-------
(13, 2560, 8) ALL distance distributions for EXTERNAL point
(8, 2560, 8) has 0 possible DDs: {}
(9, 2560, 8) has 1 possible DDs: {[0, 90, 0, 840, 0, 1260, 0, 360, 0, 10]}
(10, 2560, 8) has 6 possible DDs: {[0, 45, 45, 420, 420, 630, 630, 180, 180, 5, 5], [0, 46, 36, 456, 336, 756, 504, 264, 144, 14, 4], [0, 47, 27, 492, 252, 882, 378, 348, 108, 23, 3], [0, 48, 18, 528, 168, 1008, 252, 432, 72, 32, 2], [0, 49, 9, 564, 84, 1134, 126, 516, 36, 41, 1], [0, 50, 0, 600, 0, 1260, 0, 600, 0, 50, 0]}
(11, 2560, 8) has 28 possible DDs: {[0, 18, 85, 75, 780, 0, 1134, 90, 300, 70, 5, 3], [0, 19, 76, 111, 696, 126, 1008, 174, 264, 79, 4, 3], [0, 19, 77, 102, 732, 42, 1134, 48, 348, 43, 13, 2], [0, 20, 67, 147, 612, 252, 882, 258, 228, 88, 3, 3], [0, 20, 68, 138, 648, 168, 1008, 132, 312, 52, 12, 2], [0, 20, 69, 129, 684, 84, 1134, 6, 396, 16, 21, 1], [0, 21, 58, 183, 528, 378, 756, 342, 192, 97, 2, 3], [0, 21, 59, 174, 564, 294, 882, 216, 276, 61, 11, 2], [0, 21, 60, 165, 600, 210, 1008, 90, 360, 25, 20, 1], [0, 22, 49, 219, 444, 504, 630, 426, 156, 106, 1, 3], [0, 22, 50, 210, 480, 420, 756, 300, 240, 70, 10, 2], [0, 22, 51, 201, 516, 336, 882, 174, 324, 34, 19, 1], [0, 23, 40, 255, 360, 630, 504, 510, 120, 115, 0, 3], [0, 23, 41, 246, 396, 546, 630, 384, 204, 79, 9, 2], [0, 23, 42, 237, 432, 462, 756, 258, 288, 43, 18, 1], [0, 23, 43, 228, 468, 378, 882, 132, 372, 7, 27, 0], [0, 24, 32, 282, 312, 672, 504, 468, 168, 88, 8, 2], [0, 24, 33, 273, 348, 588, 630, 342, 252, 52, 17, 1], [0, 24, 34, 264, 384, 504, 756, 216, 336, 16, 26, 0], [0, 25, 23, 318, 228, 798, 378, 552, 132, 97, 7, 2], [0, 25, 24, 309, 264, 714, 504, 426, 216, 61, 16, 1], [0, 25, 25, 300, 300, 630, 630, 300, 300, 25, 25, 0], [0, 26, 14, 354, 144, 924, 252, 636, 96, 106, 6, 2], [0, 26, 15, 345, 180, 840, 378, 510, 180, 70, 15, 1], [0, 26, 16, 336, 216, 756, 504, 384, 264, 34, 24, 0], [0, 27, 5, 390, 60, 1050, 126, 720, 60, 115, 5, 2], [0, 27, 6, 381, 96, 966, 252, 594, 144, 79, 14, 1], [0, 27, 7, 372, 132, 882, 378, 468, 228, 43, 23, 0]}
(12, 2560, 8) has 122 possible DDs: {[0, 6, 75, 3, 558, 288, 546, 738, 72, 242, 27, 3, 2], [0, 7, 66, 39, 474, 414, 420, 822, 36, 251, 26, 3, 2], [0, 7, 67, 30, 510, 330, 546, 696, 120, 215, 35, 2, 2], [0, 7, 68, 21, 546, 246, 672, 570, 204, 179, 44, 1, 2], [0, 7, 68, 22, 537, 282, 588, 696, 78, 263, 8, 10, 1], [0, 7, 69, 12, 582, 162, 798, 444, 288, 143, 53, 0, 2], [0, 7, 69, 13, 573, 198, 714, 570, 162, 227, 17, 9, 1], [0, 7, 70, 4, 609, 114, 840, 444, 246, 191, 26, 8, 1], [0, 8, 57, 75, 390, 540, 294, 906, 0, 260, 25, 3, 2], [0, 8, 58, 66, 426, 456, 420, 780, 84, 224, 34, 2, 2], [0, 8, 59, 57, 462, 372, 546, 654, 168, 188, 43, 1, 2], [0, 8, 59, 58, 453, 408, 462, 780, 42, 272, 7, 10, 1], [0, 8, 60, 48, 498, 288, 672, 528, 252, 152, 52, 0, 2], [0, 8, 60, 49, 489, 324, 588, 654, 126, 236, 16, 9, 1], [0, 8, 61, 40, 525, 240, 714, 528, 210, 200, 25, 8, 1], [0, 8, 62, 31, 561, 156, 840, 402, 294, 164, 34, 7, 1], [0, 8, 63, 22, 597, 72, 966, 276, 378, 128, 43, 6, 1], [0, 8, 63, 23, 588, 108, 882, 402, 252, 212, 7, 15, 0], [0, 8, 64, 14, 624, 24, 1008, 276, 336, 176, 16, 14, 0], [0, 9, 49, 102, 342, 582, 294, 864, 48, 233, 33, 2, 2], [0, 9, 50, 93, 378, 498, 420, 738, 132, 197, 42, 1, 2], [0, 9, 50, 94, 369, 534, 336, 864, 6, 281, 6, 10, 1], [0, 9, 51, 84, 414, 414, 546, 612, 216, 161, 51, 0, 2], [0, 9, 51, 85, 405, 450, 462, 738, 90, 245, 15, 9, 1], [0, 9, 52, 76, 441, 366, 588, 612, 174, 209, 24, 8, 1], [0, 9, 53, 67, 477, 282, 714, 486, 258, 173, 33, 7, 1], [0, 9, 54, 58, 513, 198, 840, 360, 342, 137, 42, 6, 1], [0, 9, 54, 59, 504, 234, 756, 486, 216, 221, 6, 15, 0], [0, 9, 55, 49, 549, 114, 966, 234, 426, 101, 51, 5, 1], [0, 9, 55, 50, 540, 150, 882, 360, 300, 185, 15, 14, 0], [0, 9, 56, 40, 585, 30, 1092, 108, 510, 65, 60, 4, 1], [0, 9, 56, 41, 576, 66, 1008, 234, 384, 149, 24, 13, 0], [0, 10, 40, 138, 258, 708, 168, 948, 12, 242, 32, 2, 2], [0, 10, 41, 129, 294, 624, 294, 822, 96, 206, 41, 1, 2], [0, 10, 42, 120, 330, 540, 420, 696, 180, 170, 50, 0, 2], [0, 10, 42, 121, 321, 576, 336, 822, 54, 254, 14, 9, 1], [0, 10, 43, 112, 357, 492, 462, 696, 138, 