-------
(13, 3072, 8) ALL distance distributions for EXTERNAL point
(8, 3072, 8) has 0 possible DDs: {}
(9, 3072, 8) has 1 possible DDs: {[0, 108, 0, 1008, 0, 1512, 0, 432, 0, 12]}
(10, 3072, 8) has 7 possible DDs: {[0, 54, 54, 504, 504, 756, 756, 216, 216, 6, 6], [0, 55, 45, 540, 420, 882, 630, 300, 180, 15, 5], [0, 56, 36, 576, 336, 1008, 504, 384, 144, 24, 4], [0, 57, 27, 612, 252, 1134, 378, 468, 108, 33, 3], [0, 58, 18, 648, 168, 1260, 252, 552, 72, 42, 2], [0, 59, 9, 684, 84, 1386, 126, 636, 36, 51, 1], [0, 60, 0, 720, 0, 1512, 0, 720, 0, 60, 0]}
(11, 3072, 8) has 42 possible DDs: {[0, 22, 98, 108, 888, 84, 1260, 192, 312, 102, 2, 4], [0, 22, 99, 99, 924, 0, 1386, 66, 396, 66, 11, 3], [0, 23, 89, 144, 804, 210, 1134, 276, 276, 111, 1, 4], [0, 23, 90, 135, 840, 126, 1260, 150, 360, 75, 10, 3], [0, 23, 91, 126, 876, 42, 1386, 24, 444, 39, 19, 2], [0, 24, 80, 180, 720, 336, 1008, 360, 240, 120, 0, 4], [0, 24, 81, 171, 756, 252, 1134, 234, 324, 84, 9, 3], [0, 24, 82, 162, 792, 168, 1260, 108, 408, 48, 18, 2], [0, 25, 72, 207, 672, 378, 1008, 318, 288, 93, 8, 3], [0, 25, 73, 198, 708, 294, 1134, 192, 372, 57, 17, 2], [0, 25, 74, 189, 744, 210, 1260, 66, 456, 21, 26, 1], [0, 26, 63, 243, 588, 504, 882, 402, 252, 102, 7, 3], [0, 26, 64, 234, 624, 420, 1008, 276, 336, 66, 16, 2], [0, 26, 65, 225, 660, 336, 1134, 150, 420, 30, 25, 1], [0, 27, 54, 279, 504, 630, 756, 486, 216, 111, 6, 3], [0, 27, 55, 270, 540, 546, 882, 360, 300, 75, 15, 2], [0, 27, 56, 261, 576, 462, 1008, 234, 384, 39, 24, 1], [0, 27, 57, 252, 612, 378, 1134, 108, 468, 3, 33, 0], [0, 28, 45, 315, 420, 756, 630, 570, 180, 120, 5, 3], [0, 28, 46, 306, 456, 672, 756, 444, 264, 84, 14, 2], [0, 28, 47, 297, 492, 588, 882, 318, 348, 48, 23, 1], [0, 28, 48, 288, 528, 504, 1008, 192, 432, 12, 32, 0], [0, 29, 36, 351, 336, 882, 504, 654, 144, 129, 4, 3], [0, 29, 37, 342, 372, 798, 630, 528, 228, 93, 13, 2], [0, 29, 38, 333, 408, 714, 756, 402, 312, 57, 22, 1], [0, 29, 39, 324, 444, 630, 882, 276, 396, 21, 31, 0], [0, 30, 27, 387, 252, 1008, 378, 738, 108, 138, 3, 3], [0, 30, 28, 378, 288, 924, 504, 612, 192, 102, 12, 2], [0, 30, 29, 369, 324, 840, 630, 486, 276, 66, 21, 1], [0, 30, 30, 360, 360, 756, 756, 360, 360, 30, 30, 0], [0, 31, 18, 423, 168, 1134, 252, 822, 72, 147, 2, 3], [0, 31, 19, 414, 204, 1050, 378, 696, 156, 111, 11, 2], [0, 31, 20, 405, 240, 966, 504, 570, 240, 75, 20, 1], [0, 31, 21, 396, 276, 882, 630, 444, 324, 39, 29, 0], [0, 32, 9, 459, 84, 1260, 126, 906, 36, 156, 1, 3], [0, 32, 10, 450, 120, 1176, 252, 780, 120, 120, 10, 2], [0, 32, 11, 441, 156, 1092, 378, 654, 204, 84, 19, 1], [0, 32, 12, 432, 192, 1008, 504, 528, 288, 48, 28, 0], [0, 33, 0, 495, 0, 1386, 0, 990, 0, 165, 0, 3], [0, 33, 1, 486, 36, 1302, 126, 864, 84, 129, 9, 2], [0, 33, 2, 477, 72, 1218, 252, 738, 168, 93, 18, 1], [0, 33, 3, 468, 108, 1134, 378, 612, 252, 57, 27, 0]}
