| {"width": 1916, "height": 1916, "grid_rows": 100, "grid_cols": 100, "square_left": 191.0, "square_top": 191.0, "square_size": 1534, "num_components": 10, "num_dots": 85, "question": "How many connected components are there in the image? A connected component is a maximal group of anchor points such that any two are linked by a path of one or more strands (directly or through other anchors in the same group). Anchors not linked by any chain belong to different components, even if they appear visually close. Count every connected component and report the total. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 10, "dots": [[75, 13], [88, 11], [71, 31], [51, 73], [30, 25], [73, 55], [34, 42], [25, 52], [47, 57], [32, 75], [36, 6], [9, 7], [72, 18], [67, 10], [25, 41], [43, 8], [34, 85], [93, 36], [9, 39], [20, 53], [88, 56], [15, 14], [14, 69], [58, 7], [6, 74], [82, 24], [17, 80], [55, 29], [82, 44], [43, 40], [63, 30], [17, 38], [88, 78], [65, 53], [42, 59], [16, 33], [57, 76], [40, 66], [41, 94], [73, 69], [36, 53], [7, 68], [55, 52], [78, 8], [55, 34], [66, 77], [18, 87], [44, 47], [23, 85], [76, 26], [31, 67], [80, 36], [15, 23], [56, 83], [65, 71], [24, 9], [46, 93], [77, 81], [68, 45], [88, 35], [46, 64], [18, 59], [94, 14], [53, 21], [6, 25], [26, 30], [61, 19], [9, 59], [68, 26], [85, 72], [42, 20], [60, 42], [83, 52], [77, 88], [42, 71], [92, 31], [71, 82], [47, 22], [26, 72], [5, 44], [30, 93], [17, 73], [63, 47], [84, 64], [13, 49]], "components": [[0, 1, 2, 13, 23, 27, 30, 43, 62, 63, 66, 68, 70, 77], [3, 8, 9, 29, 34, 36, 37, 40, 45, 47, 50, 53, 54, 60, 74, 78], [4, 6, 11, 14, 18, 21, 31, 35, 52, 55, 64, 65, 79, 84], [5, 12, 20, 25, 28, 33, 42, 44, 49, 51, 58, 71, 72, 82], [7, 16, 19, 22, 24, 26, 41, 46, 48, 61, 67, 80, 81], [10, 15], [17, 59, 75], [32, 39, 69, 83], [38, 56], [57, 73, 76]], "edges": [[22, 41], [66, 68], [44, 71], [36, 53], [9, 74], [7, 19], [59, 75], [33, 82], [27, 77], [38, 56], [50, 78], [3, 60], [26, 48], [18, 84], [14, 31], [63, 66], [26, 81], [58, 71], [27, 30], [28, 72], [27, 63], [0, 13], [69, 83], [29, 47], [34, 37], [0, 43], [3, 36], [22, 61], [1, 43], [28, 51], [21, 55], [24, 41], [58, 82], [13, 66], [31, 35], [8, 60], [37, 50], [41, 67], [2, 30], [13, 23], [18, 31], [8, 47], [48, 80], [79, 84], [5, 72], [8, 34], [34, 40], [36, 54], [73, 76], [1, 62], [36, 45], [12, 49], [49, 51], [35, 52], [33, 42], [37, 74], [17, 59], [5, 33], [16, 80], [70, 77], [22, 81], [19, 61], [21, 52], [32, 69], [25, 49], [20, 72], [57, 76], [6, 14], [46, 48], [4, 65], [52, 64], [35, 65], [10, 15], [11, 21], [39, 83], [40, 50], [24, 81], [2, 68], [23, 63], [18, 35], [42, 82], [18, 79], [42, 71], [23, 43], [18, 64], [6, 65], [20, 28], [53, 74], [3, 53]], "dot_radius": 1.5, "image": "images/counting_connected_components_00000.png"} |
