 4\n7 is prime: 7^2 = 49\n7 is prime: 7^2 = 49\nD(70277) = 49 + 0 + 4 + 49 + 49 = 151\n\n\\boxed{151}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(73024) + 23424)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 73024 are [7, 3, 0, 2, 4].\nSum of digits = 7 + 3 + 0 + 2 + 4 = 16\nMax digit = 7\nA(73024) = 16 * 7 = 112\n\n112 + 23424 = 23536\n\nThe digits of 23536 are [2, 3, 5, 3, 6].\nAlternating sum of squares = 2^2 - 3^2 + 5^2 - 3^2 + 6^2 = 4 - 9 + 25 - 9 + 36 = 47\nC(23536) = |47| = 47\n\n\\boxed{47}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(C(71971) + 59490)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 71971 are [7, 1, 9, 7, 1].\nAlternating sum of squares = 7^2 - 1^2 + 9^2 - 7^2 + 1^2 = 49 - 1 + 81 - 49 + 1 = 81\nC(71971) = |81| = 81\n\n81 + 59490 = 59571\n\nThe digits of 59571 are [5, 9, 5, 7, 1].\nSum of digits = 5 + 9 + 5 + 7 + 1 = 27\nMax digit = 9\nA(59571) = 27 * 9 = 243\n\n\\boxed{243}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(22) + 70592)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 22 are [2, 2].\nMin digit = 2\n(2 - 2)^2 = 0\n(2 - 2)^2 = 0\nB(22) = 0 + 0 = 0\n\n0 + 70592 = 70592\n\nThe digits of 70592 are [7, 0, 5, 9, 2].\nRunning max: 7, 7, 7, 9, 9\nF(70592) = 7 + 7 + 7 + 9 + 9 = 39\n\n\\boxed{39}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(11913) + 77236)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 11913 are [1, 1, 9, 1, 3].\nRunning max: 1, 1, 9, 9, 9\nF(11913) = 1 + 1 + 9 + 9 + 9 = 29\n\n29 + 77236 = 77265\n\nThe digits of 77265 are [7, 7, 2, 6, 5].\nAlternating sum of squares = 7^2 - 7^2 + 2^2 - 6^2 + 5^2 = 49 - 49 + 4 - 36 + 25 = -7\nC(77265) = |-7| = 7\n\n\\boxed{7}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(79194) + 12764)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 79194 are [7, 9, 1, 9, 4].\nReversed: [4, 9, 1, 9, 7]\n7*4 + 9*9 + 1*1 + 9*9 + 4*7 = 28 + 81 + 1 + 81 + 28 = 219\nE(79194) = 219\n\n219 + 12764 = 12983\n\nThe digits of 12983 are [1, 2, 9, 8, 3].\nSum of digits = 1 + 2 + 9 + 8 + 3 = 23\nMax digit = 9\nA(12983) = 23 * 9 = 207\n\n\\boxed{207}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(A(81142) + 81889)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81142 are [8, 1, 1, 4, 2].\nSum of digits = 8 + 1 + 1 + 4 + 2 = 16\nMax digit = 8\nA(81142) = 16 * 8 = 128\n\n128 + 81889 = 82017\n\nThe digits of 82017 are [8, 2, 0, 1, 7].\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nG(82017) = 36 + 3 + 0 + 1 + 28 = 68\n\n\\boxed{68}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(83563) + 53559)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 83563 is \"83563\".\nRotations: 83563, 35638, 56383, 63835, 38356\nH(83563) = min(83563, 35638, 56383, 63835, 38356) = 35638\n\n35638 + 53559 = 89197\n\nThe digits of 89197 are [8, 9, 1, 9, 7].\nMin digit = 1\n(8 - 1)^2 = 49\n(9 - 1)^2 = 64\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(7 - 1)^2 = 36\nB(89197) = 49 + 64 + 0 + 64 + 36 = 213\n\n\\boxed{213}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(C(39924) + 94697)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 39924 are [3, 9, 9, 2, 4].\nAlternating sum of squares = 3^2 - 9^2 + 9^2 - 2^2 + 4^2 = 9 - 81 + 81 - 4 + 16 = 21\nC(39924) = |21| = 21\n\n21 + 94697 = 94718\n\nThe digits of 94718 are [9, 4, 7, 1, 8].\nSum of digits = 9 + 4 + 7 + 1 + 8 = 29\nMax digit = 9\nA(94718) = 29 * 9 = 261\n\n\\boxed{261}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(66628) + 5220)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 66628 are [6, 6, 6, 2, 8].\nRunning max: 6, 6, 6, 6, 8\nF(66628) = 6 + 6 + 6 + 6 + 8 = 32\n\n32 + 5220 = 5252\n\nThe digit string of 5252 is \"5252\".\nRotations: 5252, 2525, 5252, 2525\nH(5252) = min(5252, 2525, 5252, 2525) = 2525\n\n\\boxed{2525}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(D(73706) + 78439)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 73706 are [7, 3, 7, 0, 6].\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n7 is prime: 7^2 = 49\n0 is not prime: 0\n6 is not prime: 6\nD(73706) = 49 + 9 + 49 + 0 + 6 = 113\n\n113 + 78439 = 78552\n\nThe digits of 78552 are [7, 8, 5, 5, 2].\nSum of digits = 7 + 8 + 5 + 5 + 2 = 27\nMax digit = 8\nA(78552) = 27 * 8 = 216\n\n\\boxed{216}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(27112) + 81419)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 27112 are [2, 7, 1, 1, 2].\nT(2) = 2*3/2 = 3\nT(7) = 7*8/2 = 28\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nG(27112) = 3 + 28 + 1 + 1 + 3 = 36\n\n36 + 81419 = 81455\n\nThe digits of 81455 are [8, 1, 4, 5, 5].\nMin digit = 1\n(8 - 1)^2 = 49\n(1 - 1)^2 = 0\n(4 - 1)^2 = 9\n(5 - 1)^2 = 16\n(5 - 1)^2 = 16\nB(81455) = 49 + 0 + 9 + 16 + 16 = 90\n\n\\boxed{90}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(D(85799) + 42328)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 85799 are [8, 5, 7, 9, 9].\n8 is not prime: 8\n5 is prime: 5^2 = 25\n7 is prime: 7^2 = 49\n9 is not prime: 9\n9 is not prime: 9\nD(85799) = 8 + 25 + 49 + 9 + 9 = 100\n\n100 + 42328 = 42428\n\nThe digits of 42428 are [4, 2, 4, 2, 8].\nRunning max: 4, 4, 4, 4, 8\nF(42428) = 4 + 4 + 4 + 4 + 8 = 24\n\n\\boxed{24}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(88011) + 75619)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 88011 is \"88011\".\nRotations: 88011, 80118, 1188, 11880, 18801\nH(88011) = min(88011, 80118, 1188, 11880, 18801) = 1188\n\n1188 + 75619 = 76807\n\nThe digits of 76807 are [7, 6, 8, 0, 7].\nSum of digits = 7 + 6 + 8 + 0 + 7 = 28\nMax digit = 8\nA(76807) = 28 * 8 = 224\n\n\\boxed{224}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(C(59796) + 82587)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59796 are [5, 9, 7, 9, 6].\nAlternating sum of squares = 5^2 - 9^2 + 7^2 - 9^2 + 6^2 = 25 - 81 + 49 - 81 + 36 = -52\nC(59796) = |-52| = 52\n\n52 + 82587 = 82639\n\nThe digits of 82639 are [8, 2, 6, 3, 9].\n8 is not prime: 8\n2 is prime: 2^2 = 4\n6 is not prime: 6\n3 is prime: 3^2 = 9\n9 is not prime: 9\nD(82639) = 8 + 4 + 6 + 9 + 9 = 36\n\n\\boxed{36}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(44676) + 62115)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 44676 are [4, 4, 6, 7, 6].\nMin digit = 4\n(4 - 4)^2 = 0\n(4 - 4)^2 = 0\n(6 - 4)^2 = 4\n(7 - 4)^2 = 9\n(6 - 4)^2 = 4\nB(44676) = 0 + 0 + 4 + 9 + 4 = 17\n\n17 + 62115 = 62132\n\nThe digits of 62132 are [6, 2, 1, 3, 2].\nReversed: [2, 3, 1, 2, 6]\n6*2 + 2*3 + 1*1 + 3*2 + 2*6 = 12 + 6 + 1 + 6 + 12 = 37\nE(62132) = 37\n\n\\boxed{37}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(47624) - 6866)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 47624 is \"47624\".\nRotations: 47624, 76244, 62447, 24476, 44762\nH(47624) = min(47624, 76244, 62447, 24476, 44762) = 24476\n\n24476 - 6866 = 17610\n\nThe digits of 17610 are [1, 7, 6, 1, 0].\nSum of digits = 1 + 7 + 6 + 1 + 0 = 15\nMax digit = 7\nA(17610) = 15 * 7 = 105\n\n\\boxed{105}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(7113) + 75435)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 7113 are [7, 1, 1, 3].\n7 is prime: 7^2 = 49\n1 is not prime: 1\n1 is not prime: 1\n3 is prime: 3^2 = 9\nD(7113) = 49 + 1 + 1 + 9 = 60\n\n60 + 75435 = 75495\n\nThe digits of 75495 are [7, 5, 4, 9, 5].\nAlternating sum of squares = 7^2 - 5^2 + 4^2 - 9^2 + 5^2 = 49 - 25 + 16 - 81 + 25 = -16\nC(75495) = |-16| = 16\n\n\\boxed{16}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(29218) + 63146)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 29218 are [2, 9, 2, 1, 8].\nAlternating sum of squares = 2^2 - 9^2 + 2^2 - 1^2 + 8^2 = 4 - 81 + 4 - 1 + 64 = -10\nC(29218) = |-10| = 10\n\n10 + 63146 = 63156\n\nThe digit string of 63156 is \"63156\".\nRotations: 63156, 31566, 15663, 56631, 66315\nH(63156) = min(63156, 31566, 15663, 56631, 66315) = 15663\n\n\\boxed{15663}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(59566) + 20396)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59566 are [5, 9, 5, 6, 6].\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(5) = 5*6/2 = 15\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nG(59566) = 15 + 45 + 15 + 21 + 21 = 117\n\n117 + 20396 = 20513\n\nThe digit string of 20513 is \"20513\".\nRotations: 20513, 5132, 51320, 13205, 32051\nH(20513) = min(20513, 5132, 51320, 13205, 32051) = 5132\n\n\\boxed{5132}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(43512) + 333)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 43512 are [4, 3, 5, 1, 2].\nReversed: [2, 1, 5, 3, 4]\n4*2 + 3*1 + 5*5 + 1*3 + 2*4 = 8 + 3 + 25 + 3 + 8 = 47\nE(43512) = 47\n\n47 + 333 = 380\n\nThe digits of 380 are [3, 8, 0].\n3 is prime: 3^2 = 9\n8 is not prime: 8\n0 is not prime: 0\nD(380) = 9 + 8 + 0 = 17\n\n\\boxed{17}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(C(73420) + 72671)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 73420 are [7, 3, 4, 2, 0].\nAlternating sum of squares = 7^2 - 3^2 + 4^2 - 2^2 + 0^2 = 49 - 9 + 16 - 4 + 0 = 52\nC(73420) = |52| = 52\n\n52 + 72671 = 72723\n\nThe digits of 72723 are [7, 2, 7, 2, 3].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\nD(72723) = 49 + 4 + 49 + 4 + 9 = 115\n\n\\boxed{115}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(C(81232) + 42488)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81232 are [8, 1, 2, 3, 2].\nAlternating sum of squares = 8^2 - 1^2 + 2^2 - 3^2 + 2^2 = 64 - 1 + 4 - 9 + 4 = 62\nC(81232) = |62| = 62\n\n62 + 42488 = 42550\n\nThe digits of 42550 are [4, 2, 5, 5, 0].\n4 is not prime: 4\n2 is prime: 2^2 = 4\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\n0 is not prime: 0\nD(42550) = 4 + 4 + 25 + 25 + 0 = 58\n\n\\boxed{58}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(78636) - 34078)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 78636 is \"78636\".\nRotations: 78636, 86367, 63678, 36786, 67863\nH(78636) = min(78636, 86367, 63678, 36786, 67863) = 36786\n\n36786 - 34078 = 2708\n\nThe digits of 2708 are [2, 7, 0, 8].\nReversed: [8, 0, 7, 2]\n2*8 + 7*0 + 0*7 + 8*2 = 16 + 0 + 0 + 16 = 32\nE(2708) = 32\n\n\\boxed{32}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(62014) + 52781)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 62014 is \"62014\".