(12, 3072, 8) has 203 possible DDs: {[0, 7, 90, 12, 627, 450, 504, 1020, 18, 303, 38, 0, 3], [0, 8, 83, 31, 606, 444, 546, 978, 24, 324, 19, 7, 2], [0, 8, 84, 22, 642, 360, 672, 852, 108, 288, 28, 6, 2], [0, 8, 85, 13, 678, 276, 798, 726, 192, 252, 37, 5, 2], [0, 8, 85, 14, 669, 312, 714, 852, 66, 336, 1, 14, 1], [0, 8, 86, 4, 714, 192, 924, 600, 276, 216, 46, 4, 2], [0, 8, 86, 5, 705, 228, 840, 726, 150, 300, 10, 13, 1], [0, 9, 75, 58, 558, 486, 546, 936, 72, 297, 27, 6, 2], [0, 9, 76, 49, 594, 402, 672, 810, 156, 261, 36, 5, 2], [0, 9, 76, 50, 585, 438, 588, 936, 30, 345, 0, 14, 1], [0, 9, 77, 40, 630, 318, 798, 684, 240, 225, 45, 4, 2], [0, 9, 77, 41, 621, 354, 714, 810, 114, 309, 9, 13, 1], [0, 9, 78, 31, 666, 234, 924, 558, 324, 189, 54, 3, 2], [0, 9, 78, 32, 657, 270, 840, 684, 198, 273, 18, 12, 1], [0, 9, 79, 22, 702, 150, 1050, 432, 408, 153, 63, 2, 2], [0, 9, 79, 23, 693, 186, 966, 558, 282, 237, 27, 11, 1], [0, 9, 80, 13, 738, 66, 1176, 306, 492, 117, 72, 1, 2], [0, 9, 80, 14, 729, 102, 1092, 432, 366, 201, 36, 10, 1], [0, 9, 80, 15, 720, 138, 1008, 558, 240, 285, 0, 19, 0], [0, 9, 81, 5, 765, 18, 1218, 306, 450, 165, 45, 9, 1], [0, 9, 81, 6, 756, 54, 1134, 432, 324, 249, 9, 18, 0], [0, 10, 66, 94, 474, 612, 420, 1020, 36, 306, 26, 6, 2], [0, 10, 67, 85, 510, 528, 546, 894, 120, 270, 35, 5, 2], [0, 10, 68, 76, 546, 444, 672, 768, 204, 234, 44, 4, 2], [0, 10, 68, 77, 537, 480, 588, 894, 78, 318, 8, 13, 1], [0, 10, 69, 67, 582, 360, 798, 642, 288, 198, 53, 3, 2], [0, 10, 69, 68, 573, 396, 714, 768, 162, 282, 17, 12, 1], [0, 10, 70, 58, 618, 276, 924, 516, 372, 162, 62, 2, 2], [0, 10, 70, 59, 609, 312, 840, 642, 246, 246, 26, 11, 1], [0, 10, 71, 49, 654, 192, 1050, 390, 456, 126, 71, 1, 2], [0, 10, 71, 50, 645, 228, 966, 516, 330, 210, 35, 10, 1], [0, 10, 72, 40, 690, 108, 1176, 264, 540, 90, 80, 0, 2], [0, 10, 72, 41, 681, 144, 1092, 390, 414, 174, 44, 9, 1], [0, 10, 72, 42, 672, 180, 1008, 516, 288, 258, 8, 18, 0], [0, 10, 73, 32, 717, 60, 1218, 264, 498, 138, 53, 8, 1], [0, 10, 73, 33, 708, 96, 1134, 390, 372, 222, 17, 17, 0], [0, 10, 74, 24, 744, 12, 1260, 264, 456, 186, 26, 16, 0], [0, 11, 57, 130, 390, 738, 294, 1104, 0, 315, 25, 6, 2], [0, 11, 58, 121, 426, 654, 420, 978, 84, 279, 34, 5, 2], [0, 11, 59, 112, 462, 570, 546, 852, 168, 243, 43, 4, 2], [0, 11, 59, 113, 453, 606, 462, 978, 42, 327, 7, 13, 1], [0, 11, 60, 103, 498, 486, 672, 726, 252, 207, 52, 3, 2], [0, 11, 60, 104, 489, 522, 588, 852, 126, 291, 16, 12, 1], [0, 11, 61, 94, 534, 402, 798, 600, 336, 171, 61, 2, 2], [0, 11, 61, 95, 525, 438, 714, 726, 210, 255, 