| {"width": 1916, "height": 1916, "grid_rows": 100, "grid_cols": 100, "square_left": 191.0, "square_top": 191.0, "square_size": 1534, "num_components": 12, "num_dots": 95, "question": "How many connected components are there in the image? A connected component is a maximal group of anchor points such that any two are linked by a path of one or more strands (directly or through other anchors in the same group). Anchors not linked by any chain belong to different components, even if they appear visually close. Count every connected component and report the total. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 12, "dots": [[65, 12], [86, 94], [74, 92], [20, 25], [81, 28], [35, 56], [17, 32], [77, 19], [67, 64], [37, 51], [81, 87], [80, 71], [43, 91], [18, 94], [31, 36], [68, 57], [6, 47], [93, 69], [6, 67], [79, 13], [10, 85], [56, 87], [51, 20], [8, 59], [39, 10], [63, 72], [31, 73], [92, 87], [43, 61], [72, 39], [70, 30], [6, 34], [37, 71], [49, 64], [32, 60], [91, 5], [42, 38], [84, 21], [70, 12], [83, 6], [29, 20], [89, 54], [37, 36], [15, 59], [68, 71], [46, 84], [10, 75], [78, 45], [28, 85], [60, 5], [48, 24], [84, 11], [20, 51], [25, 31], [21, 82], [84, 56], [53, 30], [33, 7], [56, 50], [38, 5], [61, 81], [87, 80], [28, 92], [64, 31], [25, 8], [16, 76], [46, 5], [7, 42], [15, 90], [73, 22], [94, 9], [12, 43], [77, 35], [12, 49], [43, 72], [67, 81], [24, 39], [92, 46], [25, 67], [23, 91], [22, 60], [40, 21], [80, 50], [17, 69], [51, 51], [87, 64], [92, 58], [89, 15], [78, 59], [84, 47], [41, 79], [19, 46], [88, 37], [50, 81], [94, 31]], "components": [[0, 4, 7, 19, 35, 37, 38, 39, 49, 51, 69, 70, 72, 87], [1, 2, 10, 27, 61], [3, 6, 14, 16, 31, 36, 42, 53, 67, 71, 73, 76], [5, 9, 28, 33, 34], [8, 12, 15, 21, 25, 26, 32, 44, 45, 60, 74, 75, 90, 93], [11, 17, 29, 30, 41, 47, 55, 63, 77, 82, 85, 86, 88, 89], [13, 20, 68, 79], [18, 23, 43, 46, 48, 52, 54, 62, 65, 78, 80, 83, 91], [22, 50, 56, 81], [24, 40, 57, 59, 64, 66], [58, 84], [92, 94]], "edges": [[50, 81], [55, 82], [0, 38], [41, 77], [59, 66], [43, 80], [78, 80], [21, 60], [39, 51], [7, 37], [29, 30], [3, 6], [70, 87], [35, 70], [19, 38], [35, 39], [5, 28], [48, 62], [2, 10], [8, 15], [82, 89], [46, 65], [41, 55], [57, 59], [13, 68], [26, 32], [85, 86], [18, 23], [18, 46], [41, 86], [25, 44], [7, 19], [54, 65], [90, 93], [19, 39], [4, 69], [82, 88], [14, 42], [43, 52], [6, 53], [4, 7], [45, 90], [32, 74], [24, 59], [5, 34], [58, 84], [28, 33], [78, 83], [6, 76], [68, 79], [29, 47], [92, 94], [71, 73], [74, 90], [47, 82], [10, 61], [20, 68], [60, 75], [1, 10], [14, 76], [48, 54], [52, 91], [12, 45], [23, 43], [4, 72], [21, 93], [25, 75], [22, 50], [57, 64], [17, 85], [16, 73], [27, 61], [30, 63], [67, 71], [31, 67], [8, 25], [36, 42], [5, 9], [0, 49], [11, 85], [50, 56], [6, 31], [40, 64], [17, 86], [55, 86], [41, 89], [40, 57], [3, 53], [21, 45], [31, 71], [22, 56], [10, 27], [4, 37], [55, 88], [6, 71], [14, 53], [24, 40], [55, 89]], "dot_radius": 1.5, "image": "images/counting_connected_components_00001.png"} |