\nRotations: 62014, 20146, 1462, 14620, 46201\nH(62014) = min(62014, 20146, 1462, 14620, 46201) = 1462\n\n1462 + 52781 = 54243\n\nThe digits of 54243 are [5, 4, 2, 4, 3].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nT(3) = 3*4/2 = 6\nG(54243) = 15 + 10 + 3 + 10 + 6 = 44\n\n\\boxed{44}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(D(93933) + 65033)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93933 are [9, 3, 9, 3, 3].\n9 is not prime: 9\n3 is prime: 3^2 = 9\n9 is not prime: 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\nD(93933) = 9 + 9 + 9 + 9 + 9 = 45\n\n45 + 65033 = 65078\n\nThe digits of 65078 are [6, 5, 0, 7, 8].\nMin digit = 0\n(6 - 0)^2 = 36\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\n(7 - 0)^2 = 49\n(8 - 0)^2 = 64\nB(65078) = 36 + 25 + 0 + 49 + 64 = 174\n\n\\boxed{174}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(H(86136) + 52272)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 86136 is \"86136\".\nRotations: 86136, 61368, 13686, 36861, 68613\nH(86136) = min(86136, 61368, 13686, 36861, 68613) = 13686\n\n13686 + 52272 = 65958\n\nThe digits of 65958 are [6, 5, 9, 5, 8].\nReversed: [8, 5, 9, 5, 6]\n6*8 + 5*5 + 9*9 + 5*5 + 8*6 = 48 + 25 + 81 + 25 + 48 = 227\nE(65958) = 227\n\n\\boxed{227}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(47617) + 70883)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 47617 are [4, 7, 6, 1, 7].\nReversed: [7, 1, 6, 7, 4]\n4*7 + 7*1 + 6*6 + 1*7 + 7*4 = 28 + 7 + 36 + 7 + 28 = 106\nE(47617) = 106\n\n106 + 70883 = 70989\n\nThe digits of 70989 are [7, 0, 9, 8, 9].\n7 is prime: 7^2 = 49\n0 is not prime: 0\n9 is not prime: 9\n8 is not prime: 8\n9 is not prime: 9\nD(70989) = 49 + 0 + 9 + 8 + 9 = 75\n\n\\boxed{75}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(G(93836) + 74123)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93836 are [9, 3, 8, 3, 6].\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nG(93836) = 45 + 6 + 36 + 6 + 21 = 114\n\n114 + 74123 = 74237\n\nThe digit string of 74237 is \"74237\".\nRotations: 74237, 42377, 23774, 37742, 77423\nH(74237) = min(74237, 42377, 23774, 37742, 77423) = 23774\n\n\\boxed{23774}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(59314) + 21760)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59314 are [5, 9, 3, 1, 4].\nReversed: [4, 1, 3, 9, 5]\n5*4 + 9*1 + 3*3 + 1*9 + 4*5 = 20 + 9 + 9 + 9 + 20 = 67\nE(59314) = 67\n\n67 + 21760 = 21827\n\nThe digits of 21827 are [2, 1, 8, 2, 7].\n2 is prime: 2^2 = 4\n1 is not prime: 1\n8 is not prime: 8\n2 is prime: 2^2 = 4\n7 is prime: 7^2 = 49\nD(21827) = 4 + 1 + 8 + 4 + 49 = 66\n\n\\boxed{66}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(12771) + 93415)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 12771 are [1, 2, 7, 7, 1].\nSum of digits = 1 + 2 + 7 + 7 + 1 = 18\nMax digit = 7\nA(12771) = 18 * 7 = 126\n\n126 + 93415 = 93541\n\nThe digits of 93541 are [9, 3, 5, 4, 1].\nAlternating sum of squares = 9^2 - 3^2 + 5^2 - 4^2 + 1^2 = 81 - 9 + 25 - 16 + 1 = 82\nC(93541) = |82| = 82\n\n\\boxed{82}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(99525) + 42096)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 99525 is \"99525\".\nRotations: 99525, 95259, 52599, 25995, 59952\nH(99525) = min(99525, 95259, 52599, 25995, 59952) = 25995\n\n25995 + 42096 = 68091\n\nThe digits of 68091 are [6, 8, 0, 9, 1].\n6 is not prime: 6\n8 is not prime: 8\n0 is not prime: 0\n9 is not prime: 9\n1 is not prime: 1\nD(68091) = 6 + 8 + 0 + 9 + 1 = 24\n\n\\boxed{24}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(86364) + 26076)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86364 are [8, 6, 3, 6, 4].\nReversed: [4, 6, 3, 6, 8]\n8*4 + 6*6 + 3*3 + 6*6 + 4*8 = 32 + 36 + 9 + 36 + 32 = 145\nE(86364) = 145\n\n145 + 26076 = 26221\n\nThe digits of 26221 are [2, 6, 2, 2, 1].\nMin digit = 1\n(2 - 1)^2 = 1\n(6 - 1)^2 = 25\n(2 - 1)^2 = 1\n(2 - 1)^2 = 1\n(1 - 1)^2 = 0\nB(26221) = 1 + 25 + 1 + 1 + 0 = 28\n\n\\boxed{28}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(F(29064) + 35094)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 29064 are [2, 9, 0, 6, 4].\nRunning max: 2, 9, 9, 9, 9\nF(29064) = 2 + 9 + 9 + 9 + 9 = 38\n\n38 + 35094 = 35132\n\nThe digits of 35132 are [3, 5, 1, 3, 2].\nT(3) = 3*4/2 = 6\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nG(35132) = 6 + 15 + 1 + 6 + 3 = 31\n\n\\boxed{31}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(E(287) + 87128)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 287 are [2, 8, 7].\nReversed: [7, 8, 2]\n2*7 + 8*8 + 7*2 = 14 + 64 + 14 = 92\nE(287) = 92\n\n92 + 87128 = 87220\n\nThe digit string of 87220 is \"87220\".\nRotations: 87220, 72208, 22087, 20872, 8722\nH(87220) = min(87220, 72208, 22087, 20872, 8722) = 8722\n\n\\boxed{8722}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(A(44742) + 63122)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 44742 are [4, 4, 7, 4, 2].\nSum of digits = 4 + 4 + 7 + 4 + 2 = 21\nMax digit = 7\nA(44742) = 21 * 7 = 147\n\n147 + 63122 = 63269\n\nThe digits of 63269 are [6, 3, 2, 6, 9].\nMin digit = 2\n(6 - 2)^2 = 16\n(3 - 2)^2 = 1\n(2 - 2)^2 = 0\n(6 - 2)^2 = 16\n(9 - 2)^2 = 49\nB(63269) = 16 + 1 + 0 + 16 + 49 = 82\n\n\\boxed{82}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(46548) + 97210)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 46548 are [4, 6, 5, 4, 8].\nReversed: [8, 4, 5, 6, 4]\n4*8 + 6*4 + 5*5 + 4*6 + 8*4 = 32 + 24 + 25 + 24 + 32 = 137\nE(46548) = 137\n\n137 + 97210 = 97347\n\nThe digits of 97347 are [9, 7, 3, 4, 7].\nMin digit = 3\n(9 - 3)^2 = 36\n(7 - 3)^2 = 16\n(3 - 3)^2 = 0\n(4 - 3)^2 = 1\n(7 - 3)^2 = 16\nB(97347) = 36 + 16 + 0 + 1 + 16 = 69\n\n\\boxed{69}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(83055) + 2421)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 83055 are [8, 3, 0, 5, 5].\nSum of digits = 8 + 3 + 0 + 5 + 5 = 21\nMax digit = 8\nA(83055) = 21 * 8 = 168\n\n168 + 2421 = 2589\n\nThe digits of 2589 are [2, 5, 8, 9].\nRunning max: 2, 5, 8, 9\nF(2589) = 2 + 5 + 8 + 9 = 24\n\n\\boxed{24}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(38270) + 25123)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 38270 are [3, 8, 2, 7, 0].\nAlternating sum of squares = 3^2 - 8^2 + 2^2 - 7^2 + 0^2 = 9 - 64 + 4 - 49 + 0 = -100\nC(38270) = |-100| = 100\n\n100 + 25123 = 25223\n\nThe digit string of 25223 is \"25223\".\nRotations: 25223, 52232, 22325, 23252, 32522\nH(25223) = min(25223, 52232, 22325, 23252, 32522) = 22325\n\n\\boxed{22325}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(F(71786) + 36269)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 71786 are [7, 1, 7, 8, 6].\nRunning max: 7, 7, 7, 8, 8\nF(71786) = 7 + 7 + 7 + 8 + 8 = 37\n\n37 + 36269 = 36306\n\nThe digits of 36306 are [3, 6, 3, 0, 6].\nMin digit = 0\n(3 - 0)^2 = 9\n(6 - 0)^2 = 36\n(3 - 0)^2 = 9\n(0 - 0)^2 = 0\n(6 - 0)^2 = 36\nB(36306) = 9 + 36 + 9 + 0 + 36 = 90\n\n\\boxed{90}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(E(68417) + 81058)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 68417 are [6, 8, 4, 1, 7].\nReversed: [7, 1, 4, 8, 6]\n6*7 + 8*1 + 4*4 + 1*8 + 7*6 = 42 + 8 + 16 + 8 + 42 = 116\nE(68417) = 116\n\n116 + 81058 = 81174\n\nThe digits of 81174 are [8, 1, 1, 7, 4].\nAlternating sum of squares = 8^2 - 1^2 + 1^2 - 7^2 + 4^2 = 64 - 1 + 1 - 49 + 16 = 31\nC(81174) = |31| = 31\n\n\\boxed{31}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(49006) + 5917)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 49006 are [4, 9, 0, 0, 6].\n4 is not prime: 4\n9 is not prime: 9\n0 is not prime: 0\n0 is not prime: 0\n6 is not prime: 6\nD(49006) = 4 + 9 + 0 + 0 + 6 = 19\n\n19 + 5917 = 5936\n\nThe digits of 5936 are [5, 9, 3, 6].\nAlternating sum of squares = 5^2 - 9^2 + 3^2 - 6^2 = 25 - 81 + 9 - 36 = -83\nC(5936) = |-83| = 83\n\n\\boxed{83}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(92025) + 45846)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 92025 are [9, 2, 0, 2, 5].\n9 is not prime: 9\n2 is prime: 2^2 = 4\n0 is not prime: 0\n2 is prime: 2^2 = 4\n5 is prime: 5^2 = 25\nD(92025) = 9 + 4 + 0 + 4 + 25 = 42\n\n42 + 45846 = 45888\n\nThe digits of 45888 are [4, 5, 8, 8, 8].\nAlternating sum of squares = 4^2 - 5^2 + 8^2 - 8^2 + 8^2 = 16 - 25 + 64 - 64 + 64 = 55\nC(45888) = |55| = 55\n\n\\boxed{55}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(13935) + 63020)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13935 are [1, 3, 9, 3, 5].\nMin digit = 1\n(1 - 1)^2 = 0\n(3 - 1)^2 = 4\n(9 - 1)^2 = 64\n(3 - 1)^2 = 4\n(5 - 1)^2 = 16\nB(13935) = 0 + 4 + 64 + 4 + 16 = 88\n\n88 + 63020 = 63108\n\nThe digits of 63108 are [6, 3, 1, 0, 8].\nReversed: [8, 0, 1, 3, 6]\n6*8 + 3*0 + 1*1 + 0*3 + 8*6 = 48 + 0 + 1 + 0 + 48 = 97\nE(63108) = 97\n\n\\boxed{97}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(H(6000) + 68819)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 6000 is \"6000\".\nRotations: 6000, 6, 60, 600\nH(6000) = min(6000, 6, 60, 600) = 6\n\n6 + 68819 = 68825\n\nThe digits of 68825 are [6, 8, 8, 2, 5].\nAlternating sum of squares = 6^2 - 8^2 + 8^2 - 2^2 + 5^2 = 36 - 64 + 64 - 4 + 25 = 57\nC(68825) = |57| = 57\n\n\\boxed{57}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(21516) + 38292)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 21516 are [2, 1, 5, 1, 6].\nT(2) = 2*3/2 = 3\nT(1) = 1*2/2 = 1\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(6) = 6*7/2 = 21\nG(21516) = 3 + 1 + 15 + 1 + 21 = 41\n\n41 + 38292 = 38333\n\nThe digits of 38333 are [3, 8, 3, 3, 3].\nSum of digits = 3 + 8 + 3 + 3 + 3 = 20\nMax digit = 8\nA(38333) = 20 * 8 = 160\n\n\\boxed{160}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(64542) + 79340)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 64542 are [6, 4, 5, 4, 2].\nMin digit = 2\n(6 - 2)^2 = 16\n(4 - 2)^2 = 4\n(5 - 2)^2 = 9\n(4 - 2)^2 = 4\n(2 - 2)^2 = 0\nB(64542) = 16 + 4 + 9 + 4 + 0 = 33\n\n33 + 79340 = 79373\n\nThe digits of 79373 are [7, 9, 3, 7, 3].