25, 11, 1], [0, 11, 62, 85, 570, 318, 924, 474, 420, 135, 70, 1, 2], [0, 11, 62, 86, 561, 354, 840, 600, 294, 219, 34, 10, 1], [0, 11, 63, 76, 606, 234, 1050, 348, 504, 99, 79, 0, 2], [0, 11, 63, 77, 597, 270, 966, 474, 378, 183, 43, 9, 1], [0, 11, 63, 78, 588, 306, 882, 600, 252, 267, 7, 18, 0], [0, 11, 64, 68, 633, 186, 1092, 348, 462, 147, 52, 8, 1], [0, 11, 64, 69, 624, 222, 1008, 474, 336, 231, 16, 17, 0], [0, 11, 65, 59, 669, 102, 1218, 222, 546, 111, 61, 7, 1], [0, 11, 65, 60, 660, 138, 1134, 348, 420, 195, 25, 16, 0], [0, 11, 66, 50, 705, 18, 1344, 96, 630, 75, 70, 6, 1], [0, 11, 66, 51, 696, 54, 1260, 222, 504, 159, 34, 15, 0], [0, 12, 49, 157, 342, 780, 294, 1062, 48, 288, 33, 5, 2], [0, 12, 50, 148, 378, 696, 420, 936, 132, 252, 42, 4, 2], [0, 12, 50, 149, 369, 732, 336, 1062, 6, 336, 6, 13, 1], [0, 12, 51, 139, 414, 612, 546, 810, 216, 216, 51, 3, 2], [0, 12, 51, 140, 405, 648, 462, 936, 90, 300, 15, 12, 1], [0, 12, 52, 130, 450, 528, 672, 684, 300, 180, 60, 2, 2], [0, 12, 52, 131, 441, 564, 588, 810, 174, 264, 24, 11, 1], [0, 12, 53, 121, 486, 444, 798, 558, 384, 144, 69, 1, 2], [0, 12, 53, 122, 477, 480, 714, 684, 258, 228, 33, 10, 1], [0, 12, 54, 112, 522, 360, 924, 432, 468, 108, 78, 0, 2], [0, 12, 54, 113, 513, 396, 840, 558, 342, 192, 42, 9, 1], [0, 12, 54, 114, 504, 432, 756, 684, 216, 276, 6, 18, 0], [0, 12, 55, 104, 549, 312, 966, 432, 426, 156, 51, 8, 1], [0, 12, 55, 105, 540, 348, 882, 558, 300, 240, 15, 17, 0], [0, 12, 56, 95, 585, 228, 1092, 306, 510, 120, 60, 7, 1], [0, 12, 56, 96, 576, 264, 1008, 432, 384, 204, 24, 16, 0], [0, 12, 57, 86, 621, 144, 1218, 180, 594, 84, 69, 6, 1], [0, 12, 57, 87, 612, 180, 1134, 306, 468, 168, 33, 15, 0], [0, 12, 58, 77, 657, 60, 1344, 54, 678, 48, 78, 5, 1], [0, 12, 58, 78, 648, 96, 1260, 180, 552, 132, 42, 14, 0], [0, 12, 59, 69, 684, 12, 1386, 54, 636, 96, 51, 13, 0], [0, 13, 40, 193, 258, 906, 168, 1146, 12, 297, 32, 5, 2], [0, 13, 41, 184, 294, 822, 294, 1020, 96, 261, 41, 4, 2], [0, 13, 42, 175, 330, 738, 420, 894, 180, 225, 50, 3, 2], [0, 13, 42, 176, 321, 774, 336, 1020, 54, 309, 14, 12, 1], [0, 13, 43, 166, 366, 654, 546, 768, 264, 189, 59, 2, 2], [0, 13, 43, 167, 357, 690, 462, 894, 138, 273, 23, 11, 1], [0, 13, 44, 157, 402, 570, 672, 642, 348, 153, 68, 1, 2], [0, 13, 44, 158, 393, 606, 588, 768, 222, 237, 32, 10, 1], [0, 13, 45, 148, 438, 486, 798, 516, 432, 117, 77, 0, 2], [0, 13, 45, 149, 429, 522, 714, 642, 306, 201, 41, 9, 1], [0, 13, 45, 150, 420, 558, 630, 768, 180, 285, 5, 18, 0], [0, 13, 46, 140, 465, 438, 840, 516, 390, 165, 50, 8, 1], [0, 13, 46, 141, 456, 474, 756, 642, 264, 249, 14, 17, 0], [0, 13, 47, 131, 501, 354, 966, 390, 474, 129, 59, 7, 1], [0, 13, 47, 132, 492, 390, 882, 516, 348, 