| {"width": 1916, "height": 1916, "grid_rows": 100, "grid_cols": 100, "square_left": 191.0, "square_top": 191.0, "square_size": 1534, "num_components": 15, "num_dots": 108, "question": "How many connected components are there in the image? A connected component is a maximal group of anchor points such that any two are linked by a path of one or more strands (directly or through other anchors in the same group). Anchors not linked by any chain belong to different components, even if they appear visually close. Count every connected component and report the total. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 15, "dots": [[44, 11], [39, 28], [87, 17], [16, 58], [31, 32], [40, 89], [12, 20], [60, 56], [36, 32], [17, 34], [81, 31], [33, 65], [29, 56], [14, 68], [78, 74], [42, 38], [86, 73], [79, 82], [69, 30], [52, 74], [67, 44], [88, 39], [72, 48], [30, 20], [22, 39], [52, 84], [18, 92], [58, 42], [76, 86], [91, 83], [64, 86], [8, 41], [60, 94], [40, 80], [11, 77], [64, 26], [55, 22], [19, 54], [35, 13], [48, 64], [16, 50], [33, 49], [46, 87], [53, 37], [85, 7], [84, 92], [41, 52], [22, 77], [85, 60], [25, 44], [67, 9], [15, 44], [83, 26], [62, 78], [17, 11], [25, 53], [83, 68], [23, 69], [54, 55], [77, 9], [39, 57], [35, 85], [37, 39], [68, 63], [54, 10], [57, 67], [7, 16], [27, 91], [7, 23], [6, 83], [69, 25], [87, 51], [94, 32], [32, 44], [41, 62], [76, 20], [34, 54], [47, 77], [47, 59], [84, 78], [92, 60], [62, 39], [78, 43], [48, 25], [71, 74], [74, 33], [89, 77], [24, 26], [51, 49], [73, 63], [79, 65], [90, 94], [57, 74], [28, 69], [32, 77], [35, 90], [44, 5], [30, 87], [11, 54], [10, 11], [5, 68], [68, 82], [43, 16], [59, 19], [24, 34], [88, 87], [28, 8], [40, 47]], "components": [[0, 38, 64, 96, 102, 106], [1, 10, 18, 35, 36, 50, 52, 70, 75, 83, 85, 103], [2, 21, 72], [3, 9, 12, 24, 31, 37, 40, 41, 49, 51, 55, 98, 104], [4, 7, 8, 15, 23, 46, 58, 60, 62, 73, 76, 78, 87, 107], [5, 19, 25, 26, 33, 42, 61, 65, 67, 77, 94, 95, 97], [6, 54, 66, 68, 99], [11, 13, 34, 39, 47, 57, 69, 74, 93, 100], [14, 16, 29, 30, 32, 48, 56, 71, 79, 80, 84, 86, 90, 101], [17, 28], [20, 22, 27, 43, 81, 82, 88], [44, 59], [45, 91, 105], [53, 92], [63, 89]], "edges": [[73, 107], [19, 65], [35, 70], [25, 77], [16, 56], [20, 81], [12, 55], [61, 95], [11, 74], [14, 79], [43, 81], [0, 102], [33, 61], [67, 97], [3, 37], [46, 60], [41, 55], [20, 22], [39, 74], [24, 51], [79, 86], [19, 77], [9, 104], [22, 82], [58, 78], [67, 95], [25, 42], [29, 79], [37, 55], [31, 51], [45, 91], [37, 40], [48, 90], [4, 62], [62, 107], [5, 42], [33, 77], [60, 76], [57, 93], [18, 85], [0, 38], [8, 15], [6, 66], [48, 56], [70, 75], [27, 43], [15, 107], [10, 85], [46, 107], [6, 68], [30, 101], [54, 99], [44, 59], [26, 67], [33, 94], [14, 56], [17, 28], [63, 89], [24, 104], [38, 106], [4, 87], [36, 103], [41, 49], [14, 84], [13, 34], [53, 92], [60, 78], [1, 83], [23, 87], [91, 105], [48, 80], [18, 70], [84, 101], [48, 71], [0, 96], [30, 32], [24, 49], [52, 75], [47, 57], [7, 58], [36, 83], [66, 99], [13, 100], [13, 57], [3, 98], [34, 69], [35, 103], [21, 72], [11, 93], [50, 103], [0, 64], [43, 88], [2, 72], [38, 102], [20, 82], [56, 90], [40, 49], [19, 25], [8, 23], [27, 81], [3, 12], [96, 106], [5, 95], [40, 51], [3, 40], [62, 73], [50, 75], [6, 99], [70, 103], [49, 51], [11, 39]], "dot_radius": 1.5, "image": "images/counting_connected_components_00002.png"} |