218, 23, 8, 1], [0, 10, 44, 103, 393, 408, 588, 570, 222, 182, 32, 7, 1], [0, 10, 45, 94, 429, 324, 714, 444, 306, 146, 41, 6, 1], [0, 10, 45, 95, 420, 360, 630, 570, 180, 230, 5, 15, 0], [0, 10, 46, 85, 465, 240, 840, 318, 390, 110, 50, 5, 1], [0, 10, 46, 86, 456, 276, 756, 444, 264, 194, 14, 14, 0], [0, 10, 47, 76, 501, 156, 966, 192, 474, 74, 59, 4, 1], [0, 10, 47, 77, 492, 192, 882, 318, 348, 158, 23, 13, 0], [0, 10, 48, 67, 537, 72, 1092, 66, 558, 38, 68, 3, 1], [0, 10, 48, 68, 528, 108, 1008, 192, 432, 122, 32, 12, 0], [0, 10, 49, 59, 564, 24, 1134, 66, 516, 86, 41, 11, 0], [0, 11, 32, 165, 210, 750, 168, 906, 60, 215, 40, 1, 2], [0, 11, 33, 156, 246, 666, 294, 780, 144, 179, 49, 0, 2], [0, 11, 33, 157, 237, 702, 210, 906, 18, 263, 13, 9, 1], [0, 11, 34, 148, 273, 618, 336, 780, 102, 227, 22, 8, 1], [0, 11, 35, 139, 309, 534, 462, 654, 186, 191, 31, 7, 1], [0, 11, 36, 130, 345, 450, 588, 528, 270, 155, 40, 6, 1], [0, 11, 36, 131, 336, 486, 504, 654, 144, 239, 4, 15, 0], [0, 11, 37, 121, 381, 366, 714, 402, 354, 119, 49, 5, 1], [0, 11, 37, 122, 372, 402, 630, 528, 228, 203, 13, 14, 0], [0, 11, 38, 112, 417, 282, 840, 276, 438, 83, 58, 4, 1], [0, 11, 38, 113, 408, 318, 756, 402, 312, 167, 22, 13, 0], [0, 11, 39, 103, 453, 198, 966, 150, 522, 47, 67, 3, 1], [0, 11, 39, 104, 444, 234, 882, 276, 396, 131, 31, 12, 0], [0, 11, 40, 94, 489, 114, 1092, 24, 606, 11, 76, 2, 1], [0, 11, 40, 95, 480, 150, 1008, 150, 480, 95, 40, 11, 0], [0, 11, 41, 86, 516, 66, 1134, 24, 564, 59, 49, 10, 0], [0, 12, 23, 201, 126, 876, 42, 990, 24, 224, 39, 1, 2], [0, 12, 24, 192, 162, 792, 168, 864, 108, 188, 48, 0, 2], [0, 12, 25, 184, 189, 744, 210, 864, 66, 236, 21, 8, 1], [0, 12, 26, 175, 225, 660, 336, 738, 150, 200, 30, 7, 1], [0, 12, 27, 166, 261, 576, 462, 612, 234, 164, 39, 6, 1], [0, 12, 27, 167, 252, 612, 378, 738, 108, 248, 3, 15, 0], [0, 12, 28, 157, 297, 492, 588, 486, 318, 128, 48, 5, 1], [0, 12, 28, 158, 288, 528, 504, 612, 192, 212, 12, 14, 0], [0, 12, 29, 148, 333, 408, 714, 360, 402, 92, 57, 4, 1], [0, 12, 29, 149, 324, 444, 630, 486, 276, 176, 21, 13, 0], [0, 12, 30, 139, 369, 324, 840, 234, 486, 56, 66, 3, 1], [0, 12, 30, 140, 360, 360, 756, 360, 360, 140, 30, 12, 0], [0, 12, 31, 130, 405, 240, 966, 108, 570, 20, 75, 2, 1], [0, 12, 31, 131, 396, 276, 882, 234, 444, 104, 39, 11, 0], [0, 12, 32, 122, 432, 192, 1008, 108, 528, 68, 48, 10, 0], [0, 13, 15, 228, 78, 918, 42, 948, 72, 197, 47, 0, 2], [0, 13, 16, 220, 105, 870, 84, 948, 30, 245, 20, 8, 1], [0, 13, 17, 211, 141, 786, 210, 822, 114, 209, 29, 7, 1], [0, 13, 18, 202, 177, 702, 336, 696, 198, 173, 38, 6, 1], [0, 13, 18, 203, 168, 738, 252, 822, 72, 257, 2, 15, 0], [0, 13, 19, 193, 213, 618, 462, 570, 282, 137, 47, 5, 1], [0, 13, 19, 194, 204, 654, 378, 696, 156, 221, 11, 14, 0], [0, 13, 20, 184, 249, 534, 588, 444, 366, 101, 56, 4, 1], [0, 13, 20, 185, 240, 570, 504, 570, 240, 185, 20, 13, 0], [0, 13, 21, 175, 285, 450, 714, 318, 450, 65, 65, 3, 1], [0, 13, 21, 176, 276, 486, 630, 444, 324, 149, 29, 12, 0], [0, 13, 22, 166, 321, 366, 840, 192, 534, 29, 74, 2, 1], [0, 13, 22, 167, 312, 402, 756, 318, 408, 113, 38, 11, 0], [0, 13, 23, 158, 348, 318, 882, 192, 492, 77, 47, 10, 0], [0, 13, 24, 149, 384, 234, 1008, 66, 576, 41, 56, 9, 0], [0, 14, 8, 247, 57, 912, 84, 906, 78, 218, 28, 7, 1], [0, 14, 9, 238, 93, 828, 210, 780, 162, 182, 37, 6, 1], [0, 14, 9, 239, 84, 864, 126, 906, 36, 266, 1, 15, 0], [0, 14, 10, 229, 129, 744, 336, 654, 246, 146, 46, 5, 1], [0, 14, 10, 230, 120, 780, 252, 780, 120, 230, 10, 14, 0], [0, 14, 11, 220, 165, 660, 462, 528, 330, 110, 55, 4, 1], [0, 14, 11, 221, 156, 696, 378, 654, 204, 194, 19, 13, 0], [0, 14, 12, 211, 201, 576, 588, 402, 414, 74, 64, 3, 1], [0, 14, 12, 212, 192, 612, 504, 528, 288, 158, 28, 12, 0], [0, 14, 13, 202, 237, 492, 714, 276, 498, 38, 73, 2, 1], [0, 14, 13, 203, 228, 528, 630, 402, 372, 122, 37, 11, 0], [0, 14, 14, 193, 273, 408, 840, 150, 582, 2, 82, 1, 1], [0, 14, 14, 194, 264, 444, 756, 276, 456, 86, 46, 10, 0], [0, 14, 15, 185, 300, 360, 882, 150, 540, 50, 55, 9, 0], [0, 14, 16, 176, 336, 276, 1008, 24, 624, 14, 64, 8, 0], [0, 15, 0, 274, 9, 954, 