213, 23, 16, 0], [0, 13, 48, 122, 537, 270, 1092, 264, 558, 93, 68, 6, 1], [0, 13, 48, 123, 528, 306, 1008, 390, 432, 177, 32, 15, 0], [0, 13, 49, 113, 573, 186, 1218, 138, 642, 57, 77, 5, 1], [0, 13, 49, 114, 564, 222, 1134, 264, 516, 141, 41, 14, 0], [0, 13, 50, 104, 609, 102, 1344, 12, 726, 21, 86, 4, 1], [0, 13, 50, 105, 600, 138, 1260, 138, 600, 105, 50, 13, 0], [0, 13, 51, 96, 636, 54, 1386, 12, 684, 69, 59, 12, 0], [0, 14, 32, 220, 210, 948, 168, 1104, 60, 270, 40, 4, 2], [0, 14, 33, 211, 246, 864, 294, 978, 144, 234, 49, 3, 2], [0, 14, 33, 212, 237, 900, 210, 1104, 18, 318, 13, 12, 1], [0, 14, 34, 202, 282, 780, 420, 852, 228, 198, 58, 2, 2], [0, 14, 34, 203, 273, 816, 336, 978, 102, 282, 22, 11, 1], [0, 14, 35, 193, 318, 696, 546, 726, 312, 162, 67, 1, 2], [0, 14, 35, 194, 309, 732, 462, 852, 186, 246, 31, 10, 1], [0, 14, 36, 184, 354, 612, 672, 600, 396, 126, 76, 0, 2], [0, 14, 36, 185, 345, 648, 588, 726, 270, 210, 40, 9, 1], [0, 14, 36, 186, 336, 684, 504, 852, 144, 294, 4, 18, 0], [0, 14, 37, 176, 381, 564, 714, 600, 354, 174, 49, 8, 1], [0, 14, 37, 177, 372, 600, 630, 726, 228, 258, 13, 17, 0], [0, 14, 38, 167, 417, 480, 840, 474, 438, 138, 58, 7, 1], [0, 14, 38, 168, 408, 516, 756, 600, 312, 222, 22, 16, 0], [0, 14, 39, 158, 453, 396, 966, 348, 522, 102, 67, 6, 1], [0, 14, 39, 159, 444, 432, 882, 474, 396, 186, 31, 15, 0], [0, 14, 40, 149, 489, 312, 1092, 222, 606, 66, 76, 5, 1], [0, 14, 40, 150, 480, 348, 1008, 348, 480, 150, 40, 14, 0], [0, 14, 41, 140, 525, 228, 1218, 96, 690, 30, 85, 4, 1], [0, 14, 41, 141, 516, 264, 1134, 222, 564, 114, 49, 13, 0], [0, 14, 42, 132, 552, 180, 1260, 96, 648, 78, 58, 12, 0], [0, 15, 23, 256, 126, 1074, 42, 1188, 24, 279, 39, 4, 2], [0, 15, 24, 247, 162, 990, 168, 1062, 108, 243, 48, 3, 2], [0, 15, 25, 238, 198, 906, 294, 936, 192, 207, 57, 2, 2], [0, 15, 25, 239, 189, 942, 210, 1062, 66, 291, 21, 11, 1], [0, 15, 26, 229, 234, 822, 420, 810, 276, 171, 66, 1, 2], [0, 15, 26, 230, 225, 858, 336, 936, 150, 255, 30, 10, 1], [0, 15, 27, 220, 270, 738, 546, 684, 360, 135, 75, 0, 2], [0, 15, 27, 221, 261, 774, 462, 810, 234, 219, 39, 9, 1], [0, 15, 27, 222, 252, 810, 378, 936, 108, 303, 3, 18, 0], [0, 15, 28, 212, 297, 690, 588, 684, 318, 183, 48, 8, 1], [0, 15, 28, 213, 288, 726, 504, 810, 192, 267, 12, 17, 0], [0, 15, 29, 203, 333, 606, 714, 558, 402, 147, 57, 7, 1], [0, 15, 29, 204, 324, 642, 630, 684, 276, 231, 21, 16, 0], [0, 15, 30, 194, 369, 522, 840, 432, 486, 111, 66, 6, 1], [0, 15, 30, 195, 360, 558, 756, 558, 360, 195, 30, 15, 0], [0, 15, 31, 185, 405, 438, 966, 306, 570, 75, 75, 5, 1], [0, 15, 31, 186, 396, 474, 882, 432, 444, 159, 39, 14, 0], [0, 15, 32, 176, 441, 354, 1092, 180, 654, 39, 84, 4, 1], [0, 15, 32, 177, 