| {"width": 1916, "height": 1916, "grid_rows": 100, "grid_cols": 100, "square_left": 191.0, "square_top": 191.0, "square_size": 1534, "num_components": 18, "num_dots": 95, "question": "How many connected components are there in the image? A connected component is a maximal group of anchor points such that any two are linked by a path of one or more strands (directly or through other anchors in the same group). Anchors not linked by any chain belong to different components, even if they appear visually close. Count every connected component and report the total. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 18, "dots": [[20, 43], [87, 20], [29, 7], [49, 59], [13, 17], [62, 93], [22, 35], [84, 16], [40, 54], [75, 88], [94, 11], [17, 52], [89, 68], [38, 77], [92, 37], [19, 64], [59, 78], [57, 51], [41, 5], [62, 61], [53, 13], [48, 44], [31, 34], [6, 29], [79, 26], [30, 22], [92, 16], [49, 27], [63, 11], [13, 86], [6, 79], [87, 50], [6, 11], [93, 62], [80, 19], [25, 24], [51, 7], [92, 44], [7, 47], [40, 43], [22, 79], [60, 25], [51, 72], [74, 47], [68, 61], [69, 27], [58, 69], [77, 67], [21, 17], [87, 7], [33, 83], [48, 77], [81, 11], [12, 43], [92, 53], [42, 62], [87, 27], [34, 10], [20, 94], [73, 9], [29, 63], [60, 17], [73, 20], [84, 84], [57, 39], [54, 90], [83, 91], [20, 30], [42, 71], [37, 20], [6, 34], [66, 71], [7, 69], [16, 68], [83, 35], [25, 66], [67, 56], [21, 71], [27, 50], [64, 83], [10, 93], [87, 58], [37, 48], [6, 60], [71, 35], [35, 89], [36, 61], [32, 51], [49, 22], [75, 75], [18, 24], [50, 87], [16, 10], [46, 67], [9, 5]], "components": [[0, 6, 11, 22, 35, 48, 67, 78, 90], [1, 10, 24, 26, 34, 41, 45, 52, 62, 84], [2, 18, 20, 27, 28, 36, 57, 59, 61, 88], [3, 8, 21, 39, 55, 82, 86, 87, 93], [4, 32, 92, 94], [5, 65, 79, 91], [7, 49], [9, 63, 66], [12, 14, 31, 33, 37, 54, 56, 74, 81], [13, 16, 19, 42, 44, 46, 51, 68, 71, 76], [15, 30, 40, 60, 72, 73, 75, 77, 83], [17, 43, 64], [23, 70], [25, 69], [29, 58, 80], [38, 53], [47, 89], [50, 85]], "edges": [[41, 45], [24, 45], [18, 57], [19, 44], [20, 61], [75, 77], [33, 81], [42, 68], [44, 71], [11, 78], [48, 90], [45, 84], [10, 26], [29, 80], [38, 53], [56, 74], [1, 26], [14, 37], [63, 66], [92, 94], [24, 34], [20, 36], [6, 67], [4, 92], [50, 85], [0, 6], [28, 59], [15, 73], [55, 86], [1, 34], [67, 90], [31, 81], [5, 65], [34, 52], [34, 62], [20, 28], [4, 32], [12, 33], [5, 79], [40, 77], [35, 67], [0, 78], [13, 51], [15, 60], [51, 68], [2, 57], [31, 37], [82, 87], [8, 82], [9, 63], [46, 71], [7, 49], [16, 46], [6, 22], [19, 76], [14, 74], [3, 55], [42, 46], [47, 89], [55, 93], [25, 69], [72, 83], [60, 75], [18, 36], [20, 88], [72, 73], [8, 55], [39, 82], [37, 54], [23, 70], [30, 72], [21, 39], [27, 88], [58, 80], [65, 91], [43, 64], [17, 64], [44, 76], [3, 8], [32, 92], [73, 83], [19, 71], [6, 35], [61, 88], [33, 54], [65, 79], [0, 22], [15, 75], [16, 42], [40, 73], [24, 84], [1, 24]], "dot_radius": 1.5, "image": "images/counting_connected_components_00003.png"} |