84, 864, 126, 191, 36, 6, 1], [0, 15, 0, 275, 0, 990, 0, 990, 0, 275, 0, 15, 0], [0, 15, 1, 265, 45, 870, 210, 738, 210, 155, 45, 5, 1], [0, 15, 1, 266, 36, 906, 126, 864, 84, 239, 9, 14, 0], [0, 15, 2, 256, 81, 786, 336, 612, 294, 119, 54, 4, 1], [0, 15, 2, 257, 72, 822, 252, 738, 168, 203, 18, 13, 0], [0, 15, 3, 247, 117, 702, 462, 486, 378, 83, 63, 3, 1], [0, 15, 3, 248, 108, 738, 378, 612, 252, 167, 27, 12, 0], [0, 15, 4, 238, 153, 618, 588, 360, 462, 47, 72, 2, 1], [0, 15, 4, 239, 144, 654, 504, 486, 336, 131, 36, 11, 0], [0, 15, 5, 229, 189, 534, 714, 234, 546, 11, 81, 1, 1], [0, 15, 5, 230, 180, 570, 630, 360, 420, 95, 45, 10, 0], [0, 15, 6, 221, 216, 486, 756, 234, 504, 59, 54, 9, 0], [0, 15, 7, 212, 252, 402, 882, 108, 588, 23, 63, 8, 0]}
(13, 2560, 8) has 450 possible DDs: {[0, 0, 58, 10, 248, 618, 108, 852, 408, 52, 202, 2, 0, 2], [0, 0, 59, 1, 284, 534, 234, 726, 492, 16, 211, 1, 0, 2], [0, 1, 50, 37, 200, 660, 108, 810, 456, 25, 210, 1, 0, 2], [0, 1, 53, 15, 264, 579, 102, 978, 204, 211, 141, 7, 4, 1], [0, 1, 53, 16, 255, 615, 18, 1104, 78, 295, 105, 16, 3, 1], [0, 1, 54, 6, 300, 495, 228, 852, 288, 175, 150, 6, 4, 1], [0, 1, 54, 7, 291, 531, 144, 978, 162, 259, 114, 15, 3, 1], [0, 1, 54, 8, 282, 567, 60, 1104, 36, 343, 78, 24, 2, 1], [0, 2, 45, 42, 216, 621, 102, 936, 252, 184, 149, 6, 4, 1], [0, 2, 45, 43, 207, 657, 18, 1062, 126, 268, 113, 15, 3, 1], [0, 2, 46, 33, 252, 537, 228, 810, 336, 148, 158, 5, 4, 1], [0, 2, 46, 34, 243, 573, 144, 936, 210, 232, 122, 14, 3, 1], [0, 2, 46, 35, 234, 609, 60, 1062, 84, 316, 86, 23, 2, 1], [0, 2, 47, 24, 288, 453, 354, 684, 420, 112, 167, 4, 4, 1], [0, 2, 47, 25, 279, 489, 270, 810, 294, 196, 131, 13, 3, 1], [0, 2, 47, 26, 270, 525, 186, 936, 168, 280, 95, 22, 2, 1], [0, 2, 47, 27, 261, 561, 102, 1062, 42, 364, 59, 31, 1, 1], [0, 2, 47, 28, 253, 588, 54, 1104, 42, 322, 107, 4, 9, 0], [0, 2, 48, 15, 324, 369, 480, 558, 504, 76, 176, 3, 4, 1], [0, 2, 48, 16, 315, 405, 396, 684, 378, 160, 140, 12, 3, 1], [0, 2, 48, 17, 306, 441, 312, 810, 252, 244, 104, 21, 2, 1], [0, 2, 48, 18, 297, 477, 228, 936, 126, 328, 68, 30, 1, 1], [0, 2, 48, 19, 288, 513, 144, 1062, 0, 412, 32, 39, 0, 1], [0, 2, 48, 19, 289, 504, 180, 978, 126, 286, 116, 3, 9, 0], [0, 2, 48, 20, 280, 540, 96, 1104, 0, 370, 80, 12, 8, 0], [0, 2, 49, 6, 360, 285, 606, 432, 588, 40, 185, 2, 4, 1], [0, 2, 49, 7, 351, 321, 522, 558, 462, 124, 149, 11, 3, 1], [0, 2, 49, 8, 342, 357, 438, 684, 336, 208, 113, 20, 2, 1], [0, 2, 49, 9, 333, 393, 354, 810, 210, 292, 77, 29, 1, 1], [0, 2, 49, 10, 324, 429, 270, 936, 84, 376, 41, 38, 0, 1], [0, 2, 49, 10, 325, 420, 306, 852, 210, 250, 125, 2, 9, 0], [0, 2, 49, 11, 316, 456, 222, 978, 84, 334, 89, 11, 8, 0], [0, 2, 50, 0, 369, 309, 480, 684, 294, 256, 86, 28, 1, 1], [0, 2, 50, 1, 360, 345, 396, 810, 168, 340, 50, 37, 0, 1], [0, 2, 50, 1, 361, 336, 432, 726, 294, 214, 134, 1, 9, 0], [0, 2, 50, 2, 352, 372, 348, 852, 168, 298, 98, 10, 8, 0], [0, 2, 50, 3, 343, 408, 264, 978, 42, 382, 62, 19, 7, 0], [0, 3, 37, 69, 168, 663, 102, 894, 300, 157, 157, 5, 4, 1], [0, 3, 37, 70, 159, 699, 18, 1020, 174, 241, 121, 14, 3, 1], [0, 3, 38, 60, 204, 579, 228, 768, 384, 121, 166, 4, 4, 1], [0, 3, 38, 61, 195, 615, 144, 894, 258, 205, 130, 13, 3, 1], [0, 3, 38, 62, 186, 651, 60, 1020, 132, 289, 94, 22, 2, 1], [0, 3, 39, 51, 240, 495, 354, 642, 468, 85, 175, 3, 4, 1], [0, 3, 39, 52, 231, 531, 270, 768, 342, 169, 139, 12, 3, 1], [0, 3, 39, 53, 222, 567, 186, 894, 216, 253, 103, 21, 2, 1], [0, 3, 39, 54, 213, 603, 102, 1020, 90, 337, 67, 30, 1, 1], [0, 3, 39, 55, 205, 630, 54, 1062, 90, 295, 115, 3, 9, 0], [0, 3, 40, 42, 276, 411, 480, 516, 552, 49, 184, 2, 4, 1], [0, 3, 40, 43, 267, 447, 396, 642, 426, 133, 148, 11, 3, 1], [0, 3, 40, 44, 258, 483, 312, 768, 300, 217, 112, 20, 2, 1], [0, 3, 40, 45, 249, 519, 228, 894, 174, 301, 76, 29, 1, 1], [0, 3, 40, 46, 240, 555, 144, 1020, 48, 385, 40, 38, 0, 1], [0, 3, 40, 46, 241, 546, 180, 936, 174, 259, 124, 2, 9, 0], [0, 3, 40, 47, 232, 582, 96, 1062, 48, 343, 88, 11, 8, 0], [0, 3, 41, 33, 312, 327, 606, 390, 636, 13, 193, 1, 4, 1], [0, 3, 41, 34, 303, 363, 522, 516, 510, 97, 