\nRunning max: 7, 9, 9, 9, 9\nF(79373) = 7 + 9 + 9 + 9 + 9 = 43\n\n\\boxed{43}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(18408) + 98730)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 18408 are [1, 8, 4, 0, 8].\nRunning max: 1, 8, 8, 8, 8\nF(18408) = 1 + 8 + 8 + 8 + 8 = 33\n\n33 + 98730 = 98763\n\nThe digits of 98763 are [9, 8, 7, 6, 3].\nAlternating sum of squares = 9^2 - 8^2 + 7^2 - 6^2 + 3^2 = 81 - 64 + 49 - 36 + 9 = 39\nC(98763) = |39| = 39\n\n\\boxed{39}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(E(93959) + 1775)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93959 are [9, 3, 9, 5, 9].\nReversed: [9, 5, 9, 3, 9]\n9*9 + 3*5 + 9*9 + 5*3 + 9*9 = 81 + 15 + 81 + 15 + 81 = 273\nE(93959) = 273\n\n273 + 1775 = 2048\n\nThe digits of 2048 are [2, 0, 4, 8].\nRunning max: 2, 2, 4, 8\nF(2048) = 2 + 2 + 4 + 8 = 16\n\n\\boxed{16}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(97322) - 17888)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 97322 is \"97322\".\nRotations: 97322, 73229, 32297, 22973, 29732\nH(97322) = min(97322, 73229, 32297, 22973, 29732) = 22973\n\n22973 - 17888 = 5085\n\nThe digits of 5085 are [5, 0, 8, 5].\nMin digit = 0\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\n(8 - 0)^2 = 64\n(5 - 0)^2 = 25\nB(5085) = 25 + 0 + 64 + 25 = 114\n\n\\boxed{114}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(B(94576) + 96170)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 94576 are [9, 4, 5, 7, 6].\nMin digit = 4\n(9 - 4)^2 = 25\n(4 - 4)^2 = 0\n(5 - 4)^2 = 1\n(7 - 4)^2 = 9\n(6 - 4)^2 = 4\nB(94576) = 25 + 0 + 1 + 9 + 4 = 39\n\n39 + 96170 = 96209\n\nThe digits of 96209 are [9, 6, 2, 0, 9].\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nT(9) = 9*10/2 = 45\nG(96209) = 45 + 21 + 3 + 0 + 45 = 114\n\n\\boxed{114}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(53636) + 52771)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 53636 are [5, 3, 6, 3, 6].\nReversed: [6, 3, 6, 3, 5]\n5*6 + 3*3 + 6*6 + 3*3 + 6*5 = 30 + 9 + 36 + 9 + 30 = 114\nE(53636) = 114\n\n114 + 52771 = 52885\n\nThe digits of 52885 are [5, 2, 8, 8, 5].\nMin digit = 2\n(5 - 2)^2 = 9\n(2 - 2)^2 = 0\n(8 - 2)^2 = 36\n(8 - 2)^2 = 36\n(5 - 2)^2 = 9\nB(52885) = 9 + 0 + 36 + 36 + 9 = 90\n\n\\boxed{90}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(14019) + 83486)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 14019 are [1, 4, 0, 1, 9].\nMin digit = 0\n(1 - 0)^2 = 1\n(4 - 0)^2 = 16\n(0 - 0)^2 = 0\n(1 - 0)^2 = 1\n(9 - 0)^2 = 81\nB(14019) = 1 + 16 + 0 + 1 + 81 = 99\n\n99 + 83486 = 83585\n\nThe digits of 83585 are [8, 3, 5, 8, 5].\nRunning max: 8, 8, 8, 8, 8\nF(83585) = 8 + 8 + 8 + 8 + 8 = 40\n\n\\boxed{40}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(D(33330) + 45497)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 33330 are [3, 3, 3, 3, 0].\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n0 is not prime: 0\nD(33330) = 9 + 9 + 9 + 9 + 0 = 36\n\n36 + 45497 = 45533\n\nThe digits of 45533 are [4, 5, 5, 3, 3].\nRunning max: 4, 5, 5, 5, 5\nF(45533) = 4 + 5 + 5 + 5 + 5 = 24\n\n\\boxed{24}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(80065) + 12513)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 80065 are [8, 0, 0, 6, 5].\n8 is not prime: 8\n0 is not prime: 0\n0 is not prime: 0\n6 is not prime: 6\n5 is prime: 5^2 = 25\nD(80065) = 8 + 0 + 0 + 6 + 25 = 39\n\n39 + 12513 = 12552\n\nThe digit string of 12552 is \"12552\".\nRotations: 12552, 25521, 55212, 52125, 21255\nH(12552) = min(12552, 25521, 55212, 52125, 21255) = 12552\n\n\\boxed{12552}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(25679) + 60955)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 25679 are [2, 5, 6, 7, 9].\nReversed: [9, 7, 6, 5, 2]\n2*9 + 5*7 + 6*6 + 7*5 + 9*2 = 18 + 35 + 36 + 35 + 18 = 142\nE(25679) = 142\n\n142 + 60955 = 61097\n\nThe digits of 61097 are [6, 1, 0, 9, 7].\nSum of digits = 6 + 1 + 0 + 9 + 7 = 23\nMax digit = 9\nA(61097) = 23 * 9 = 207\n\n\\boxed{207}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(24581) + 10461)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 24581 are [2, 4, 5, 8, 1].\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(1) = 1*2/2 = 1\nG(24581) = 3 + 10 + 15 + 36 + 1 = 65\n\n65 + 10461 = 10526\n\nThe digits of 10526 are [1, 0, 5, 2, 6].\nMin digit = 0\n(1 - 0)^2 = 1\n(0 - 0)^2 = 0\n(5 - 0)^2 = 25\n(2 - 0)^2 = 4\n(6 - 0)^2 = 36\nB(10526) = 1 + 0 + 25 + 4 + 36 = 66\n\n\\boxed{66}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(15826) + 92794)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 15826 are [1, 5, 8, 2, 6].\nMin digit = 1\n(1 - 1)^2 = 0\n(5 - 1)^2 = 16\n(8 - 1)^2 = 49\n(2 - 1)^2 = 1\n(6 - 1)^2 = 25\nB(15826) = 0 + 16 + 49 + 1 + 25 = 91\n\n91 + 92794 = 92885\n\nThe digits of 92885 are [9, 2, 8, 8, 5].\n9 is not prime: 9\n2 is prime: 2^2 = 4\n8 is not prime: 8\n8 is not prime: 8\n5 is prime: 5^2 = 25\nD(92885) = 9 + 4 + 8 + 8 + 25 = 54\n\n\\boxed{54}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(51497) + 26285)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 51497 are [5, 1, 4, 9, 7].\nAlternating sum of squares = 5^2 - 1^2 + 4^2 - 9^2 + 7^2 = 25 - 1 + 16 - 81 + 49 = 8\nC(51497) = |8| = 8\n\n8 + 26285 = 26293\n\nThe digits of 26293 are [2, 6, 2, 9, 3].\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nG(26293) = 3 + 21 + 3 + 45 + 6 = 78\n\n\\boxed{78}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(28257) - 896)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 28257 is \"28257\".\nRotations: 28257, 82572, 25728, 57282, 72825\nH(28257) = min(28257, 82572, 25728, 57282, 72825) = 25728\n\n25728 - 896 = 24832\n\nThe digits of 24832 are [2, 4, 8, 3, 2].\nRunning max: 2, 4, 8, 8, 8\nF(24832) = 2 + 4 + 8 + 8 + 8 = 30\n\n\\boxed{30}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(G(59905) + 3543)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59905 are [5, 9, 9, 0, 5].\nT(5) = 5*6/2 = 15\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nT(5) = 5*6/2 = 15\nG(59905) = 15 + 45 + 45 + 0 + 15 = 120\n\n120 + 3543 = 3663\n\nThe digits of 3663 are [3, 6, 6, 3].\n3 is prime: 3^2 = 9\n6 is not prime: 6\n6 is not prime: 6\n3 is prime: 3^2 = 9\nD(3663) = 9 + 6 + 6 + 9 = 30\n\n\\boxed{30}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(93950) + 27265)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93950 are [9, 3, 9, 5, 0].\nMin digit = 0\n(9 - 0)^2 = 81\n(3 - 0)^2 = 9\n(9 - 0)^2 = 81\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\nB(93950) = 81 + 9 + 81 + 25 + 0 = 196\n\n196 + 27265 = 27461\n\nThe digits of 27461 are [2, 7, 4, 6, 1].\n2 is prime: 2^2 = 4\n7 is prime: 7^2 = 49\n4 is not prime: 4\n6 is not prime: 6\n1 is not prime: 1\nD(27461) = 4 + 49 + 4 + 6 + 1 = 64\n\n\\boxed{64}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(D(44293) + 88261)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 44293 are [4, 4, 2, 9, 3].\n4 is not prime: 4\n4 is not prime: 4\n2 is prime: 2^2 = 4\n9 is not prime: 9\n3 is prime: 3^2 = 9\nD(44293) = 4 + 4 + 4 + 9 + 9 = 30\n\n30 + 88261 = 88291\n\nThe digits of 88291 are [8, 8, 2, 9, 1].\nSum of digits = 8 + 8 + 2 + 9 + 1 = 28\nMax digit = 9\nA(88291) = 28 * 9 = 252\n\n\\boxed{252}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(14125) + 38061)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 14125 are [1, 4, 1, 2, 5].\nReversed: [5, 2, 1, 4, 1]\n1*5 + 4*2 + 1*1 + 2*4 + 5*1 = 5 + 8 + 1 + 8 + 5 = 27\nE(14125) = 27\n\n27 + 38061 = 38088\n\nThe digits of 38088 are [3, 8, 0, 8, 8].\nSum of digits = 3 + 8 + 0 + 8 + 8 = 27\nMax digit = 8\nA(38088) = 27 * 8 = 216\n\n\\boxed{216}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(99241) + 4209)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 99241 are [9, 9, 2, 4, 1].\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(2) = 2*3/2 = 3\nT(4) = 4*5/2 = 10\nT(1) = 1*2/2 = 1\nG(99241) = 45 + 45 + 3 + 10 + 1 = 104\n\n104 + 4209 = 4313\n\nThe digits of 4313 are [4, 3, 1, 3].\nReversed: [3, 1, 3, 4]\n4*3 + 3*1 + 1*3 + 3*4 = 12 + 3 + 3 + 12 = 30\nE(4313) = 30\n\n\\boxed{30}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(E(54325) + 3225)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 54325 are [5, 4, 3, 2, 5].\nReversed: [5, 2, 3, 4, 5]\n5*5 + 4*2 + 3*3 + 2*4 + 5*5 = 25 + 8 + 9 + 8 + 25 = 75\nE(54325) = 75\n\n75 + 3225 = 3300\n\nThe digits of 3300 are [3, 3, 0, 0].\nRunning max: 3, 3, 3, 3\nF(3300) = 3 + 3 + 3 + 3 = 12\n\n\\boxed{12}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(F(6094) + 22017)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6094 are [6, 0, 9, 4].\nRunning max: 6, 6, 9, 9\nF(6094) = 6 + 6 + 9 + 9 = 30\n\n30 + 22017 = 22047\n\nThe digits of 22047 are [2, 2, 0, 4, 7].\nT(2) = 2*3/2 = 3\nT(2) = 2*3/2 = 3\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nG(22047) = 3 + 3 + 0 + 10 + 28 = 44\n\n\\boxed{44}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(B(83000) + 92858)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 83000 are [8, 3, 0, 0, 0].\nMin digit = 0\n(8 - 0)^2 = 64\n(3 - 0)^2 = 9\n(0 - 0)^2 = 0\n(0 - 0)^2 = 0\n(0 - 0)^2 = 0\nB(83000) = 64 + 9 + 0 + 0 + 0 = 73\n\n73 + 92858 = 92931\n\nThe digit string of 92931 is \"92931\".\nRotations: 92931, 29319, 93192, 31929, 19293\nH(92931) = min(92931, 29319, 93192, 31929, 19293) = 19293\n\n\\boxed{19293}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(88098) + 31979)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88098 are [8, 8, 0, 9, 8].\nReversed: [8, 9, 0, 8, 8]\n8*8 + 8*9 + 0*0 + 9*8 + 8*8 = 64 + 72 + 0 + 72 + 64 = 272\nE(88098) = 272\n\n272 + 31979 = 32251\n\nThe digits of 32251 are [3, 2, 2, 5, 1].\nMin digit = 1\n(3 - 1)^2 = 4\n(2 - 1)^2 = 1\n(2 - 1)^2 = 1\n(5 - 1)^2 = 16\n(1 - 1)^2 = 0\nB(32251) = 4 + 1 + 1 + 16 + 0 = 22\n\n\\boxed{22}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(F(77176) + 48973)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 77176 are [7, 7, 1, 7, 6].\nRunning max: 7, 7, 7, 7, 7\nF(77176) = 7 + 7 + 7 + 7 + 7 = 35\n\n35 + 48973 = 49008\n\nThe digits of 49008 are [4, 9, 0, 0, 8].\nSum of digits = 4 + 9 + 0 + 0 + 8 = 21\nMax digit = 9\nA(49008) = 21 * 9 = 189\n\n\\boxed{189}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(16150) + 38309)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 16150 is \"16150\".