| {"width": 1916, "height": 1916, "grid_rows": 100, "grid_cols": 100, "square_left": 191.0, "square_top": 191.0, "square_size": 1534, "num_components": 20, "num_dots": 108, "question": "How many connected components are there in the image? A connected component is a maximal group of anchor points such that any two are linked by a path of one or more strands (directly or through other anchors in the same group). Anchors not linked by any chain belong to different components, even if they appear visually close. Count every connected component and report the total. Provide your final answer enclosed in <answer>...</answer> tags.", "answer": 20, "dots": [[42, 38], [42, 67], [10, 15], [66, 41], [52, 56], [28, 61], [52, 67], [78, 52], [92, 80], [32, 10], [57, 83], [42, 88], [70, 26], [37, 43], [59, 89], [42, 9], [18, 49], [75, 89], [76, 15], [8, 85], [85, 35], [35, 6], [89, 41], [19, 33], [52, 28], [81, 58], [32, 83], [89, 15], [83, 46], [20, 23], [5, 75], [25, 73], [33, 58], [79, 29], [72, 64], [71, 47], [8, 31], [77, 9], [25, 51], [72, 53], [74, 41], [20, 64], [45, 49], [5, 25], [17, 80], [68, 33], [37, 76], [90, 27], [66, 55], [25, 25], [18, 91], [31, 78], [9, 54], [85, 77], [81, 87], [52, 42], [38, 63], [66, 46], [5, 81], [45, 62], [10, 59], [26, 13], [55, 62], [12, 64], [28, 5], [67, 66], [30, 54], [84, 64], [51, 80], [17, 10], [10, 72], [61, 63], [66, 15], [47, 35], [89, 67], [58, 24], [70, 70], [20, 76], [47, 14], [90, 34], [57, 72], [93, 73], [76, 57], [70, 10], [88, 20], [14, 87], [37, 38], [26, 44], [47, 29], [87, 93], [32, 88], [83, 70], [52, 49], [57, 56], [34, 18], [22, 37], [94, 59], [65, 28], [45, 5], [93, 91], [27, 86], [37, 87], [52, 34], [47, 87], [53, 18], [20, 56], [94, 51], [89, 53]], "components": [[0, 4, 13, 42, 55, 73, 86, 88, 92, 102], [1, 6, 56, 59, 62, 71, 80, 93], [2, 69], [3, 12, 15, 24, 45, 75, 78, 97, 98, 104], [5, 16, 32, 38, 41, 63, 66, 70, 87, 105], [7, 22, 25, 28, 35, 39, 40, 48, 57, 107], [8, 53, 67, 74, 81, 91], [9, 21, 61, 64, 94], [10, 11, 14, 68, 103], [17, 54, 89, 99], [18, 37, 72, 83], [19, 30, 31, 44, 50, 58, 77, 85], [20, 27, 33, 47, 79, 84], [23, 95], [26, 46, 51, 90, 100, 101], [29, 49], [34, 65, 76, 82], [36, 43], [52, 60], [96, 106]], "edges": [[7, 39], [4, 92], [96, 106], [26, 90], [89, 99], [9, 94], [26, 100], [71, 93], [18, 83], [48, 57], [62, 71], [55, 102], [36, 43], [20, 47], [28, 107], [34, 82], [46, 51], [55, 92], [15, 98], [38, 105], [88, 102], [41, 63], [24, 75], [9, 61], [35, 40], [34, 76], [53, 81], [44, 77], [39, 48], [74, 81], [54, 89], [10, 68], [73, 88], [44, 85], [78, 104], [20, 33], [5, 105], [25, 107], [78, 98], [32, 66], [22, 28], [16, 38], [7, 25], [42, 92], [0, 13], [6, 59], [6, 80], [65, 76], [63, 70], [51, 100], [18, 37], [72, 83], [67, 91], [3, 45], [75, 104], [61, 64], [13, 86], [12, 97], [5, 66], [21, 64], [12, 45], [2, 69], [47, 79], [35, 57], [1, 59], [5, 41], [11, 103], [6, 62], [68, 103], [38, 87], [56, 59], [0, 73], [50, 85], [31, 77], [75, 97], [30, 58], [53, 91], [47, 84], [19, 85], [52, 60], [27, 84], [10, 14], [17, 54], [29, 49], [90, 101], [19, 58], [8, 53], [23, 95], [0, 86], [18, 72], [42, 55], [35, 39], [37, 83], [4, 42], [0, 88], [9, 64], [10, 103], [8, 81], [55, 73], [41, 70], [33, 47], [19, 44], [7, 40], [90, 100], [14, 103], [39, 57]], "dot_radius": 1.5, "image": "images/counting_connected_components_00004.png"} |
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