157, 10, 3, 1], [0, 3, 41, 35, 294, 399, 438, 642, 384, 181, 121, 19, 2, 1], [0, 3, 41, 36, 285, 435, 354, 768, 258, 265, 85, 28, 1, 1], [0, 3, 41, 37, 276, 471, 270, 894, 132, 349, 49, 37, 0, 1], [0, 3, 41, 37, 277, 462, 306, 810, 258, 223, 133, 1, 9, 0], [0, 3, 41, 38, 268, 498, 222, 936, 132, 307, 97, 10, 8, 0], [0, 3, 41, 39, 259, 534, 138, 1062, 6, 391, 61, 19, 7, 0], [0, 3, 42, 25, 339, 279, 648, 390, 594, 61, 166, 9, 3, 1], [0, 3, 42, 26, 330, 315, 564, 516, 468, 145, 130, 18, 2, 1], [0, 3, 42, 27, 321, 351, 480, 642, 342, 229, 94, 27, 1, 1], [0, 3, 42, 28, 312, 387, 396, 768, 216, 313, 58, 36, 0, 1], [0, 3, 42, 28, 313, 378, 432, 684, 342, 187, 142, 0, 9, 0], [0, 3, 42, 29, 304, 414, 348, 810, 216, 271, 106, 9, 8, 0], [0, 3, 42, 30, 295, 450, 264, 936, 90, 355, 70, 18, 7, 0], [0, 3, 43, 16, 375, 195, 774, 264, 678, 25, 175, 8, 3, 1], [0, 3, 43, 17, 366, 231, 690, 390, 552, 109, 139, 17, 2, 1], [0, 3, 43, 18, 357, 267, 606, 516, 426, 193, 103, 26, 1, 1], [0, 3, 43, 19, 348, 303, 522, 642, 300, 277, 67, 35, 0, 1], [0, 3, 43, 20, 340, 330, 474, 684, 300, 235, 115, 8, 8, 0], [0, 3, 43, 21, 331, 366, 390, 810, 174, 319, 79, 17, 7, 0], [0, 3, 43, 22, 322, 402, 306, 936, 48, 403, 43, 26, 6, 0], [0, 3, 44, 8, 402, 147, 816, 264, 636, 73, 148, 16, 2, 1], [0, 3, 44, 9, 393, 183, 732, 390, 510, 157, 112, 25, 1, 1], [0, 3, 44, 10, 384, 219, 648, 516, 384, 241, 76, 34, 0, 1], [0, 3, 44, 11, 376, 246, 600, 558, 384, 199, 124, 7, 8, 0], [0, 3, 44, 12, 367, 282, 516, 684, 258, 283, 88, 16, 7, 0], [0, 3, 44, 13, 358, 318, 432, 810, 132, 367, 52, 25, 6, 0], [0, 3, 44, 14, 349, 354, 348, 936, 6, 451, 16, 34, 5, 0], [0, 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282, 307, 57, 29, 5, 0], [0, 7, 13, 114, 184, 474, 390, 768, 156, 391, 21, 38, 4, 0], [0, 7, 14, 100, 264, 219, 900, 96, 744, 61, 126, 28, 0, 1], [0, 7, 14, 101, 256, 246, 852, 138, 744, 19, 174, 1, 8, 0], [0, 7, 14, 102, 247, 282, 768, 264, 618, 103, 138, 10, 7, 0], [0, 7, 14, 103, 238, 318, 684, 390, 492, 187, 102, 19, 6, 0], [0, 7, 14, 104, 229, 354, 600, 516, 366, 271, 66, 28, 5, 0], [0, 7, 14, 105, 220, 390, 516, 642, 240, 355, 30, 37, 4, 0], [0, 7, 15, 93, 283, 198, 894, 138, 702, 67, 147, 9, 7, 0], [0, 7, 15, 94, 274, 234, 810, 264, 576, 151, 111, 18, 6, 0], [0, 7, 15, 95, 265, 270, 726, 390, 450, 235, 75, 27, 5, 0], [0, 7, 15, 96, 256, 306, 642, 516, 324, 319, 39, 36, 4, 0], [0, 7, 15, 97, 247, 342, 558, 642, 198, 403, 3, 45, 3, 0], [0, 7, 16, 84, 319, 114, 1020, 12, 786, 31, 156, 8, 7, 0], [0, 7, 16, 85, 310, 150, 936, 138, 660, 115, 120, 17, 6, 0], [0, 7, 16, 86, 301, 186, 852, 264, 534, 199, 84, 26, 5, 0], [0, 7, 16, 87, 292, 222, 768, 390, 408, 283, 48, 35, 4, 0], [0, 7, 16, 88, 283, 258, 684, 516, 282, 367, 12, 44, 3, 0], [0, 7, 17, 76, 346, 66, 1062, 12, 744, 79, 129, 16, 6, 0], [0, 7, 17, 77, 337, 102, 978, 138, 618, 163, 93, 25, 5, 0], [0, 7, 17, 78, 328, 138, 894, 264, 492, 247, 57, 34, 4, 0], [0, 7, 17, 79, 319, 174, 810, 390, 366, 331, 21, 43, 3, 0], [0, 7, 18, 68, 373, 18, 1104, 12, 702, 127, 102, 24, 5, 0], [0, 7, 18, 69, 364, 54, 1020, 138, 576, 211, 66, 33, 4, 0], [0, 7, 18, 70, 355, 90, 936, 264, 450, 295, 30, 42, 3, 0], [0, 7, 19, 61, 391, 6, 1062, 138, 534, 259, 39, 41, 3, 0], [0, 7, 19, 62, 382, 42, 978, 264, 408, 343, 3, 50, 2, 0], [0, 8, 0, 179, 18, 693, 312, 558, 540, 82, 152, 15, 2, 1], [0, 8, 0, 180, 9, 729, 228, 684, 414, 166, 116, 24, 1, 1], [0, 8, 0, 181, 0, 765, 144, 810, 288, 250, 80, 33, 0, 1], [0, 8, 1, 170, 54, 609, 438, 432, 624, 46, 161, 14, 2, 1], [0, 8, 1, 171, 45, 645, 354, 558, 498, 130, 125, 23, 1, 1], [0, 8, 1, 172, 36, 681, 270, 684, 372, 214, 89, 32, 0, 1], [0, 8, 1, 173, 28, 708, 222, 726, 372, 172, 137, 5, 8, 0], [0, 8, 1, 174, 19, 744, 138, 852, 246, 256, 101, 14, 7, 0], [0, 8, 1, 175, 10, 780, 54, 978, 120, 340, 65, 23, 6, 0], [0, 8, 2, 161, 90, 525, 564, 306, 708, 10, 170, 13, 2, 1], [0, 8, 2, 162, 81, 561, 480, 432, 582, 94, 134, 22, 1, 1], [0, 8, 2, 163, 72, 597, 396, 558, 456, 178, 98, 31, 0, 1], [0, 8, 2, 164, 64, 624, 348, 600, 456, 136, 146, 4, 8, 0], [0, 8, 2, 165, 55, 660, 264, 726, 330, 220, 110, 13, 7, 0], [0, 8, 2, 166, 46, 696, 