432, 390, 1008, 306, 528, 123, 48, 13, 0], [0, 15, 33, 167, 477, 270, 1218, 54, 738, 3, 93, 3, 1], [0, 15, 33, 168, 468, 306, 1134, 180, 612, 87, 57, 12, 0], [0, 15, 34, 159, 504, 222, 1260, 54, 696, 51, 66, 11, 0], [0, 16, 15, 283, 78, 1116, 42, 1146, 72, 252, 47, 3, 2], [0, 16, 16, 274, 114, 1032, 168, 1020, 156, 216, 56, 2, 2], [0, 16, 16, 275, 105, 1068, 84, 1146, 30, 300, 20, 11, 1], [0, 16, 17, 265, 150, 948, 294, 894, 240, 180, 65, 1, 2], [0, 16, 17, 266, 141, 984, 210, 1020, 114, 264, 29, 10, 1], [0, 16, 18, 256, 186, 864, 420, 768, 324, 144, 74, 0, 2], [0, 16, 18, 257, 177, 900, 336, 894, 198, 228, 38, 9, 1], [0, 16, 18, 258, 168, 936, 252, 1020, 72, 312, 2, 18, 0], [0, 16, 19, 248, 213, 816, 462, 768, 282, 192, 47, 8, 1], [0, 16, 19, 249, 204, 852, 378, 894, 156, 276, 11, 17, 0], [0, 16, 20, 239, 249, 732, 588, 642, 366, 156, 56, 7, 1], [0, 16, 20, 240, 240, 768, 504, 768, 240, 240, 20, 16, 0], [0, 16, 21, 230, 285, 648, 714, 516, 450, 120, 65, 6, 1], [0, 16, 21, 231, 276, 684, 630, 642, 324, 204, 29, 15, 0], [0, 16, 22, 221, 321, 564, 840, 390, 534, 84, 74, 5, 1], [0, 16, 22, 222, 312, 600, 756, 516, 408, 168, 38, 14, 0], [0, 16, 23, 212, 357, 480, 966, 264, 618, 48, 83, 4, 1], [0, 16, 23, 213, 348, 516, 882, 390, 492, 132, 47, 13, 0], [0, 16, 24, 203, 393, 396, 1092, 138, 702, 12, 92, 3, 1], [0, 16, 24, 204, 384, 432, 1008, 264, 576, 96, 56, 12, 0], [0, 16, 25, 195, 420, 348, 1134, 138, 660, 60, 65, 11, 0], [0, 16, 26, 186, 456, 264, 1260, 12, 744, 24, 74, 10, 0], [0, 17, 7, 310, 30, 1158, 42, 1104, 120, 225, 55, 2, 2], [0, 17, 8, 301, 66, 1074, 168, 978, 204, 189, 64, 1, 2], [0, 17, 8, 302, 57, 1110, 84, 1104, 78, 273, 28, 10, 1], [0, 17, 9, 292, 102, 990, 294, 852, 288, 153, 73, 0, 2], [0, 17, 9, 293, 93, 1026, 210, 978, 162, 237, 37, 9, 1], [0, 17, 9, 294, 84, 1062, 126, 1104, 36, 321, 1, 18, 0], [0, 17, 10, 284, 129, 942, 336, 852, 246, 201, 46, 8, 1], [0, 17, 10, 285, 120, 978, 252, 978, 120, 285, 10, 17, 0], [0, 17, 11, 275, 165, 858, 462, 726, 330, 165, 55, 7, 1], [0, 17, 11, 276, 156, 894, 378, 852, 204, 249, 19, 16, 0], [0, 17, 12, 266, 201, 774, 588, 600, 414, 129, 64, 6, 1], [0, 17, 12, 267, 192, 810, 504, 726, 288, 213, 28, 15, 0], [0, 17, 13, 257, 237, 690, 714, 474, 498, 93, 73, 5, 1], [0, 17, 13, 258, 228, 726, 630, 600, 372, 177, 37, 14, 0], [0, 17, 14, 248, 273, 606, 840, 348, 582, 57, 82, 4, 1], [0, 17, 14, 249, 264, 642, 756, 474, 456, 141, 46, 13, 0], [0, 17, 15, 239, 309, 522, 966, 222, 666, 21, 91, 3, 1], [0, 17, 15, 240, 300, 558, 882, 348, 540, 105, 55, 12, 0], [0, 17, 16, 231, 336, 474, 1008, 222, 624, 69, 64, 11, 0], [0, 17, 17, 222, 372, 390, 1134, 96, 708, 33, 73, 10, 0], [0, 18, 0, 328, 18, 1116, 168, 936, 252, 162, 72, 0, 2], [0, 18, 