\nRotations: 16150, 61501, 15016, 50161, 1615\nH(16150) = min(16150, 61501, 15016, 50161, 1615) = 1615\n\n1615 + 38309 = 39924\n\nThe digits of 39924 are [3, 9, 9, 2, 4].\n3 is prime: 3^2 = 9\n9 is not prime: 9\n9 is not prime: 9\n2 is prime: 2^2 = 4\n4 is not prime: 4\nD(39924) = 9 + 9 + 9 + 4 + 4 = 35\n\n\\boxed{35}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(A(59950) + 53081)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59950 are [5, 9, 9, 5, 0].\nSum of digits = 5 + 9 + 9 + 5 + 0 = 28\nMax digit = 9\nA(59950) = 28 * 9 = 252\n\n252 + 53081 = 53333\n\nThe digits of 53333 are [5, 3, 3, 3, 3].\nAlternating sum of squares = 5^2 - 3^2 + 3^2 - 3^2 + 3^2 = 25 - 9 + 9 - 9 + 9 = 25\nC(53333) = |25| = 25\n\n\\boxed{25}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(86305) + 77226)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86305 are [8, 6, 3, 0, 5].\n8 is not prime: 8\n6 is not prime: 6\n3 is prime: 3^2 = 9\n0 is not prime: 0\n5 is prime: 5^2 = 25\nD(86305) = 8 + 6 + 9 + 0 + 25 = 48\n\n48 + 77226 = 77274\n\nThe digit string of 77274 is \"77274\".\nRotations: 77274, 72747, 27477, 74772, 47727\nH(77274) = min(77274, 72747, 27477, 74772, 47727) = 27477\n\n\\boxed{27477}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(77242) + 81623)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 77242 are [7, 7, 2, 4, 2].\nAlternating sum of squares = 7^2 - 7^2 + 2^2 - 4^2 + 2^2 = 49 - 49 + 4 - 16 + 4 = -8\nC(77242) = |-8| = 8\n\n8 + 81623 = 81631\n\nThe digits of 81631 are [8, 1, 6, 3, 1].\nReversed: [1, 3, 6, 1, 8]\n8*1 + 1*3 + 6*6 + 3*1 + 1*8 = 8 + 3 + 36 + 3 + 8 = 58\nE(81631) = 58\n\n\\boxed{58}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(F(66086) + 52713)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 66086 are [6, 6, 0, 8, 6].\nRunning max: 6, 6, 6, 8, 8\nF(66086) = 6 + 6 + 6 + 8 + 8 = 34\n\n34 + 52713 = 52747\n\nThe digits of 52747 are [5, 2, 7, 4, 7].\nReversed: [7, 4, 7, 2, 5]\n5*7 + 2*4 + 7*7 + 4*2 + 7*5 = 35 + 8 + 49 + 8 + 35 = 135\nE(52747) = 135\n\n\\boxed{135}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(D(17647) + 41833)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 17647 are [1, 7, 6, 4, 7].\n1 is not prime: 1\n7 is prime: 7^2 = 49\n6 is not prime: 6\n4 is not prime: 4\n7 is prime: 7^2 = 49\nD(17647) = 1 + 49 + 6 + 4 + 49 = 109\n\n109 + 41833 = 41942\n\nThe digits of 41942 are [4, 1, 9, 4, 2].\nMin digit = 1\n(4 - 1)^2 = 9\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(4 - 1)^2 = 9\n(2 - 1)^2 = 1\nB(41942) = 9 + 0 + 64 + 9 + 1 = 83\n\n\\boxed{83}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(65382) + 85715)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 65382 are [6, 5, 3, 8, 2].\nMin digit = 2\n(6 - 2)^2 = 16\n(5 - 2)^2 = 9\n(3 - 2)^2 = 1\n(8 - 2)^2 = 36\n(2 - 2)^2 = 0\nB(65382) = 16 + 9 + 1 + 36 + 0 = 62\n\n62 + 85715 = 85777\n\nThe digits of 85777 are [8, 5, 7, 7, 7].\nRunning max: 8, 8, 8, 8, 8\nF(85777) = 8 + 8 + 8 + 8 + 8 = 40\n\n\\boxed{40}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(D(568) + 98165)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 568 are [5, 6, 8].\n5 is prime: 5^2 = 25\n6 is not prime: 6\n8 is not prime: 8\nD(568) = 25 + 6 + 8 = 39\n\n39 + 98165 = 98204\n\nThe digit string of 98204 is \"98204\".\nRotations: 98204, 82049, 20498, 4982, 49820\nH(98204) = min(98204, 82049, 20498, 4982, 49820) = 4982\n\n\\boxed{4982}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(D(69515) + 74288)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 69515 are [6, 9, 5, 1, 5].\n6 is not prime: 6\n9 is not prime: 9\n5 is prime: 5^2 = 25\n1 is not prime: 1\n5 is prime: 5^2 = 25\nD(69515) = 6 + 9 + 25 + 1 + 25 = 66\n\n66 + 74288 = 74354\n\nThe digits of 74354 are [7, 4, 3, 5, 4].\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nT(3) = 3*4/2 = 6\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nG(74354) = 28 + 10 + 6 + 15 + 10 = 69\n\n\\boxed{69}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(96497) + 9535)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 96497 are [9, 6, 4, 9, 7].\nMin digit = 4\n(9 - 4)^2 = 25\n(6 - 4)^2 = 4\n(4 - 4)^2 = 0\n(9 - 4)^2 = 25\n(7 - 4)^2 = 9\nB(96497) = 25 + 4 + 0 + 25 + 9 = 63\n\n63 + 9535 = 9598\n\nThe digits of 9598 are [9, 5, 9, 8].\nReversed: [8, 9, 5, 9]\n9*8 + 5*9 + 9*5 + 8*9 = 72 + 45 + 45 + 72 = 234\nE(9598) = 234\n\n\\boxed{234}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(6366) + 69893)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6366 are [6, 3, 6, 6].\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nT(6) = 6*7/2 = 21\nG(6366) = 21 + 6 + 21 + 21 = 69\n\n69 + 69893 = 69962\n\nThe digits of 69962 are [6, 9, 9, 6, 2].\nMin digit = 2\n(6 - 2)^2 = 16\n(9 - 2)^2 = 49\n(9 - 2)^2 = 49\n(6 - 2)^2 = 16\n(2 - 2)^2 = 0\nB(69962) = 16 + 49 + 49 + 16 + 0 = 130\n\n\\boxed{130}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(F(56729) + 17012)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 56729 are [5, 6, 7, 2, 9].\nRunning max: 5, 6, 7, 7, 9\nF(56729) = 5 + 6 + 7 + 7 + 9 = 34\n\n34 + 17012 = 17046\n\nThe digits of 17046 are [1, 7, 0, 4, 6].\n1 is not prime: 1\n7 is prime: 7^2 = 49\n0 is not prime: 0\n4 is not prime: 4\n6 is not prime: 6\nD(17046) = 1 + 49 + 0 + 4 + 6 = 60\n\n\\boxed{60}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(76692) + 24063)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 76692 are [7, 6, 6, 9, 2].\nReversed: [2, 9, 6, 6, 7]\n7*2 + 6*9 + 6*6 + 9*6 + 2*7 = 14 + 54 + 36 + 54 + 14 = 172\nE(76692) = 172\n\n172 + 24063 = 24235\n\nThe digits of 24235 are [2, 4, 2, 3, 5].\n2 is prime: 2^2 = 4\n4 is not prime: 4\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n5 is prime: 5^2 = 25\nD(24235) = 4 + 4 + 4 + 9 + 25 = 46\n\n\\boxed{46}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(A(23226) + 89235)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 23226 are [2, 3, 2, 2, 6].\nSum of digits = 2 + 3 + 2 + 2 + 6 = 15\nMax digit = 6\nA(23226) = 15 * 6 = 90\n\n90 + 89235 = 89325\n\nThe digits of 89325 are [8, 9, 3, 2, 5].\nRunning max: 8, 9, 9, 9, 9\nF(89325) = 8 + 9 + 9 + 9 + 9 = 44\n\n\\boxed{44}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(B(90677) + 33366)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90677 are [9, 0, 6, 7, 7].\nMin digit = 0\n(9 - 0)^2 = 81\n(0 - 0)^2 = 0\n(6 - 0)^2 = 36\n(7 - 0)^2 = 49\n(7 - 0)^2 = 49\nB(90677) = 81 + 0 + 36 + 49 + 49 = 215\n\n215 + 33366 = 33581\n\nThe digits of 33581 are [3, 3, 5, 8, 1].\nSum of digits = 3 + 3 + 5 + 8 + 1 = 20\nMax digit = 8\nA(33581) = 20 * 8 = 160\n\n\\boxed{160}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(F(75832) + 11815)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 75832 are [7, 5, 8, 3, 2].\nRunning max: 7, 7, 8, 8, 8\nF(75832) = 7 + 7 + 8 + 8 + 8 = 38\n\n38 + 11815 = 11853\n\nThe digit string of 11853 is \"11853\".\nRotations: 11853, 18531, 85311, 53118, 31185\nH(11853) = min(11853, 18531, 85311, 53118, 31185) = 11853\n\n\\boxed{11853}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(C(22760) + 572)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 22760 are [2, 2, 7, 6, 0].\nAlternating sum of squares = 2^2 - 2^2 + 7^2 - 6^2 + 0^2 = 4 - 4 + 49 - 36 + 0 = 13\nC(22760) = |13| = 13\n\n13 + 572 = 585\n\nThe digits of 585 are [5, 8, 5].\nSum of digits = 5 + 8 + 5 = 18\nMax digit = 8\nA(585) = 18 * 8 = 144\n\n\\boxed{144}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(95747) + 14298)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 95747 are [9, 5, 7, 4, 7].\n9 is not prime: 9\n5 is prime: 5^2 = 25\n7 is prime: 7^2 = 49\n4 is not prime: 4\n7 is prime: 7^2 = 49\nD(95747) = 9 + 25 + 49 + 4 + 49 = 136\n\n136 + 14298 = 14434\n\nThe digits of 14434 are [1, 4, 4, 3, 4].\nReversed: [4, 3, 4, 4, 1]\n1*4 + 4*3 + 4*4 + 3*4 + 4*1 = 4 + 12 + 16 + 12 + 4 = 48\nE(14434) = 48\n\n\\boxed{48}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(16827) + 84425)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 16827 are [1, 6, 8, 2, 7].\nT(1) = 1*2/2 = 1\nT(6) = 6*7/2 = 21\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nT(7) = 7*8/2 = 28\nG(16827) = 1 + 21 + 36 + 3 + 28 = 89\n\n89 + 84425 = 84514\n\nThe digits of 84514 are [8, 4, 5, 1, 4].\nMin digit = 1\n(8 - 1)^2 = 49\n(4 - 1)^2 = 9\n(5 - 1)^2 = 16\n(1 - 1)^2 = 0\n(4 - 1)^2 = 9\nB(84514) = 49 + 9 + 16 + 0 + 9 = 83\n\n\\boxed{83}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(13573) + 97834)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13573 are [1, 3, 5, 7, 3].\nReversed: [3, 7, 5, 3, 1]\n1*3 + 3*7 + 5*5 + 7*3 + 3*1 = 3 + 21 + 25 + 21 + 3 = 73\nE(13573) = 73\n\n73 + 97834 = 97907\n\nThe digits of 97907 are [9, 7, 9, 0, 7].\nSum of digits = 9 + 7 + 9 + 0 + 7 = 32\nMax digit = 9\nA(97907) = 32 * 9 = 288\n\n\\boxed{288}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(B(50778) + 54729)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 50778 are [5, 0, 7, 7, 8].\nMin digit = 0\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\n(7 - 0)^2 = 49\n(7 - 0)^2 = 49\n(8 - 0)^2 = 64\nB(50778) = 25 + 0 + 49 + 49 + 64 = 187\n\n187 + 54729 = 54916\n\nThe digits of 54916 are [5, 4, 9, 1, 6].\nSum of digits = 5 + 4 + 9 + 1 + 6 = 25\nMax digit = 9\nA(54916) = 25 * 9 = 225\n\n\\boxed{225}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(86182) + 99753)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 86182 are [8, 6, 1, 8, 2].\nT(8) = 8*9/2 = 36\nT(6) = 6*7/2 = 21\nT(1) = 1*2/2 = 1\nT(8) = 8*9/2 = 36\nT(2) = 2*3/2 = 3\nG(86182) = 36 + 21 + 1 + 36 + 3 = 97\n\n97 + 99753 = 99850\n\nThe digits of 99850 are [9, 9, 8, 5, 0].\nMin digit = 0\n(9 - 0)^2 = 81\n(9 - 0)^2 = 81\n(8 - 0)^2 = 64\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\nB(99850) = 81 + 81 + 64 + 25 + 0 = 251\n\n\\boxed{251}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(F(78714) + 40212)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 78714 are [7, 8, 7, 1, 4].\nRunning max: 7, 8, 8, 8, 8\nF(78714) = 7 + 8 + 8 + 8 + 8 = 39\n\n39 + 40212 = 40251\n\nThe digits of 40251 are [4, 0, 2, 5, 1].