180, 852, 204, 304, 74, 22, 6, 0], [0, 8, 2, 167, 37, 732, 96, 978, 78, 388, 38, 31, 5, 0], [0, 8, 3, 153, 117, 477, 606, 306, 666, 58, 143, 21, 1, 1], [0, 8, 3, 154, 108, 513, 522, 432, 540, 142, 107, 30, 0, 1], [0, 8, 3, 155, 100, 540, 474, 474, 540, 100, 155, 3, 8, 0], [0, 8, 3, 156, 91, 576, 390, 600, 414, 184, 119, 12, 7, 0], [0, 8, 3, 157, 82, 612, 306, 726, 288, 268, 83, 21, 6, 0], [0, 8, 3, 158, 73, 648, 222, 852, 162, 352, 47, 30, 5, 0], [0, 8, 3, 159, 64, 684, 138, 978, 36, 436, 11, 39, 4, 0], [0, 8, 4, 144, 153, 393, 732, 180, 750, 22, 152, 20, 1, 1], [0, 8, 4, 145, 144, 429, 648, 306, 624, 106, 116, 29, 0, 1], [0, 8, 4, 146, 136, 456, 600, 348, 624, 64, 164, 2, 8, 0], [0, 8, 4, 147, 127, 492, 516, 474, 498, 148, 128, 11, 7, 0], [0, 8, 4, 148, 118, 528, 432, 600, 372, 232, 92, 20, 6, 0], [0, 8, 4, 149, 109, 564, 348, 726, 246, 316, 56, 29, 5, 0], [0, 8, 4, 150, 100, 600, 264, 852, 120, 400, 20, 38, 4, 0], [0, 8, 5, 136, 180, 345, 774, 180, 708, 70, 125, 28, 0, 1], [0, 8, 5, 137, 172, 372, 726, 222, 708, 28, 173, 1, 8, 0], [0, 8, 5, 138, 163, 408, 642, 348, 582, 112, 137, 10, 7, 0], [0, 8, 5, 139, 154, 444, 558, 474, 456, 196, 101, 19, 6, 0], [0, 8, 5, 140, 145, 480, 474, 600, 330, 280, 65, 28, 5, 0], [0, 8, 5, 141, 136, 516, 390, 726, 204, 364, 29, 37, 4, 0], [0, 8, 6, 127, 216, 261, 900, 54, 792, 34, 134, 27, 0, 1], [0, 8, 6, 129, 199, 324, 768, 222, 666, 76, 146, 9, 7, 0], [0, 8, 6, 130, 190, 360, 684, 348, 540, 160, 110, 18, 6, 0], [0, 8, 6, 131, 181, 396, 600, 474, 414, 244, 74, 27, 5, 0], [0, 8, 6, 132, 172, 432, 516, 600, 288, 328, 38, 36, 4, 0], [0, 8, 6, 133, 163, 468, 432, 726, 162, 412, 2, 45, 3, 0], [0, 8, 7, 120, 235, 240, 894, 96, 750, 40, 155, 8, 7, 0], [0, 8, 7, 121, 226, 276, 810, 222, 624, 124, 119, 17, 6, 0], [0, 8, 7, 122, 217, 312, 726, 348, 498, 208, 83, 26, 5, 0], [0, 8, 7, 123, 208, 348, 642, 474, 372, 292, 47, 35, 4, 0], [0, 8, 7, 124, 199, 384, 558, 600, 246, 376, 11, 44, 3, 0], [0, 8, 8, 112, 262, 192, 936, 96, 708, 88, 128, 16, 6, 0], [0, 8, 8, 113, 253, 228, 852, 222, 582, 172, 92, 25, 5, 0], [0, 8, 8, 114, 244, 264, 768, 348, 456, 256, 56, 34, 4, 0], [0, 8, 8, 115, 235, 300, 684, 474, 330, 340, 20, 43, 3, 0], [0, 8, 9, 104, 289, 144, 978, 96, 666, 136, 101, 24, 5, 0], [0, 8, 9, 105, 280, 180, 894, 222, 540, 220, 65, 33, 4, 0], [0, 8, 9, 106, 271, 216, 810, 348, 414, 304, 29, 42, 3, 0], [0, 8, 10, 96, 316, 96, 1020, 96, 624, 184, 74, 32, 4, 0], [0, 8, 10, 97, 307, 132, 936, 222, 498, 268, 38, 41, 3, 0], [0, 8, 10, 98, 298, 168, 852, 348, 372, 352, 2, 50, 2, 0], [0, 8, 11, 88, 343, 48, 1062, 96, 582, 232, 47, 40, 3, 0], [0, 8, 11, 89, 334, 84, 978, 222, 456, 316, 11, 49, 2, 0], [0, 8, 12, 80, 370, 0, 1104, 96, 540, 280, 20, 48, 2, 0], [0, 9, 0, 139, 214, 234, 936, 54, 756, 61, 136, 15, 6, 0], [0, 9, 0, 140, 205, 270, 852, 180, 630, 145, 100, 24, 5, 0], [0, 9, 0, 141, 196, 306, 768, 306, 504, 229, 64, 33, 4, 0], [0, 9, 0, 142, 187, 342, 684, 432, 378, 313, 28, 42, 3, 0], [0, 9, 1, 131, 241, 186, 978, 54, 714, 109, 109, 23, 5, 0], [0, 9, 1, 132, 232, 222, 894, 180, 588, 193, 73, 32, 4, 0], [0, 9, 1, 133, 223, 258, 810, 306, 462, 277, 37, 41, 3, 0], [0, 9, 1, 134, 214, 294, 726, 432, 336, 361, 1, 50, 2, 0], [0, 9, 2, 123, 268, 138, 1020, 54, 672, 157, 82, 31, 4, 0], [0, 9, 2, 124, 259, 174, 936, 180, 546, 241, 46, 40, 3, 0], [0, 9, 2, 125, 250, 210, 852, 306, 420, 325, 10, 49, 2, 0], [0, 9, 3, 115, 295, 90, 1062, 54, 630, 205, 55, 39, 3, 0], [0, 9, 3, 116, 286, 126, 978, 180, 504, 289, 19, 48, 2, 0], [0, 9, 4, 107, 322, 42, 1104, 54, 588, 253, 28, 47, 2, 0]}
-------
(13, 2560, 8) ALL distance distributions for EXTERNAL point
(8, 2560, 8) has 0 possible DDs: {}
(9, 2560, 8) has 1 possible DDs: {[0, 90, 0, 840, 0, 1260, 0, 360, 0, 10]}
(10, 2560, 8) has 6 possible DDs: {[0, 45, 45, 420, 420, 630, 630, 180, 180, 5, 5], [0, 46, 36, 456, 336, 756, 504, 264, 144, 14, 4], [0, 47, 27, 492, 252, 882, 378, 348, 108, 23, 3], [0, 48, 18, 528, 168, 1008, 252, 432, 72, 32, 2], [0, 49, 9, 564, 84, 1134, 126, 516, 36, 41, 1], [0, 50, 0, 600, 0, 1260, 0, 600, 0, 50, 0]}