0, 329, 9, 1152, 84, 1062, 126, 246, 36, 9, 1], [0, 18, 0, 330, 0, 1188, 0, 1188, 0, 330, 0, 18, 0], [0, 18, 1, 320, 45, 1068, 210, 936, 210, 210, 45, 8, 1], [0, 18, 1, 321, 36, 1104, 126, 1062, 84, 294, 9, 17, 0], [0, 18, 2, 311, 81, 984, 336, 810, 294, 174, 54, 7, 1], [0, 18, 2, 312, 72, 1020, 252, 936, 168, 258, 18, 16, 0], [0, 18, 3, 302, 117, 900, 462, 684, 378, 138, 63, 6, 1], [0, 18, 3, 303, 108, 936, 378, 810, 252, 222, 27, 15, 0], [0, 18, 4, 293, 153, 816, 588, 558, 462, 102, 72, 5, 1], [0, 18, 4, 294, 144, 852, 504, 684, 336, 186, 36, 14, 0], [0, 18, 5, 284, 189, 732, 714, 432, 546, 66, 81, 4, 1], [0, 18, 5, 285, 180, 768, 630, 558, 420, 150, 45, 13, 0], [0, 18, 6, 275, 225, 648, 840, 306, 630, 30, 90, 3, 1], [0, 18, 6, 276, 216, 684, 756, 432, 504, 114, 54, 12, 0], [0, 18, 7, 267, 252, 600, 882, 306, 588, 78, 63, 11, 0], [0, 18, 8, 258, 288, 516, 1008, 180, 672, 42, 72, 10, 0], [0, 18, 9, 249, 324, 432, 1134, 54, 756, 6, 81, 9, 0], [0, 19, 0, 285, 240, 558, 1008, 138, 720, 15, 80, 9, 0]}
(13, 3072, 8) has 886 possible DDs: {[0, 0, 70, 10, 298, 762, 60, 1140, 372, 132, 222, 2, 2, 2], [0, 0, 71, 1, 334, 678, 186, 1014, 456, 96, 231, 1, 2, 2], [0, 0, 71, 2, 325, 714, 102, 1140, 330, 180, 195, 10, 1, 2], [0, 0, 71, 3, 316, 750, 18, 1266, 204, 264, 159, 19, 0, 2], [0, 1, 62, 37, 250, 804, 60, 1098, 420, 105, 230, 1, 2, 2], [0, 1, 63, 28, 286, 720, 186, 972, 504, 69, 239, 0, 2, 2], [0, 1, 63, 29, 277, 756, 102, 1098, 378, 153, 203, 9, 1, 2], [0, 1, 63, 30, 268, 792, 18, 1224, 252, 237, 167, 18, 0, 2], [0, 1, 64, 20, 313, 672, 228, 972, 462, 117, 212, 8, 1, 2], [0, 1, 64, 21, 304, 708, 144, 1098, 336, 201, 176, 17, 0, 2], [0, 1, 65, 11, 349, 588, 354, 846, 546, 81, 221, 7, 1, 2], [0, 1, 65, 12, 340, 624, 270, 972, 420, 165, 185, 16, 0, 2], [0, 1, 65, 15, 314, 723, 54, 1266, 168, 291, 161, 7, 6, 1], [0, 1, 66, 2, 385, 504, 480, 720, 630, 45, 230, 6, 1, 2], [0, 1, 66, 3, 376, 540, 396, 846, 504, 129, 194, 15, 0, 2], [0, 1, 66, 6, 350, 639, 180, 1140, 252, 255, 170, 6, 6, 1], [0, 1, 66, 7, 341, 675, 96, 1266, 126, 339, 134, 15, 5, 1], [0, 1, 66, 8, 332, 711, 12, 1392, 0, 423, 98, 24, 4, 1], [0, 2, 54, 64, 202, 846, 60, 1056, 468, 78, 238, 0, 2, 2], [0, 2, 55, 56, 229, 798, 102, 1056, 426, 126, 211, 8, 1, 2], [0, 2, 55, 57, 220, 834, 18, 1182, 300, 210, 175, 17, 0, 2], [0, 2, 56, 47, 265, 714, 228, 930, 510, 90, 220, 7, 1, 2], [0, 2, 56, 48, 256, 750, 144, 1056, 384, 174, 184, 16, 0, 2], [0, 2, 57, 38, 301, 630, 354, 804, 594, 54, 229, 6, 1, 2], [0, 2, 57, 39, 292, 666, 270, 930, 468, 138, 193, 15, 0, 2], [0, 2, 57, 42, 266, 765, 54, 1224, 216, 264, 169, 6, 6, 1], [0, 2, 58, 29, 337, 546, 480, 678, 678, 18, 238, 5, 1, 2], [0, 2, 58, 30, 328, 582, 396, 804, 552, 102, 202, 