\nT(4) = 4*5/2 = 10\nT(0) = 0*1/2 = 0\nT(2) = 2*3/2 = 3\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nG(40251) = 10 + 0 + 3 + 15 + 1 = 29\n\n\\boxed{29}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(B(79450) + 91442)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 79450 are [7, 9, 4, 5, 0].\nMin digit = 0\n(7 - 0)^2 = 49\n(9 - 0)^2 = 81\n(4 - 0)^2 = 16\n(5 - 0)^2 = 25\n(0 - 0)^2 = 0\nB(79450) = 49 + 81 + 16 + 25 + 0 = 171\n\n171 + 91442 = 91613\n\nThe digit string of 91613 is \"91613\".\nRotations: 91613, 16139, 61391, 13916, 39161\nH(91613) = min(91613, 16139, 61391, 13916, 39161) = 13916\n\n\\boxed{13916}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(42184) + 18714)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 42184 are [4, 2, 1, 8, 4].\nReversed: [4, 8, 1, 2, 4]\n4*4 + 2*8 + 1*1 + 8*2 + 4*4 = 16 + 16 + 1 + 16 + 16 = 65\nE(42184) = 65\n\n65 + 18714 = 18779\n\nThe digits of 18779 are [1, 8, 7, 7, 9].\nMin digit = 1\n(1 - 1)^2 = 0\n(8 - 1)^2 = 49\n(7 - 1)^2 = 36\n(7 - 1)^2 = 36\n(9 - 1)^2 = 64\nB(18779) = 0 + 49 + 36 + 36 + 64 = 185\n\n\\boxed{185}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(F(66074) + 71661)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 66074 are [6, 6, 0, 7, 4].\nRunning max: 6, 6, 6, 7, 7\nF(66074) = 6 + 6 + 6 + 7 + 7 = 32\n\n32 + 71661 = 71693\n\nThe digits of 71693 are [7, 1, 6, 9, 3].\nReversed: [3, 9, 6, 1, 7]\n7*3 + 1*9 + 6*6 + 9*1 + 3*7 = 21 + 9 + 36 + 9 + 21 = 96\nE(71693) = 96\n\n\\boxed{96}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(50418) + 18013)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 50418 is \"50418\".\nRotations: 50418, 4185, 41850, 18504, 85041\nH(50418) = min(50418, 4185, 41850, 18504, 85041) = 4185\n\n4185 + 18013 = 22198\n\nThe digits of 22198 are [2, 2, 1, 9, 8].\nRunning max: 2, 2, 2, 9, 9\nF(22198) = 2 + 2 + 2 + 9 + 9 = 24\n\n\\boxed{24}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(D(54875) + 52231)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 54875 are [5, 4, 8, 7, 5].\n5 is prime: 5^2 = 25\n4 is not prime: 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\nD(54875) = 25 + 4 + 8 + 49 + 25 = 111\n\n111 + 52231 = 52342\n\nThe digits of 52342 are [5, 2, 3, 4, 2].\nMin digit = 2\n(5 - 2)^2 = 9\n(2 - 2)^2 = 0\n(3 - 2)^2 = 1\n(4 - 2)^2 = 4\n(2 - 2)^2 = 0\nB(52342) = 9 + 0 + 1 + 4 + 0 = 14\n\n\\boxed{14}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(A(90769) + 45902)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90769 are [9, 0, 7, 6, 9].\nSum of digits = 9 + 0 + 7 + 6 + 9 = 31\nMax digit = 9\nA(90769) = 31 * 9 = 279\n\n279 + 45902 = 46181\n\nThe digits of 46181 are [4, 6, 1, 8, 1].\nReversed: [1, 8, 1, 6, 4]\n4*1 + 6*8 + 1*1 + 8*6 + 1*4 = 4 + 48 + 1 + 48 + 4 = 105\nE(46181) = 105\n\n\\boxed{105}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(E(99925) + 63189)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 99925 are [9, 9, 9, 2, 5].\nReversed: [5, 2, 9, 9, 9]\n9*5 + 9*2 + 9*9 + 2*9 + 5*9 = 45 + 18 + 81 + 18 + 45 = 207\nE(99925) = 207\n\n207 + 63189 = 63396\n\nThe digits of 63396 are [6, 3, 3, 9, 6].\n6 is not prime: 6\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n9 is not prime: 9\n6 is not prime: 6\nD(63396) = 6 + 9 + 9 + 9 + 6 = 39\n\n\\boxed{39}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(32537) + 18399)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 32537 are [3, 2, 5, 3, 7].\nSum of digits = 3 + 2 + 5 + 3 + 7 = 20\nMax digit = 7\nA(32537) = 20 * 7 = 140\n\n140 + 18399 = 18539\n\nThe digits of 18539 are [1, 8, 5, 3, 9].\n1 is not prime: 1\n8 is not prime: 8\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\n9 is not prime: 9\nD(18539) = 1 + 8 + 25 + 9 + 9 = 52\n\n\\boxed{52}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(H(35860) + 71914)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 35860 is \"35860\".\nRotations: 35860, 58603, 86035, 60358, 3586\nH(35860) = min(35860, 58603, 86035, 60358, 3586) = 3586\n\n3586 + 71914 = 75500\n\nThe digits of 75500 are [7, 5, 5, 0, 0].\nSum of digits = 7 + 5 + 5 + 0 + 0 = 17\nMax digit = 7\nA(75500) = 17 * 7 = 119\n\n\\boxed{119}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(A(52149) + 14941)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 52149 are [5, 2, 1, 4, 9].\nSum of digits = 5 + 2 + 1 + 4 + 9 = 21\nMax digit = 9\nA(52149) = 21 * 9 = 189\n\n189 + 14941 = 15130\n\nThe digit string of 15130 is \"15130\".\nRotations: 15130, 51301, 13015, 30151, 1513\nH(15130) = min(15130, 51301, 13015, 30151, 1513) = 1513\n\n\\boxed{1513}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(G(44939) + 22701)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 44939 are [4, 4, 9, 3, 9].\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(9) = 9*10/2 = 45\nG(44939) = 10 + 10 + 45 + 6 + 45 = 116\n\n116 + 22701 = 22817\n\nThe digits of 22817 are [2, 2, 8, 1, 7].\nAlternating sum of squares = 2^2 - 2^2 + 8^2 - 1^2 + 7^2 = 4 - 4 + 64 - 1 + 49 = 112\nC(22817) = |112| = 112\n\n\\boxed{112}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(38557) + 1351)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 38557 are [3, 8, 5, 5, 7].\nReversed: [7, 5, 5, 8, 3]\n3*7 + 8*5 + 5*5 + 5*8 + 7*3 = 21 + 40 + 25 + 40 + 21 = 147\nE(38557) = 147\n\n147 + 1351 = 1498\n\nThe digits of 1498 are [1, 4, 9, 8].\nMin digit = 1\n(1 - 1)^2 = 0\n(4 - 1)^2 = 9\n(9 - 1)^2 = 64\n(8 - 1)^2 = 49\nB(1498) = 0 + 9 + 64 + 49 = 122\n\n\\boxed{122}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(59355) + 87389)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 59355 are [5, 9, 3, 5, 5].\n5 is prime: 5^2 = 25\n9 is not prime: 9\n3 is prime: 3^2 = 9\n5 is prime: 5^2 = 25\n5 is prime: 5^2 = 25\nD(59355) = 25 + 9 + 9 + 25 + 25 = 93\n\n93 + 87389 = 87482\n\nThe digits of 87482 are [8, 7, 4, 8, 2].\nAlternating sum of squares = 8^2 - 7^2 + 4^2 - 8^2 + 2^2 = 64 - 49 + 16 - 64 + 4 = -29\nC(87482) = |-29| = 29\n\n\\boxed{29}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(H(17481) + 79558)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 17481 is \"17481\".\nRotations: 17481, 74811, 48117, 81174, 11748\nH(17481) = min(17481, 74811, 48117, 81174, 11748) = 11748\n\n11748 + 79558 = 91306\n\nThe digits of 91306 are [9, 1, 3, 0, 6].\nAlternating sum of squares = 9^2 - 1^2 + 3^2 - 0^2 + 6^2 = 81 - 1 + 9 - 0 + 36 = 125\nC(91306) = |125| = 125\n\n\\boxed{125}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(E(18111) + 2711)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 18111 are [1, 8, 1, 1, 1].\nReversed: [1, 1, 1, 8, 1]\n1*1 + 8*1 + 1*1 + 1*8 + 1*1 = 1 + 8 + 1 + 8 + 1 = 19\nE(18111) = 19\n\n19 + 2711 = 2730\n\nThe digits of 2730 are [2, 7, 3, 0].\nT(2) = 2*3/2 = 3\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nG(2730) = 3 + 28 + 6 + 0 = 37\n\n\\boxed{37}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(F(54099) + 7830)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 54099 are [5, 4, 0, 9, 9].\nRunning max: 5, 5, 5, 9, 9\nF(54099) = 5 + 5 + 5 + 9 + 9 = 33\n\n33 + 7830 = 7863\n\nThe digits of 7863 are [7, 8, 6, 3].\nReversed: [3, 6, 8, 7]\n7*3 + 8*6 + 6*8 + 3*7 = 21 + 48 + 48 + 21 = 138\nE(7863) = 138\n\n\\boxed{138}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(78974) + 19287)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 78974 is \"78974\".\nRotations: 78974, 89747, 97478, 74789, 47897\nH(78974) = min(78974, 89747, 97478, 74789, 47897) = 47897\n\n47897 + 19287 = 67184\n\nThe digits of 67184 are [6, 7, 1, 8, 4].\nMin digit = 1\n(6 - 1)^2 = 25\n(7 - 1)^2 = 36\n(1 - 1)^2 = 0\n(8 - 1)^2 = 49\n(4 - 1)^2 = 9\nB(67184) = 25 + 36 + 0 + 49 + 9 = 119\n\n\\boxed{119}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(91752) + 26895)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 91752 is \"91752\".\nRotations: 91752, 17529, 75291, 52917, 29175\nH(91752) = min(91752, 17529, 75291, 52917, 29175) = 17529\n\n17529 + 26895 = 44424\n\nThe digits of 44424 are [4, 4, 4, 2, 4].\n4 is not prime: 4\n4 is not prime: 4\n4 is not prime: 4\n2 is prime: 2^2 = 4\n4 is not prime: 4\nD(44424) = 4 + 4 + 4 + 4 + 4 = 20\n\n\\boxed{20}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(98097) + 78881)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 98097 is \"98097\".\nRotations: 98097, 80979, 9798, 97980, 79809\nH(98097) = min(98097, 80979, 9798, 97980, 79809) = 9798\n\n9798 + 78881 = 88679\n\nThe digits of 88679 are [8, 8, 6, 7, 9].\nT(8) = 8*9/2 = 36\nT(8) = 8*9/2 = 36\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nG(88679) = 36 + 36 + 21 + 28 + 45 = 166\n\n\\boxed{166}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(67147) + 17070)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 67147 are [6, 7, 1, 4, 7].\n6 is not prime: 6\n7 is prime: 7^2 = 49\n1 is not prime: 1\n4 is not prime: 4\n7 is prime: 7^2 = 49\nD(67147) = 6 + 49 + 1 + 4 + 49 = 109\n\n109 + 17070 = 17179\n\nThe digits of 17179 are [1, 7, 1, 7, 9].\nAlternating sum of squares = 1^2 - 7^2 + 1^2 - 7^2 + 9^2 = 1 - 49 + 1 - 49 + 81 = -15\nC(17179) = |-15| = 15\n\n\\boxed{15}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(B(39179) + 86157)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 39179 are [3, 9, 1, 7, 9].\nMin digit = 1\n(3 - 1)^2 = 4\n(9 - 1)^2 = 64\n(1 - 1)^2 = 0\n(7 - 1)^2 = 36\n(9 - 1)^2 = 64\nB(39179) = 4 + 64 + 0 + 36 + 64 = 168\n\n168 + 86157 = 86325\n\nThe digits of 86325 are [8, 6, 3, 2, 5].\nT(8) = 8*9/2 = 36\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(2) = 2*3/2 = 3\nT(5) = 5*6/2 = 15\nG(86325) = 36 + 21 + 6 + 3 + 15 = 81\n\n\\boxed{81}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(B(71802) + 47121)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 71802 are [7, 1, 8, 0, 2].\nMin digit = 0\n(7 - 0)^2 = 49\n(1 - 0)^2 = 1\n(8 - 0)^2 = 64\n(0 - 0)^2 = 0\n(2 - 0)^2 = 4\nB(71802) = 49 + 1 + 64 + 0 + 4 = 118\n\n118 + 47121 = 47239\n\nThe digits of 47239 are [4, 7, 2, 3, 9].