(11, 2560, 8) has 28 possible DDs: {[0, 18, 85, 75, 780, 0, 1134, 90, 300, 70, 5, 3], [0, 19, 76, 111, 696, 126, 1008, 174, 264, 79, 4, 3], [0, 19, 77, 102, 732, 42, 1134, 48, 348, 43, 13, 2], [0, 20, 67, 147, 612, 252, 882, 258, 228, 88, 3, 3], [0, 20, 68, 138, 648, 168, 1008, 132, 312, 52, 12, 2], [0, 20, 69, 129, 684, 84, 1134, 6, 396, 16, 21, 1], [0, 21, 58, 183, 528, 378, 756, 342, 192, 97, 2, 3], [0, 21, 59, 174, 564, 294, 882, 216, 276, 61, 11, 2], [0, 21, 60, 165, 600, 210, 1008, 90, 360, 25, 20, 1], [0, 22, 49, 219, 444, 504, 630, 426, 156, 106, 1, 3], [0, 22, 50, 210, 480, 420, 756, 300, 240, 70, 10, 2], [0, 22, 51, 201, 516, 336, 882, 174, 324, 34, 19, 1], [0, 23, 40, 255, 360, 630, 504, 510, 120, 115, 0, 3], [0, 23, 41, 246, 396, 546, 630, 384, 204, 79, 9, 2], [0, 23, 42, 237, 432, 462, 756, 258, 288, 43, 18, 1], [0, 23, 43, 228, 468, 378, 882, 132, 372, 7, 27, 0], [0, 24, 32, 282, 312, 672, 504, 468, 168, 88, 8, 2], [0, 24, 33, 273, 348, 588, 630, 342, 252, 52, 17, 1], [0, 24, 34, 264, 384, 504, 756, 216, 336, 16, 26, 0], [0, 25, 23, 318, 228, 798, 378, 552, 132, 97, 7, 2], [0, 25, 24, 309, 264, 714, 504, 426, 216, 61, 16, 1], [0, 25, 25, 300, 300, 630, 630, 300, 300, 25, 25, 0], [0, 26, 14, 354, 144, 924, 252, 636, 96, 106, 6, 2], [0, 26, 15, 345, 180, 840, 378, 510, 180, 70, 15, 1], [0, 26, 16, 336, 216, 756, 504, 384, 264, 34, 24, 0], [0, 27, 5, 390, 60, 1050, 126, 720, 60, 115, 5, 2], [0, 27, 6, 381, 96, 966, 252, 594, 144, 79, 14, 1], [0, 27, 7, 372, 132, 882, 378, 468, 228, 43, 23, 0]}
(12, 2560, 8) has 122 possible DDs: {[0, 6, 75, 3, 558, 288, 546, 738, 72, 242, 27, 3, 2], [0, 7, 66, 39, 474, 414, 420, 822, 36, 251, 26, 3, 2], [0, 7, 67, 30, 510, 330, 546, 696, 120, 215, 35, 2, 2], [0, 7, 68, 21, 546, 246, 672, 570, 204, 179, 44, 1, 2], [0, 7, 68, 22, 537, 282, 588, 696, 78, 263, 8, 10, 1], [0, 7, 69, 12, 582, 162, 798, 444, 288, 143, 53, 0, 2], [0, 7, 69, 13, 573, 198, 714, 570, 162, 227, 17, 9, 1], [0, 7, 70, 4, 609, 114, 840, 444, 246, 191, 26, 8, 1], [0, 8, 57, 75, 390, 540, 294, 906, 0, 260, 25, 3, 2], [0, 8, 58, 66, 426, 456, 420, 780, 84, 224, 34, 2, 2], [0, 8, 59, 57, 462, 372, 546, 654, 168, 188, 43, 1, 2], [0, 8, 59, 58, 453, 408, 462, 780, 42, 272, 7, 10, 1], [0, 8, 60, 48, 498, 288, 672, 528, 252, 152, 52, 0, 2], [0, 8, 60, 49, 489, 324, 588, 654, 126, 236, 16, 9, 1], [0, 8, 61, 40, 525, 240, 714, 528, 210, 200, 25, 8, 1], [0, 8, 62, 31, 561, 156, 840, 402, 294, 164, 34, 7, 1], [0, 8, 63, 22, 597, 72, 966, 276, 378, 128, 43, 6, 1], [0, 8, 63, 23, 588, 108, 882, 402, 252, 212, 7, 15, 0], [0, 8, 64, 14, 624, 24, 1008, 276, 336, 176, 16, 14, 0], [0, 9, 49, 102, 342, 582, 294, 864, 48, 233, 33, 2, 2], [0, 9, 50, 93, 378, 498, 420, 738, 132, 197, 42, 1, 2], [0, 9, 50, 94, 369, 534, 336, 864, 6, 281, 6, 10, 1], [0, 9, 51, 84, 414, 414, 546, 612, 216, 161, 51, 0, 2], [0, 9, 51, 85, 405, 450, 462, 738, 90, 245, 15, 9, 1], [0, 9, 52, 76, 441, 366, 588, 612, 174, 209, 24, 8, 1], [0, 9, 53, 67, 477, 282, 714, 486, 258, 173, 33, 7, 1], [0, 9, 54, 58, 513, 198, 840, 360, 342, 137, 42, 6, 1], [0, 9, 54, 59, 504, 234, 756, 486, 216, 221, 6, 15, 0], [0, 9, 55, 49, 549, 114, 966, 234, 426, 101, 51, 5, 1], [0, 9, 55, 50, 540, 150, 882, 360, 300, 185, 15, 14, 0], [0, 9, 56, 40, 585, 30, 1092, 108, 510, 65, 60, 4, 1], [0, 9, 56, 41, 576, 66, 1008, 234, 384, 149, 24, 13, 0], [0, 10, 40, 138, 258, 708, 168, 948, 12, 242, 32, 2, 2], [0, 10, 41, 129, 294, 624, 294, 822, 96, 206, 41, 1, 2], [0, 10, 42, 120, 330, 540, 420, 696, 180, 170, 50, 0, 2], [0, 10, 42, 121, 321, 576, 336, 822, 54, 254, 14, 9, 1], [0, 10, 43, 112, 357, 492, 462, 696, 138, 218, 23, 8, 1], [0, 10, 44, 103, 393, 408, 588, 570, 222, 182, 32, 7, 1], [0, 10, 45, 94, 429, 324, 714, 444, 306, 146, 41, 6, 1], [0, 10, 45, 95, 420, 360, 630, 570, 180, 230, 5, 15, 0], [0, 10, 46, 85, 465, 240, 840, 318, 390, 110, 50, 5, 1], [0, 10, 46, 86, 456, 276, 756, 444, 264, 194, 14, 14, 0], [0, 10, 47, 76, 501, 156, 966, 192, 474, 74, 59, 4, 1], [0, 10, 47, 77, 492, 192, 882, 318, 348, 158, 23, 13, 0], [0, 10, 48, 67, 537, 72, 1092, 66, 558, 38, 68, 3, 1], [0, 10, 48, 68, 528, 108, 1008, 192, 432, 122, 32, 12, 0], [0, 10, 49, 59, 564, 24, 1134, 66, 