14, 0, 2], [0, 2, 58, 33, 302, 681, 180, 1098, 300, 228, 178, 5, 6, 1], [0, 2, 58, 34, 293, 717, 96, 1224, 174, 312, 142, 14, 5, 1], [0, 2, 58, 35, 284, 753, 12, 1350, 48, 396, 106, 23, 4, 1], [0, 2, 59, 21, 364, 498, 522, 678, 636, 66, 211, 13, 0, 2], [0, 2, 59, 24, 338, 597, 306, 972, 384, 192, 187, 4, 6, 1], [0, 2, 59, 25, 329, 633, 222, 1098, 258, 276, 151, 13, 5, 1], [0, 2, 59, 26, 320, 669, 138, 1224, 132, 360, 115, 22, 4, 1], [0, 2, 59, 27, 311, 705, 54, 1350, 6, 444, 79, 31, 3, 1], [0, 2, 59, 28, 303, 732, 6, 1392, 6, 402, 127, 4, 11, 0], [0, 2, 60, 12, 400, 414, 648, 552, 720, 30, 220, 12, 0, 2], [0, 2, 60, 15, 374, 513, 432, 846, 468, 156, 196, 3, 6, 1], [0, 2, 60, 16, 365, 549, 348, 972, 342, 240, 160, 12, 5, 1], [0, 2, 60, 17, 356, 585, 264, 1098, 216, 324, 124, 21, 4, 1], [0, 2, 60, 18, 347, 621, 180, 1224, 90, 408, 88, 30, 3, 1], [0, 2, 60, 19, 339, 648, 132, 1266, 90, 366, 136, 3, 11, 0], [0, 2, 61, 6, 410, 429, 558, 720, 552, 120, 205, 2, 6, 1], [0, 2, 61, 7, 401, 465, 474, 846, 426, 204, 169, 11, 5, 1], [0, 2, 61, 8, 392, 501, 390, 972, 300, 288, 133, 20, 4, 1], [0, 2, 61, 9, 383, 537, 306, 1098, 174, 372, 97, 29, 3, 1], [0, 2, 61, 10, 374, 573, 222, 1224, 48, 456, 61, 38, 2, 1], [0, 2, 61, 10, 375, 564, 258, 1140, 174, 330, 145, 2, 11, 0], [0, 2, 61, 11, 366, 600, 174, 1266, 48, 414, 109, 11, 10, 0], [0, 2, 62, 0, 419, 453, 432, 972, 258, 336, 106, 28, 3, 1], [0, 2, 62, 1, 410, 489, 348, 1098, 132, 420, 70, 37, 2, 1], [0, 2, 62, 1, 411, 480, 384, 1014, 258, 294, 154, 1, 11, 0], [0, 2, 62, 2, 401, 525, 264, 1224, 6, 504, 34, 46, 1, 1], [0, 2, 62, 2, 402, 516, 300, 1140, 132, 378, 118, 10, 10, 0], [0, 2, 62, 3, 393, 552, 216, 1266, 6, 462, 82, 19, 9, 0], [0, 3, 47, 83, 181, 840, 102, 1014, 474, 99, 219, 7, 1, 2], [0, 3, 47, 84, 172, 876, 18, 1140, 348, 183, 183, 16, 0, 2], [0, 3, 48, 74, 217, 756, 228, 888, 558, 63, 228, 6, 1, 2], [0, 3, 48, 75, 208, 792, 144, 1014, 432, 147, 192, 15, 0, 2], [0, 3, 49, 65, 253, 672, 354, 762, 642, 27, 237, 5, 1, 2], [0, 3, 49, 66, 244, 708, 270, 888, 516, 111, 201, 14, 0, 2], [0, 3, 49, 69, 218, 807, 54, 1182, 264, 237, 177, 5, 6, 1], [0, 3, 50, 57, 280, 624, 396, 762, 600, 75, 210, 13, 0, 2], [0, 3, 50, 60, 254, 723, 180, 1056, 348, 201, 186, 4, 6, 1], [0, 3, 50, 61, 245, 759, 96, 1182, 222, 285, 150, 13, 5, 1], [0, 3, 50, 62, 236, 795, 12, 1308, 96, 369, 114, 22, 4, 1], [0, 3, 51, 48, 316, 540, 522, 636, 684, 39, 219, 12, 0, 2], [0, 3, 51, 51, 290, 639, 306, 930, 432, 165, 195, 3, 6, 1], [0, 3, 51, 52, 281, 675, 222, 1056, 306, 249, 159, 12, 5, 1], [0, 3, 51, 53, 272, 711, 138, 1182, 180, 333, 123, 21, 4, 1], [0, 3, 51, 54, 263, 747, 54, 1308, 54, 417, 87, 30, 3, 1], [0, 3, 51, 55, 255, 774, 6, 1350, 54, 375, 135, 3, 11, 