\n4 is not prime: 4\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n3 is prime: 3^2 = 9\n9 is not prime: 9\nD(47239) = 4 + 49 + 4 + 9 + 9 = 75\n\n\\boxed{75}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(41144) + 6751)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 41144 are [4, 1, 1, 4, 4].\nReversed: [4, 4, 1, 1, 4]\n4*4 + 1*4 + 1*1 + 4*1 + 4*4 = 16 + 4 + 1 + 4 + 16 = 41\nE(41144) = 41\n\n41 + 6751 = 6792\n\nThe digits of 6792 are [6, 7, 9, 2].\nSum of digits = 6 + 7 + 9 + 2 = 24\nMax digit = 9\nA(6792) = 24 * 9 = 216\n\n\\boxed{216}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(B(93306) + 11057)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93306 are [9, 3, 3, 0, 6].\nMin digit = 0\n(9 - 0)^2 = 81\n(3 - 0)^2 = 9\n(3 - 0)^2 = 9\n(0 - 0)^2 = 0\n(6 - 0)^2 = 36\nB(93306) = 81 + 9 + 9 + 0 + 36 = 135\n\n135 + 11057 = 11192\n\nThe digits of 11192 are [1, 1, 1, 9, 2].\nReversed: [2, 9, 1, 1, 1]\n1*2 + 1*9 + 1*1 + 9*1 + 2*1 = 2 + 9 + 1 + 9 + 2 = 23\nE(11192) = 23\n\n\\boxed{23}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(B(96576) + 251)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 96576 are [9, 6, 5, 7, 6].\nMin digit = 5\n(9 - 5)^2 = 16\n(6 - 5)^2 = 1\n(5 - 5)^2 = 0\n(7 - 5)^2 = 4\n(6 - 5)^2 = 1\nB(96576) = 16 + 1 + 0 + 4 + 1 = 22\n\n22 + 251 = 273\n\nThe digits of 273 are [2, 7, 3].\nT(2) = 2*3/2 = 3\nT(7) = 7*8/2 = 28\nT(3) = 3*4/2 = 6\nG(273) = 3 + 28 + 6 = 37\n\n\\boxed{37}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(72559) - 22235)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 72559 is \"72559\".\nRotations: 72559, 25597, 55972, 59725, 97255\nH(72559) = min(72559, 25597, 55972, 59725, 97255) = 25597\n\n25597 - 22235 = 3362\n\nThe digits of 3362 are [3, 3, 6, 2].\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nG(3362) = 6 + 6 + 21 + 3 = 36\n\n\\boxed{36}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(A(82913) + 79686)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 82913 are [8, 2, 9, 1, 3].\nSum of digits = 8 + 2 + 9 + 1 + 3 = 23\nMax digit = 9\nA(82913) = 23 * 9 = 207\n\n207 + 79686 = 79893\n\nThe digits of 79893 are [7, 9, 8, 9, 3].\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nG(79893) = 28 + 45 + 36 + 45 + 6 = 160\n\n\\boxed{160}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(28487) - 25887)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 28487 is \"28487\".\nRotations: 28487, 84872, 48728, 87284, 72848\nH(28487) = min(28487, 84872, 48728, 87284, 72848) = 28487\n\n28487 - 25887 = 2600\n\nThe digits of 2600 are [2, 6, 0, 0].\n2 is prime: 2^2 = 4\n6 is not prime: 6\n0 is not prime: 0\n0 is not prime: 0\nD(2600) = 4 + 6 + 0 + 0 = 10\n\n\\boxed{10}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(26330) + 77454)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 26330 are [2, 6, 3, 3, 0].\n2 is prime: 2^2 = 4\n6 is not prime: 6\n3 is prime: 3^2 = 9\n3 is prime: 3^2 = 9\n0 is not prime: 0\nD(26330) = 4 + 6 + 9 + 9 + 0 = 28\n\n28 + 77454 = 77482\n\nThe digits of 77482 are [7, 7, 4, 8, 2].\nAlternating sum of squares = 7^2 - 7^2 + 4^2 - 8^2 + 2^2 = 49 - 49 + 16 - 64 + 4 = -44\nC(77482) = |-44| = 44\n\n\\boxed{44}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(A(27487) + 75595)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 27487 are [2, 7, 4, 8, 7].\nSum of digits = 2 + 7 + 4 + 8 + 7 = 28\nMax digit = 8\nA(27487) = 28 * 8 = 224\n\n224 + 75595 = 75819\n\nThe digit string of 75819 is \"75819\".\nRotations: 75819, 58197, 81975, 19758, 97581\nH(75819) = min(75819, 58197, 81975, 19758, 97581) = 19758\n\n\\boxed{19758}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(B(81810) + 38850)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 81810 are [8, 1, 8, 1, 0].\nMin digit = 0\n(8 - 0)^2 = 64\n(1 - 0)^2 = 1\n(8 - 0)^2 = 64\n(1 - 0)^2 = 1\n(0 - 0)^2 = 0\nB(81810) = 64 + 1 + 64 + 1 + 0 = 130\n\n130 + 38850 = 38980\n\nThe digits of 38980 are [3, 8, 9, 8, 0].\nT(3) = 3*4/2 = 6\nT(8) = 8*9/2 = 36\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nT(0) = 0*1/2 = 0\nG(38980) = 6 + 36 + 45 + 36 + 0 = 123\n\n\\boxed{123}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(G(93635) + 80960)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93635 are [9, 3, 6, 3, 5].\nT(9) = 9*10/2 = 45\nT(3) = 3*4/2 = 6\nT(6) = 6*7/2 = 21\nT(3) = 3*4/2 = 6\nT(5) = 5*6/2 = 15\nG(93635) = 45 + 6 + 21 + 6 + 15 = 93\n\n93 + 80960 = 81053\n\nThe digits of 81053 are [8, 1, 0, 5, 3].\n8 is not prime: 8\n1 is not prime: 1\n0 is not prime: 0\n5 is prime: 5^2 = 25\n3 is prime: 3^2 = 9\nD(81053) = 8 + 1 + 0 + 25 + 9 = 43\n\n\\boxed{43}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(38086) + 83327)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 38086 are [3, 8, 0, 8, 6].\n3 is prime: 3^2 = 9\n8 is not prime: 8\n0 is not prime: 0\n8 is not prime: 8\n6 is not prime: 6\nD(38086) = 9 + 8 + 0 + 8 + 6 = 31\n\n31 + 83327 = 83358\n\nThe digits of 83358 are [8, 3, 3, 5, 8].\nAlternating sum of squares = 8^2 - 3^2 + 3^2 - 5^2 + 8^2 = 64 - 9 + 9 - 25 + 64 = 103\nC(83358) = |103| = 103\n\n\\boxed{103}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(89995) + 85711)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 89995 are [8, 9, 9, 9, 5].\nT(8) = 8*9/2 = 36\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(9) = 9*10/2 = 45\nT(5) = 5*6/2 = 15\nG(89995) = 36 + 45 + 45 + 45 + 15 = 186\n\n186 + 85711 = 85897\n\nThe digits of 85897 are [8, 5, 8, 9, 7].\nReversed: [7, 9, 8, 5, 8]\n8*7 + 5*9 + 8*8 + 9*5 + 7*8 = 56 + 45 + 64 + 45 + 56 = 266\nE(85897) = 266\n\n\\boxed{266}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(E(45258) + 41926)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 45258 are [4, 5, 2, 5, 8].\nReversed: [8, 5, 2, 5, 4]\n4*8 + 5*5 + 2*2 + 5*5 + 8*4 = 32 + 25 + 4 + 25 + 32 = 118\nE(45258) = 118\n\n118 + 41926 = 42044\n\nThe digits of 42044 are [4, 2, 0, 4, 4].\nRunning max: 4, 4, 4, 4, 4\nF(42044) = 4 + 4 + 4 + 4 + 4 = 20\n\n\\boxed{20}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(F(88129) + 72246)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88129 are [8, 8, 1, 2, 9].\nRunning max: 8, 8, 8, 8, 9\nF(88129) = 8 + 8 + 8 + 8 + 9 = 41\n\n41 + 72246 = 72287\n\nThe digits of 72287 are [7, 2, 2, 8, 7].\n7 is prime: 7^2 = 49\n2 is prime: 2^2 = 4\n2 is prime: 2^2 = 4\n8 is not prime: 8\n7 is prime: 7^2 = 49\nD(72287) = 49 + 4 + 4 + 8 + 49 = 114\n\n\\boxed{114}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(D(17389) + 22498)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 17389 are [1, 7, 3, 8, 9].\n1 is not prime: 1\n7 is prime: 7^2 = 49\n3 is prime: 3^2 = 9\n8 is not prime: 8\n9 is not prime: 9\nD(17389) = 1 + 49 + 9 + 8 + 9 = 76\n\n76 + 22498 = 22574\n\nThe digits of 22574 are [2, 2, 5, 7, 4].\nSum of digits = 2 + 2 + 5 + 7 + 4 = 20\nMax digit = 7\nA(22574) = 20 * 7 = 140\n\n\\boxed{140}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(93113) + 19578)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93113 are [9, 3, 1, 1, 3].\nAlternating sum of squares = 9^2 - 3^2 + 1^2 - 1^2 + 3^2 = 81 - 9 + 1 - 1 + 9 = 81\nC(93113) = |81| = 81\n\n81 + 19578 = 19659\n\nThe digit string of 19659 is \"19659\".\nRotations: 19659, 96591, 65919, 59196, 91965\nH(19659) = min(19659, 96591, 65919, 59196, 91965) = 19659\n\n\\boxed{19659}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(85208) + 65171)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 85208 are [8, 5, 2, 0, 8].\nReversed: [8, 0, 2, 5, 8]\n8*8 + 5*0 + 2*2 + 0*5 + 8*8 = 64 + 0 + 4 + 0 + 64 = 132\nE(85208) = 132\n\n132 + 65171 = 65303\n\nThe digits of 65303 are [6, 5, 3, 0, 3].\nSum of digits = 6 + 5 + 3 + 0 + 3 = 17\nMax digit = 6\nA(65303) = 17 * 6 = 102\n\n\\boxed{102}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(23306) + 12679)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 23306 are [2, 3, 3, 0, 6].\nAlternating sum of squares = 2^2 - 3^2 + 3^2 - 0^2 + 6^2 = 4 - 9 + 9 - 0 + 36 = 40\nC(23306) = |40| = 40\n\n40 + 12679 = 12719\n\nThe digits of 12719 are [1, 2, 7, 1, 9].\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nT(7) = 7*8/2 = 28\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nG(12719) = 1 + 3 + 28 + 1 + 45 = 78\n\n\\boxed{78}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(71105) + 90994)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 71105 is \"71105\".\nRotations: 71105, 11057, 10571, 5711, 57110\nH(71105) = min(71105, 11057, 10571, 5711, 57110) = 5711\n\n5711 + 90994 = 96705\n\nThe digits of 96705 are [9, 6, 7, 0, 5].\nT(9) = 9*10/2 = 45\nT(6) = 6*7/2 = 21\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nT(5) = 5*6/2 = 15\nG(96705) = 45 + 21 + 28 + 0 + 15 = 109\n\n\\boxed{109}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(E(91004) + 86655)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 91004 are [9, 1, 0, 0, 4].\nReversed: [4, 0, 0, 1, 9]\n9*4 + 1*0 + 0*0 + 0*1 + 4*9 = 36 + 0 + 0 + 0 + 36 = 72\nE(91004) = 72\n\n72 + 86655 = 86727\n\nThe digits of 86727 are [8, 6, 7, 2, 7].\nSum of digits = 8 + 6 + 7 + 2 + 7 = 30\nMax digit = 8\nA(86727) = 30 * 8 = 240\n\n\\boxed{240}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(83476) + 19443)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 83476 are [8, 3, 4, 7, 6].\nT(8) = 8*9/2 = 36\nT(3) = 3*4/2 = 6\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nT(6) = 6*7/2 = 21\nG(83476) = 36 + 6 + 10 + 28 + 21 = 101\n\n101 + 19443 = 19544\n\nThe digits of 19544 are [1, 9, 5, 4, 4].\nMin digit = 1\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(5 - 1)^2 = 16\n(4 - 1)^2 = 9\n(4 - 1)^2 = 9\nB(19544) = 0 + 64 + 16 + 9 + 9 = 98\n\n\\boxed{98}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(A(42255) + 8045)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 42255 are [4, 2, 2, 5, 5].\nSum of digits = 4 + 2 + 2 + 5 + 5 = 18\nMax digit = 5\nA(42255) = 18 * 5 = 90\n\n90 + 8045 = 8135\n\nThe digits of 8135 are [8, 1, 3, 5].\n8 is not prime: 8\n1 is not prime: 1\n3 is prime: 3^2 = 9\n5 is prime: 5^2 = 25\nD(8135) = 8 + 1 + 9 + 25 = 43\n\n\\boxed{43}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(D(93107) + 87669)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93107 are [9, 3, 1, 0, 7].