516, 86, 41, 11, 0], [0, 11, 32, 165, 210, 750, 168, 906, 60, 215, 40, 1, 2], [0, 11, 33, 156, 246, 666, 294, 780, 144, 179, 49, 0, 2], [0, 11, 33, 157, 237, 702, 210, 906, 18, 263, 13, 9, 1], [0, 11, 34, 148, 273, 618, 336, 780, 102, 227, 22, 8, 1], [0, 11, 35, 139, 309, 534, 462, 654, 186, 191, 31, 7, 1], [0, 11, 36, 130, 345, 450, 588, 528, 270, 155, 40, 6, 1], [0, 11, 36, 131, 336, 486, 504, 654, 144, 239, 4, 15, 0], [0, 11, 37, 121, 381, 366, 714, 402, 354, 119, 49, 5, 1], [0, 11, 37, 122, 372, 402, 630, 528, 228, 203, 13, 14, 0], [0, 11, 38, 112, 417, 282, 840, 276, 438, 83, 58, 4, 1], [0, 11, 38, 113, 408, 318, 756, 402, 312, 167, 22, 13, 0], [0, 11, 39, 103, 453, 198, 966, 150, 522, 47, 67, 3, 1], [0, 11, 39, 104, 444, 234, 882, 276, 396, 131, 31, 12, 0], [0, 11, 40, 94, 489, 114, 1092, 24, 606, 11, 76, 2, 1], [0, 11, 40, 95, 480, 150, 1008, 150, 480, 95, 40, 11, 0], [0, 11, 41, 86, 516, 66, 1134, 24, 564, 59, 49, 10, 0], [0, 12, 23, 201, 126, 876, 42, 990, 24, 224, 39, 1, 2], [0, 12, 24, 192, 162, 792, 168, 864, 108, 188, 48, 0, 2], [0, 12, 25, 184, 189, 744, 210, 864, 66, 236, 21, 8, 1], [0, 12, 26, 175, 225, 660, 336, 738, 150, 200, 30, 7, 1], [0, 12, 27, 166, 261, 576, 462, 612, 234, 164, 39, 6, 1], [0, 12, 27, 167, 252, 612, 378, 738, 108, 248, 3, 15, 0], [0, 12, 28, 157, 297, 492, 588, 486, 318, 128, 48, 5, 1], [0, 12, 28, 158, 288, 528, 504, 612, 192, 212, 12, 14, 0], [0, 12, 29, 148, 333, 408, 714, 360, 402, 92, 57, 4, 1], [0, 12, 29, 149, 324, 444, 630, 486, 276, 176, 21, 13, 0], [0, 12, 30, 139, 369, 324, 840, 234, 486, 56, 66, 3, 1], [0, 12, 30, 140, 360, 360, 756, 360, 360, 140, 30, 12, 0], [0, 12, 31, 130, 405, 240, 966, 108, 570, 20, 75, 2, 1], [0, 12, 31, 131, 396, 276, 882, 234, 444, 104, 39, 11, 0], [0, 12, 32, 122, 432, 192, 1008, 108, 528, 68, 48, 10, 0], [0, 13, 15, 228, 78, 918, 42, 948, 72, 197, 47, 0, 2], [0, 13, 16, 220, 105, 870, 84, 948, 30, 245, 20, 8, 1], [0, 13, 17, 211, 141, 786, 210, 822, 114, 209, 29, 7, 1], [0, 13, 18, 202, 177, 702, 336, 696, 198, 173, 38, 6, 1], [0, 13, 18, 203, 168, 738, 252, 822, 72, 257, 2, 15, 0], [0, 13, 19, 193, 213, 618, 462, 570, 282, 137, 47, 5, 1], [0, 13, 19, 194, 204, 654, 378, 696, 156, 221, 11, 14, 0], [0, 13, 20, 184, 249, 534, 588, 444, 366, 101, 56, 4, 1], [0, 13, 20, 185, 240, 570, 504, 570, 240, 185, 20, 13, 0], [0, 13, 21, 175, 285, 450, 714, 318, 450, 65, 65, 3, 1], [0, 13, 21, 176, 276, 486, 630, 444, 324, 149, 29, 12, 0], [0, 13, 22, 166, 321, 366, 840, 192, 534, 29, 74, 2, 1], [0, 13, 22, 167, 312, 402, 756, 318, 408, 113, 38, 11, 0], [0, 13, 23, 158, 348, 318, 882, 192, 492, 77, 47, 10, 0], [0, 13, 24, 149, 384, 234, 1008, 66, 576, 41, 56, 9, 0], [0, 14, 8, 247, 57, 912, 84, 906, 78, 218, 28, 7, 1], [0, 14, 9, 238, 93, 828, 210, 780, 162, 182, 37, 6, 1], [0, 14, 9, 239, 84, 864, 126, 906, 36, 266, 1, 15, 0], [0, 14, 10, 229, 129, 744, 336, 654, 246, 146, 46, 5, 1], [0, 14, 10, 230, 120, 780, 252, 780, 120, 230, 10, 14, 0], [0, 14, 11, 220, 165, 660, 462, 528, 330, 110, 55, 4, 1], [0, 14, 11, 221, 156, 696, 378, 654, 204, 194, 19, 13, 0], [0, 14, 12, 211, 201, 576, 588, 402, 414, 74, 64, 3, 1], [0, 14, 12, 212, 192, 612, 504, 528, 288, 158, 28, 12, 0], [0, 14, 13, 202, 237, 492, 714, 276, 498, 38, 73, 2, 1], [0, 14, 13, 203, 228, 528, 630, 402, 372, 122, 37, 11, 0], [0, 14, 14, 193, 273, 408, 840, 150, 582, 2, 82, 1, 1], [0, 14, 14, 194, 264, 444, 756, 276, 456, 86, 46, 10, 0], [0, 14, 15, 185, 300, 360, 882, 150, 540, 50, 55, 9, 0], [0, 14, 16, 176, 336, 276, 1008, 24, 624, 14, 64, 8, 0], [0, 15, 0, 274, 9, 954, 84, 864, 126, 191, 36, 6, 1], [0, 15, 0, 275, 0, 990, 0, 990, 0, 275, 0, 15, 0], [0, 15, 1, 265, 45, 870, 210, 738, 210, 155, 45, 5, 1], [0, 15, 1, 266, 36, 906, 126, 864, 84, 239, 9, 14, 0], [0, 15, 2, 256, 81, 786, 336, 612, 294, 119, 54, 4, 1], [0, 15, 2, 257, 72, 822, 252, 738, 168, 203, 18, 13, 0], [0, 15, 3, 247, 117, 702, 462, 486, 378, 83, 63, 3, 1], [0, 15, 3, 248, 108, 738, 378, 612, 252, 167, 27, 12, 0], [0, 15, 4, 238, 153, 618, 588, 360, 462, 47, 72, 2, 1], [0, 15, 4, 239, 144, 654, 504, 486, 336, 131, 36, 11, 0], [0, 15, 5, 229, 189, 534, 714, 234, 546, 11, 81, 1, 1], [0, 15, 5, 230, 180, 570, 630, 360, 420, 95, 45, 10, 0], [0, 15, 6, 221, 216, 486, 756, 234, 504, 59, 54, 9, 0], [0, 15, 7, 212, 252, 402, 882, 108, 588, 23, 63, 8, 0]}