0], [0, 3, 52, 39, 352, 456, 648, 510, 768, 3, 228, 11, 0, 2], [0, 3, 52, 42, 326, 555, 432, 804, 516, 129, 204, 2, 6, 1], [0, 3, 52, 43, 317, 591, 348, 930, 390, 213, 168, 11, 5, 1], [0, 3, 52, 44, 308, 627, 264, 1056, 264, 297, 132, 20, 4, 1], [0, 3, 52, 45, 299, 663, 180, 1182, 138, 381, 96, 29, 3, 1], [0, 3, 52, 46, 290, 699, 96, 1308, 12, 465, 60, 38, 2, 1], [0, 3, 52, 46, 291, 690, 132, 1224, 138, 339, 144, 2, 11, 0], [0, 3, 52, 47, 282, 726, 48, 1350, 12, 423, 108, 11, 10, 0], [0, 3, 53, 33, 362, 471, 558, 678, 600, 93, 213, 1, 6, 1], [0, 3, 53, 34, 353, 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159, 17, 4, 1], [0, 3, 55, 18, 407, 411, 558, 804, 390, 273, 123, 26, 3, 1], [0, 3, 55, 19, 398, 447, 474, 930, 264, 357, 87, 35, 2, 1], [0, 3, 55, 20, 389, 483, 390, 1056, 138, 441, 51, 44, 1, 1], [0, 3, 55, 20, 390, 474, 426, 972, 264, 315, 135, 8, 10, 0], [0, 3, 55, 21, 380, 519, 306, 1182, 12, 525, 15, 53, 0, 1], [0, 3, 55, 21, 381, 510, 342, 1098, 138, 399, 99, 17, 9, 0], [0, 3, 55, 22, 372, 546, 258, 1224, 12, 483, 63, 26, 8, 0], [0, 3, 56, 7, 461, 255, 852, 426, 726, 69, 204, 7, 5, 1], [0, 3, 56, 8, 452, 291, 768, 552, 600, 153, 168, 16, 4, 1], [0, 3, 56, 9, 443, 327, 684, 678, 474, 237, 132, 25, 3, 1], [0, 3, 56, 10, 434, 363, 600, 804, 348, 321, 96, 34, 2, 1], [0, 3, 56, 11, 425, 399, 516, 930, 222, 405, 60, 43, 1, 1], [0, 3, 56, 11, 426, 390, 552, 846, 348, 279, 144, 7, 10, 0], [0, 3, 56, 12, 416, 435, 432, 1056, 96, 489, 24, 52, 0, 1], [0, 3, 56, 12, 417, 426, 468, 972, 222, 363, 108, 16, 9, 0], [0, 3, 56, 13, 408, 462, 384, 1098, 96, 447, 72, 25, 8, 0], [0, 3, 57, 0, 479, 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[0, 4, 42, 88, 197, 801, 96, 1140, 270, 258, 158, 12, 5, 1], [0, 4, 42, 89, 188, 837, 12, 1266, 144, 342, 122, 21, 4, 1], [0, 4, 43, 75, 268, 582, 522, 594, 732, 12, 227, 11, 0, 2], [0, 4, 43, 78, 242, 681, 306, 888, 480, 138, 203, 2, 6, 1], [0, 4, 43, 79, 233, 717, 222, 1014, 354, 222, 167, 11, 5, 1], [0, 4, 43, 80, 224, 753, 138, 1140, 228, 306, 131, 20, 4, 1], [0, 4, 43, 81, 215, 789, 54, 1266, 102, 390, 95, 29, 3, 1], [0, 4, 43, 82, 207, 816, 6, 1308, 102, 348, 143, 2, 11, 0], [0, 4, 44, 69, 278, 597, 432, 762, 564, 102, 212, 1, 6, 1], [0, 4, 44, 70, 269, 633, 348, 888, 438, 186, 176, 10, 5, 1], [0, 4, 44, 71, 260, 669, 264, 1014, 312, 270, 140, 19, 4, 1], [0, 4, 44, 72, 251, 705, 180, 1140, 186, 354, 104, 28, 3, 1], [0, 4, 44, 73, 242, 741, 96, 1266, 60, 438, 68, 37, 2, 1], [0, 4, 44, 73, 243, 732, 132, 1182, 186, 312, 152, 1, 11, 0], [0, 4, 44, 74, 234, 768, 48, 1308, 60, 396, 116, 10, 10, 0], [0, 4, 45, 60, 314, 513, 558, 636, 648, 66, 221, 0, 6, 1], [0, 4, 45, 61, 305, 549, 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