\n9 is not prime: 9\n3 is prime: 3^2 = 9\n1 is not prime: 1\n0 is not prime: 0\n7 is prime: 7^2 = 49\nD(93107) = 9 + 9 + 1 + 0 + 49 = 68\n\n68 + 87669 = 87737\n\nThe digits of 87737 are [8, 7, 7, 3, 7].\nReversed: [7, 3, 7, 7, 8]\n8*7 + 7*3 + 7*7 + 3*7 + 7*8 = 56 + 21 + 49 + 21 + 56 = 203\nE(87737) = 203\n\n\\boxed{203}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(C(15126) + 45188)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 15126 are [1, 5, 1, 2, 6].\nAlternating sum of squares = 1^2 - 5^2 + 1^2 - 2^2 + 6^2 = 1 - 25 + 1 - 4 + 36 = 9\nC(15126) = |9| = 9\n\n9 + 45188 = 45197\n\nThe digits of 45197 are [4, 5, 1, 9, 7].\nMin digit = 1\n(4 - 1)^2 = 9\n(5 - 1)^2 = 16\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(7 - 1)^2 = 36\nB(45197) = 9 + 16 + 0 + 64 + 36 = 125\n\n\\boxed{125}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(H(99716) + 74052)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 99716 is \"99716\".\nRotations: 99716, 97169, 71699, 16997, 69971\nH(99716) = min(99716, 97169, 71699, 16997, 69971) = 16997\n\n16997 + 74052 = 91049\n\nThe digits of 91049 are [9, 1, 0, 4, 9].\nT(9) = 9*10/2 = 45\nT(1) = 1*2/2 = 1\nT(0) = 0*1/2 = 0\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nG(91049) = 45 + 1 + 0 + 10 + 45 = 101\n\n\\boxed{101}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(H(46168) + 63724)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 46168 is \"46168\".\nRotations: 46168, 61684, 16846, 68461, 84616\nH(46168) = min(46168, 61684, 16846, 68461, 84616) = 16846\n\n16846 + 63724 = 80570\n\nThe digits of 80570 are [8, 0, 5, 7, 0].\nRunning max: 8, 8, 8, 8, 8\nF(80570) = 8 + 8 + 8 + 8 + 8 = 40\n\n\\boxed{40}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(73699) + 15900)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 73699 is \"73699\".\nRotations: 73699, 36997, 69973, 99736, 97369\nH(73699) = min(73699, 36997, 69973, 99736, 97369) = 36997\n\n36997 + 15900 = 52897\n\nThe digits of 52897 are [5, 2, 8, 9, 7].\n5 is prime: 5^2 = 25\n2 is prime: 2^2 = 4\n8 is not prime: 8\n9 is not prime: 9\n7 is prime: 7^2 = 49\nD(52897) = 25 + 4 + 8 + 9 + 49 = 95\n\n\\boxed{95}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(A(62963) + 59278)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 62963 are [6, 2, 9, 6, 3].\nSum of digits = 6 + 2 + 9 + 6 + 3 = 26\nMax digit = 9\nA(62963) = 26 * 9 = 234\n\n234 + 59278 = 59512\n\nThe digits of 59512 are [5, 9, 5, 1, 2].\nMin digit = 1\n(5 - 1)^2 = 16\n(9 - 1)^2 = 64\n(5 - 1)^2 = 16\n(1 - 1)^2 = 0\n(2 - 1)^2 = 1\nB(59512) = 16 + 64 + 16 + 0 + 1 = 97\n\n\\boxed{97}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(B(76389) + 58786)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 76389 are [7, 6, 3, 8, 9].\nMin digit = 3\n(7 - 3)^2 = 16\n(6 - 3)^2 = 9\n(3 - 3)^2 = 0\n(8 - 3)^2 = 25\n(9 - 3)^2 = 36\nB(76389) = 16 + 9 + 0 + 25 + 36 = 86\n\n86 + 58786 = 58872\n\nThe digits of 58872 are [5, 8, 8, 7, 2].\nT(5) = 5*6/2 = 15\nT(8) = 8*9/2 = 36\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(2) = 2*3/2 = 3\nG(58872) = 15 + 36 + 36 + 28 + 3 = 118\n\n\\boxed{118}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(74794) + 56379)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 74794 are [7, 4, 7, 9, 4].\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nT(4) = 4*5/2 = 10\nG(74794) = 28 + 10 + 28 + 45 + 10 = 121\n\n121 + 56379 = 56500\n\nThe digits of 56500 are [5, 6, 5, 0, 0].\nSum of digits = 5 + 6 + 5 + 0 + 0 = 16\nMax digit = 6\nA(56500) = 16 * 6 = 96\n\n\\boxed{96}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(E(87445) + 44827)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 87445 are [8, 7, 4, 4, 5].\nReversed: [5, 4, 4, 7, 8]\n8*5 + 7*4 + 4*4 + 4*7 + 5*8 = 40 + 28 + 16 + 28 + 40 = 152\nE(87445) = 152\n\n152 + 44827 = 44979\n\nThe digits of 44979 are [4, 4, 9, 7, 9].\nT(4) = 4*5/2 = 10\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(7) = 7*8/2 = 28\nT(9) = 9*10/2 = 45\nG(44979) = 10 + 10 + 45 + 28 + 45 = 138\n\n\\boxed{138}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(C(93077) + 92106)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 93077 are [9, 3, 0, 7, 7].\nAlternating sum of squares = 9^2 - 3^2 + 0^2 - 7^2 + 7^2 = 81 - 9 + 0 - 49 + 49 = 72\nC(93077) = |72| = 72\n\n72 + 92106 = 92178\n\nThe digits of 92178 are [9, 2, 1, 7, 8].\nRunning max: 9, 9, 9, 9, 9\nF(92178) = 9 + 9 + 9 + 9 + 9 = 45\n\n\\boxed{45}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(54719) + 45998)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 54719 are [5, 4, 7, 1, 9].\nT(5) = 5*6/2 = 15\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nT(1) = 1*2/2 = 1\nT(9) = 9*10/2 = 45\nG(54719) = 15 + 10 + 28 + 1 + 45 = 99\n\n99 + 45998 = 46097\n\nThe digits of 46097 are [4, 6, 0, 9, 7].\nReversed: [7, 9, 0, 6, 4]\n4*7 + 6*9 + 0*0 + 9*6 + 7*4 = 28 + 54 + 0 + 54 + 28 = 164\nE(46097) = 164\n\n\\boxed{164}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(F(88374) + 89172)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 88374 are [8, 8, 3, 7, 4].\nRunning max: 8, 8, 8, 8, 8\nF(88374) = 8 + 8 + 8 + 8 + 8 = 40\n\n40 + 89172 = 89212\n\nThe digits of 89212 are [8, 9, 2, 1, 2].\n8 is not prime: 8\n9 is not prime: 9\n2 is prime: 2^2 = 4\n1 is not prime: 1\n2 is prime: 2^2 = 4\nD(89212) = 8 + 9 + 4 + 1 + 4 = 26\n\n\\boxed{26}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(98024) + 48413)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 98024 are [9, 8, 0, 2, 4].\nAlternating sum of squares = 9^2 - 8^2 + 0^2 - 2^2 + 4^2 = 81 - 64 + 0 - 4 + 16 = 29\nC(98024) = |29| = 29\n\n29 + 48413 = 48442\n\nThe digits of 48442 are [4, 8, 4, 4, 2].\nReversed: [2, 4, 4, 8, 4]\n4*2 + 8*4 + 4*4 + 4*8 + 2*4 = 8 + 32 + 16 + 32 + 8 = 96\nE(48442) = 96\n\n\\boxed{96}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(69979) - 11117)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 69979 is \"69979\".\nRotations: 69979, 99796, 97969, 79699, 96997\nH(69979) = min(69979, 99796, 97969, 79699, 96997) = 69979\n\n69979 - 11117 = 58862\n\nThe digits of 58862 are [5, 8, 8, 6, 2].\nMin digit = 2\n(5 - 2)^2 = 9\n(8 - 2)^2 = 36\n(8 - 2)^2 = 36\n(6 - 2)^2 = 16\n(2 - 2)^2 = 0\nB(58862) = 9 + 36 + 36 + 16 + 0 = 97\n\n\\boxed{97}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(G(37477) + 82)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 37477 are [3, 7, 4, 7, 7].\nT(3) = 3*4/2 = 6\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nT(7) = 7*8/2 = 28\nG(37477) = 6 + 28 + 10 + 28 + 28 = 100\n\n100 + 82 = 182\n\nThe digits of 182 are [1, 8, 2].\nMin digit = 1\n(1 - 1)^2 = 0\n(8 - 1)^2 = 49\n(2 - 1)^2 = 1\nB(182) = 0 + 49 + 1 = 50\n\n\\boxed{50}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(C(55363) + 57480)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 55363 are [5, 5, 3, 6, 3].\nAlternating sum of squares = 5^2 - 5^2 + 3^2 - 6^2 + 3^2 = 25 - 25 + 9 - 36 + 9 = -18\nC(55363) = |-18| = 18\n\n18 + 57480 = 57498\n\nThe digits of 57498 are [5, 7, 4, 9, 8].\nT(5) = 5*6/2 = 15\nT(7) = 7*8/2 = 28\nT(4) = 4*5/2 = 10\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nG(57498) = 15 + 28 + 10 + 45 + 36 = 134\n\n\\boxed{134}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(1673) + 74150)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 1673 are [1, 6, 7, 3].\nMin digit = 1\n(1 - 1)^2 = 0\n(6 - 1)^2 = 25\n(7 - 1)^2 = 36\n(3 - 1)^2 = 4\nB(1673) = 0 + 25 + 36 + 4 = 65\n\n65 + 74150 = 74215\n\nThe digits of 74215 are [7, 4, 2, 1, 5].\nRunning max: 7, 7, 7, 7, 7\nF(74215) = 7 + 7 + 7 + 7 + 7 = 35\n\n\\boxed{35}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(68515) + 2812)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 68515 are [6, 8, 5, 1, 5].\nRunning max: 6, 8, 8, 8, 8\nF(68515) = 6 + 8 + 8 + 8 + 8 = 38\n\n38 + 2812 = 2850\n\nThe digits of 2850 are [2, 8, 5, 0].\nAlternating sum of squares = 2^2 - 8^2 + 5^2 - 0^2 = 4 - 64 + 25 - 0 = -35\nC(2850) = |-35| = 35\n\n\\boxed{35}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(B(13955) + 29198)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 13955 are [1, 3, 9, 5, 5].\nMin digit = 1\n(1 - 1)^2 = 0\n(3 - 1)^2 = 4\n(9 - 1)^2 = 64\n(5 - 1)^2 = 16\n(5 - 1)^2 = 16\nB(13955) = 0 + 4 + 64 + 16 + 16 = 100\n\n100 + 29198 = 29298\n\nThe digits of 29298 are [2, 9, 2, 9, 8].\nRunning max: 2, 9, 9, 9, 9\nF(29298) = 2 + 9 + 9 + 9 + 9 = 38\n\n\\boxed{38}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(3312) + 93726)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 3312 are [3, 3, 1, 2].\nT(3) = 3*4/2 = 6\nT(3) = 3*4/2 = 6\nT(1) = 1*2/2 = 1\nT(2) = 2*3/2 = 3\nG(3312) = 6 + 6 + 1 + 3 = 16\n\n16 + 93726 = 93742\n\nThe digits of 93742 are [9, 3, 7, 4, 2].\nReversed: [2, 4, 7, 3, 9]\n9*2 + 3*4 + 7*7 + 4*3 + 2*9 = 18 + 12 + 49 + 12 + 18 = 109\nE(93742) = 109\n\n\\boxed{109}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(F(49921) + 84251)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 49921 are [4, 9, 9, 2, 1].\nRunning max: 4, 9, 9, 9, 9\nF(49921) = 4 + 9 + 9 + 9 + 9 = 40\n\n40 + 84251 = 84291\n\nThe digits of 84291 are [8, 4, 2, 9, 1].\nAlternating sum of squares = 8^2 - 4^2 + 2^2 - 9^2 + 1^2 = 64 - 16 + 4 - 81 + 1 = -28\nC(84291) = |-28| = 28\n\n\\boxed{28}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(F(19048) + 68074)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 19048 are [1, 9, 0, 4, 8].\nRunning max: 1, 9, 9, 9, 9\nF(19048) = 1 + 9 + 9 + 9 + 9 = 37\n\n37 + 68074 = 68111\n\nThe digits of 68111 are [6, 8, 1, 1, 1].\nT(6) = 6*7/2 = 21\nT(8) = 8*9/2 = 36\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nT(1) = 1*2/2 = 1\nG(68111) = 21 + 36 + 1 + 1 + 1 = 60\n\n\\boxed{60}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(C(6955) + 81069)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 6955 are [6, 9, 5, 5].\nAlternating sum of squares = 6^2 - 9^2 + 5^2 - 5^2 = 36 - 81 + 25 - 25 = -45\nC(6955) = |-45| = 45\n\n45 + 81069 = 81114\n\nThe digits of 81114 are [8, 1, 1, 1, 4].\nMin digit = 1\n(8 - 1)^2 = 49\n(1 - 1)^2 = 0\n(1 - 1)^2 = 0\n(1 - 1)^2 = 0\n(4 - 1)^2 = 9\nB(81114) = 49 + 0 + 0 + 0 + 9 = 58\n\n\\boxed{58}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of F(E(87851) + 54217)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 87851 are [8, 7, 8, 5, 1].\nReversed: [1, 5, 8, 7, 8]\n8*1 + 7*5 + 8*8 + 5*7 + 1*8 = 8 + 35 + 64 + 35 + 8 = 150\nE(87851) = 150\n\n150 + 54217 = 54367\n\nThe digits of 54367 are [5, 4, 3, 6, 7].\nRunning max: 5, 5, 5, 6, 7\nF(54367) = 5 + 5 + 5 + 6 + 7 = 28\n\n\\boxed{28}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(E(7419) + 35263)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 7419 are [7, 4, 1, 9].\nReversed: [9, 1, 4, 7]\n7*9 + 4*1 + 1*4 + 9*7 = 63 + 4 + 4 + 63 = 134\nE(7419) = 134\n\n134 + 35263 = 35397\n\nThe digits of 35397 are [3, 5, 3, 9, 7].\nMin digit = 3\n(3 - 3)^2 = 0\n(5 - 3)^2 = 4\n(3 - 3)^2 = 0\n(9 - 3)^2 = 36\n(7 - 3)^2 = 16\nB(35397) = 0 + 4 + 0 + 36 + 16 = 56\n\n\\boxed{56}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(C(26201) + 6723)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 26201 are [2, 6, 2, 0, 1].\nAlternating sum of squares = 2^2 - 6^2 + 2^2 - 0^2 + 1^2 = 4 - 36 + 4 - 0 + 1 = -27\nC(26201) = |-27| = 27\n\n27 + 6723 = 6750\n\nThe digits of 6750 are [6, 7, 5, 0].\nReversed: [0, 5, 7, 6]\n6*0 + 7*5 + 5*7 + 0*6 = 0 + 35 + 35 + 0 = 70\nE(6750) = 70\n\n\\boxed{70}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(A(98328) + 60810)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 98328 are [9, 8, 3, 2, 8].\nSum of digits = 9 + 8 + 3 + 2 + 8 = 30\nMax digit = 9\nA(98328) = 30 * 9 = 270\n\n270 + 60810 = 61080\n\nThe digits of 61080 are [6, 1, 0, 8, 0].\nReversed: [0, 8, 0, 1, 6]\n6*0 + 1*8 + 0*0 + 8*1 + 0*6 = 0 + 8 + 0 + 8 + 0 = 16\nE(61080) = 16\n\n\\boxed{16}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(H(21094) + 54590)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 21094 is \"21094\".\nRotations: 21094, 10942, 9421, 94210, 42109\nH(21094) = min(21094, 10942, 9421, 94210, 42109) = 9421\n\n9421 + 54590 = 64011\n\nThe digits of 64011 are [6, 4, 0, 1, 1].\nMin digit = 0\n(6 - 0)^2 = 36\n(4 - 0)^2 = 16\n(0 - 0)^2 = 0\n(1 - 0)^2 = 1\n(1 - 0)^2 = 1\nB(64011) = 36 + 16 + 0 + 1 + 1 = 54\n\n\\boxed{54}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(D(37567) + 1423)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 37567 are [3, 7, 5, 6, 7].\n3 is prime: 3^2 = 9\n7 is prime: 7^2 = 49\n5 is prime: 5^2 = 25\n6 is not prime: 6\n7 is prime: 7^2 = 49\nD(37567) = 9 + 49 + 25 + 6 + 49 = 138\n\n138 + 1423 = 1561\n\nThe digits of 1561 are [1, 5, 6, 1].\nSum of digits = 1 + 5 + 6 + 1 = 13\nMax digit = 6\nA(1561) = 13 * 6 = 78\n\n\\boxed{78}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of G(E(89573) + 26052)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 89573 are [8, 9, 5, 7, 3].\nReversed: [3, 7, 5, 9, 8]\n8*3 + 9*7 + 5*5 + 7*9 + 3*8 = 24 + 63 + 25 + 63 + 24 = 199\nE(89573) = 199\n\n199 + 26052 = 26251\n\nThe digits of 26251 are [2, 6, 2, 5, 1].\nT(2) = 2*3/2 = 3\nT(6) = 6*7/2 = 21\nT(2) = 2*3/2 = 3\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nG(26251) = 3 + 21 + 3 + 15 + 1 = 43\n\n\\boxed{43}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(D(32841) + 95329)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 32841 are [3, 2, 8, 4, 1].\n3 is prime: 3^2 = 9\n2 is prime: 2^2 = 4\n8 is not prime: 8\n4 is not prime: 4\n1 is not prime: 1\nD(32841) = 9 + 4 + 8 + 4 + 1 = 26\n\n26 + 95329 = 95355\n\nThe digits of 95355 are [9, 5, 3, 5, 5].\nAlternating sum of squares = 9^2 - 5^2 + 3^2 - 5^2 + 5^2 = 81 - 25 + 9 - 25 + 25 = 65\nC(95355) = |65| = 65\n\n\\boxed{65}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(A(19192) + 55622)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 19192 are [1, 9, 1, 9, 2].\nSum of digits = 1 + 9 + 1 + 9 + 2 = 22\nMax digit = 9\nA(19192) = 22 * 9 = 198\n\n198 + 55622 = 55820\n\nThe digits of 55820 are [5, 5, 8, 2, 0].\nReversed: [0, 2, 8, 5, 5]\n5*0 + 5*2 + 8*8 + 2*5 + 0*5 = 0 + 10 + 64 + 10 + 0 = 84\nE(55820) = 84\n\n\\boxed{84}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(G(8130) + 24930)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 8130 are [8, 1, 3, 0].\nT(8) = 8*9/2 = 36\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nT(0) = 0*1/2 = 0\nG(8130) = 36 + 1 + 6 + 0 = 43\n\n43 + 24930 = 24973\n\nThe digits of 24973 are [2, 4, 9, 7, 3].\nReversed: [3, 7, 9, 4, 2]\n2*3 + 4*7 + 9*9 + 7*4 + 3*2 = 6 + 28 + 81 + 28 + 6 = 149\nE(24973) = 149\n\n\\boxed{149}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(90517) + 15671)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 90517 are [9, 0, 5, 1, 7].\nT(9) = 9*10/2 = 45\nT(0) = 0*1/2 = 0\nT(5) = 5*6/2 = 15\nT(1) = 1*2/2 = 1\nT(7) = 7*8/2 = 28\nG(90517) = 45 + 0 + 15 + 1 + 28 = 89\n\n89 + 15671 = 15760\n\nThe digits of 15760 are [1, 5, 7, 6, 0].\nSum of digits = 1 + 5 + 7 + 6 + 0 = 19\nMax digit = 7\nA(15760) = 19 * 7 = 133\n\n\\boxed{133}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of H(C(26738) + 86376)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 26738 are [2, 6, 7, 3, 8].\nAlternating sum of squares = 2^2 - 6^2 + 7^2 - 3^2 + 8^2 = 4 - 36 + 49 - 9 + 64 = 72\nC(26738) = |72| = 72\n\n72 + 86376 = 86448\n\nThe digit string of 86448 is \"86448\".\nRotations: 86448, 64488, 44886, 48864, 88644\nH(86448) = min(86448, 64488, 44886, 48864, 88644) = 44886\n\n\\boxed{44886}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of C(G(98775) + 91399)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 98775 are [9, 8, 7, 7, 5].\nT(9) = 9*10/2 = 45\nT(8) = 8*9/2 = 36\nT(7) = 7*8/2 = 28\nT(7) = 7*8/2 = 28\nT(5) = 5*6/2 = 15\nG(98775) = 45 + 36 + 28 + 28 + 15 = 152\n\n152 + 91399 = 91551\n\nThe digits of 91551 are [9, 1, 5, 5, 1].\nAlternating sum of squares = 9^2 - 1^2 + 5^2 - 5^2 + 1^2 = 81 - 1 + 25 - 25 + 1 = 81\nC(91551) = |81| = 81\n\n\\boxed{81}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of E(F(70932) + 41063)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 70932 are [7, 0, 9, 3, 2].\nRunning max: 7, 7, 9, 9, 9\nF(70932) = 7 + 7 + 9 + 9 + 9 = 41\n\n41 + 41063 = 41104\n\nThe digits of 41104 are [4, 1, 1, 0, 4].\nReversed: [4, 0, 1, 1, 4]\n4*4 + 1*0 + 1*1 + 0*1 + 4*4 = 16 + 0 + 1 + 0 + 16 = 33\nE(41104) = 33\n\n\\boxed{33}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of B(F(4234) + 1953)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 4234 are [4, 2, 3, 4].\nRunning max: 4, 4, 4, 4\nF(4234) = 4 + 4 + 4 + 4 = 16\n\n16 + 1953 = 1969\n\nThe digits of 1969 are [1, 9, 6, 9].\nMin digit = 1\n(1 - 1)^2 = 0\n(9 - 1)^2 = 64\n(6 - 1)^2 = 25\n(9 - 1)^2 = 64\nB(1969) = 0 + 64 + 25 + 64 = 153\n\n\\boxed{153}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of A(G(47013) + 34846)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digits of 47013 are [4, 7, 0, 1, 3].\nT(4) = 4*5/2 = 10\nT(7) = 7*8/2 = 28\nT(0) = 0*1/2 = 0\nT(1) = 1*2/2 = 1\nT(3) = 3*4/2 = 6\nG(47013) = 10 + 28 + 0 + 1 + 6 = 45\n\n45 + 34846 = 34891\n\nThe digits of 34891 are [3, 4, 8, 9, 1].\nSum of digits = 3 + 4 + 8 + 9 + 1 = 25\nMax digit = 9\nA(34891) = 25 * 9 = 225\n\n\\boxed{225}"}
-{"instruction": "Based on the input–output examples below, infer the rules implemented by the functions. Then apply the same rules to determine the output for the given expression.\n\nExamples for function A:\nInput: 328\nOutput: 104\n\nInput: 41\nOutput: 20\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 306\n\nInput: 242\nOutput: 32\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 234\n\nInput: 21395\nOutput: 180\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 216\n\nExamples for function B:\nInput: 328\nOutput: 37\n\nInput: 41\nOutput: 9\n\nInput: 45\nOutput: 1\n\nInput: 87397\nOutput: 93\n\nInput: 242\nOutput: 4\n\nInput: 1\nOutput: 0\n\nInput: 9935\nOutput: 76\n\nInput: 21395\nOutput: 85\n\nInput: 2\nOutput: 0\n\nInput: 2679\nOutput: 90\n\nExamples for function C:\nInput: 328\nOutput: 69\n\nInput: 41\nOutput: 15\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 8\n\nInput: 242\nOutput: 8\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 16\n\nInput: 21395\nOutput: 44\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 64\n\nExamples for function D:\nInput: 328\nOutput: 21\n\nInput: 41\nOutput: 5\n\nInput: 45\nOutput: 29\n\nInput: 87397\nOutput: 124\n\nInput: 242\nOutput: 12\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 52\n\nInput: 21395\nOutput: 48\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 68\n\nExamples for function E:\nInput: 328\nOutput: 52\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 40\n\nInput: 87397\nOutput: 247\n\nInput: 242\nOutput: 24\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 144\n\nInput: 21395\nOutput: 47\n\nInput: 2\nOutput: 4\n\nInput: 2679\nOutput: 120\n\nExamples for function F:\nInput: 328\nOutput: 14\n\nInput: 41\nOutput: 8\n\nInput: 45\nOutput: 9\n\nInput: 87397\nOutput: 42\n\nInput: 242\nOutput: 10\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 36\n\nInput: 21395\nOutput: 25\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 24\n\nExamples for function G:\nInput: 328\nOutput: 45\n\nInput: 41\nOutput: 11\n\nInput: 45\nOutput: 25\n\nInput: 87397\nOutput: 143\n\nInput: 242\nOutput: 16\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 111\n\nInput: 21395\nOutput: 70\n\nInput: 2\nOutput: 3\n\nInput: 2679\nOutput: 97\n\nExamples for function H:\nInput: 328\nOutput: 283\n\nInput: 41\nOutput: 14\n\nInput: 45\nOutput: 45\n\nInput: 87397\nOutput: 39787\n\nInput: 242\nOutput: 224\n\nInput: 1\nOutput: 1\n\nInput: 9935\nOutput: 3599\n\nInput: 21395\nOutput: 13952\n\nInput: 2\nOutput: 2\n\nInput: 2679\nOutput: 2679\n\nQuestion:\nWhat is the output of D(H(59322) + 48881)?\n\n\n\nPlease reason step by step, and put your final answer within \\boxed{}.", "input": "", "output": "The digit string of 59322 is \"59322\".\nRotations: 59322, 93225, 32259, 22593, 25932\nH(59322) = min(59322, 93225, 32259, 22593, 25932) = 22593\n\n22593 + 48881 = 71474\n\nThe digits of 71474 are [7, 1, 4, 7, 4].\n7 is prime: 7^2 = 49\n1 is not prime: 1\n4 is not prime: 4\n7 is prime: 7^2 = 49\n4 is not prime: 4\nD(71474) = 49 + 1 + 4 + 49 + 4 = 107\n\n\\boxed{107}"}