(13, 2560, 8) has 450 possible DDs: {[0, 0, 58, 10, 248, 618, 108, 852, 408, 52, 202, 2, 0, 2], [0, 0, 59, 1, 284, 534, 234, 726, 492, 16, 211, 1, 0, 2], [0, 1, 50, 37, 200, 660, 108, 810, 456, 25, 210, 1, 0, 2], [0, 1, 53, 15, 264, 579, 102, 978, 204, 211, 141, 7, 4, 1], [0, 1, 53, 16, 255, 615, 18, 1104, 78, 295, 105, 16, 3, 1], [0, 1, 54, 6, 300, 495, 228, 852, 288, 175, 150, 6, 4, 1], [0, 1, 54, 7, 291, 531, 144, 978, 162, 259, 114, 15, 3, 1], [0, 1, 54, 8, 282, 567, 60, 1104, 36, 343, 78, 24, 2, 1], [0, 2, 45, 42, 216, 621, 102, 936, 252, 184, 149, 6, 4, 1], [0, 2, 45, 43, 207, 657, 18, 1062, 126, 268, 113, 15, 3, 1], [0, 2, 46, 33, 252, 537, 228, 810, 336, 148, 158, 5, 4, 1], [0, 2, 46, 34, 243, 573, 144, 936, 210, 232, 122, 14, 3, 1], [0, 2, 46, 35, 234, 609, 60, 1062, 84, 316, 86, 23, 2, 1], [0, 2, 47, 24, 288, 453, 354, 684, 420, 112, 167, 4, 4, 1], [0, 2, 47, 25, 279, 489, 270, 810, 294, 196, 131, 13, 3, 1], [0, 2, 47, 26, 270, 525, 186, 936, 168, 280, 95, 22, 2, 1], [0, 2, 47, 27, 261, 561, 102, 1062, 42, 364, 59, 31, 1, 1], [0, 2, 47, 28, 253, 588, 54, 1104, 42, 322, 107, 4, 9, 0], [0, 2, 48, 15, 324, 369, 480, 558, 504, 76, 176, 3, 4, 1], [0, 2, 48, 16, 315, 405, 396, 684, 378, 160, 140, 12, 3, 1], [0, 2, 48, 17, 306, 441, 312, 810, 252, 244, 104, 21, 2, 1], [0, 2, 48, 18, 297, 477, 228, 936, 126, 328, 68, 30, 1, 1], [0, 2, 48, 19, 288, 513, 144, 1062, 0, 412, 32, 39, 0, 1], [0, 2, 48, 19, 289, 504, 180, 978, 126, 286, 116, 3, 9, 0], [0, 2, 48, 20, 280, 540, 96, 1104, 0, 370, 80, 12, 8, 0], [0, 2, 49, 6, 360, 285, 606, 432, 588, 40, 185, 2, 4, 1], [0, 2, 49, 7, 351, 321, 522, 558, 462, 124, 149, 11, 3, 1], [0, 2, 49, 8, 342, 357, 438, 684, 336, 208, 113, 20, 2, 1], [0, 2, 49, 9, 333, 393, 354, 810, 210, 292, 77, 29, 1, 1], [0, 2, 49, 10, 324, 429, 270, 936, 84, 376, 41, 38, 0, 1], [0, 2, 49, 10, 325, 420, 306, 852, 210, 250, 125, 2, 9, 0], [0, 2, 49, 11, 316, 456, 222, 978, 84, 334, 89, 11, 8, 0], [0, 2, 50, 0, 369, 309, 480, 684, 294, 256, 86, 28, 1, 1], [0, 2, 50, 1, 360, 345, 396, 810, 168, 340, 50, 37, 0, 1], [0, 2, 50, 1, 361, 336, 432, 726, 294, 214, 134, 1, 9, 0], [0, 2, 50, 2, 352, 372, 348, 852, 168, 298, 98, 10, 8, 0], [0, 2, 50, 3, 343, 408, 264, 978, 42, 382, 62, 19, 7, 0], [0, 3, 37, 69, 168, 663, 102, 894, 300, 157, 157, 5, 4, 1], [0, 3, 37, 70, 159, 699, 18, 1020, 174, 241, 121, 14, 3, 1], [0, 3, 38, 60, 204, 579, 228, 768, 384, 121, 166, 4, 4, 1], [0, 3, 38, 61, 195, 615, 144, 894, 258, 205, 130, 13, 3, 1], [0, 3, 38, 62, 186, 651, 60, 1020, 132, 289, 94, 22, 2, 1], [0, 3, 39, 51, 240, 495, 354, 642, 468, 85, 175, 3, 4, 1], [0, 3, 39, 52, 231, 531, 270, 768, 342, 169, 139, 12, 3, 1], [0, 3, 39, 53, 222, 567, 186, 894, 216, 253, 103, 21, 2, 1], [0, 3, 39, 54, 213, 603, 102, 1020, 90, 337, 67, 30, 1, 1], [0, 3, 39, 55, 205, 630, 54, 1062, 90, 295, 115, 3, 9, 0], [0, 3, 40, 42, 276, 411, 480, 516, 552, 49, 184, 2, 4, 1], [0, 3, 40, 43, 267, 447, 396, 642, 426, 133, 148, 11, 3, 1], [0, 3, 40, 44, 258, 483, 312, 768, 300, 217, 112, 20, 2, 1], [0, 3, 40, 45, 249, 519, 228, 894, 174, 301, 76, 29, 1, 1], [0, 3, 40, 46, 240, 555, 144, 1020, 48, 385, 40, 38, 0, 1], [0, 3, 40, 46, 241, 546, 180, 936, 174, 259, 124, 2, 9, 0], [0, 3, 40, 47, 232, 582, 96, 1062, 48, 343, 88, 11, 8, 0], [0, 3, 41, 33, 312, 327, 606, 390, 636, 13, 193, 1, 4, 1], [0, 3, 41, 34, 303, 363, 522, 516, 510, 97, 157, 10, 3, 1], [0, 3, 41, 35, 294, 399, 438, 642, 384, 181, 121, 19, 2, 1], [0, 3, 41, 36, 285, 435, 354, 768, 258, 265, 85, 28, 1, 1], [0, 3, 41, 37, 276, 471, 270, 894, 132, 349, 49, 37, 0, 1], [0, 3, 41, 37, 277, 462, 306, 810, 258, 223, 133, 1, 9, 0], [0, 3, 41, 38, 268, 498, 222, 936, 132, 307, 97, 10, 8, 0], [0, 3, 41, 39, 259, 534, 138, 1062, 6, 391, 61, 19, 7, 0], [0, 3, 42, 25, 339, 279, 648, 390, 594, 61, 166, 9, 3, 1], [0, 3, 42, 26, 330, 315, 564, 516, 468, 145, 130, 18, 2, 1], [0, 3, 42, 27, 321, 351, 480, 642, 342, 229, 94, 27, 1, 1], [0, 3, 42, 28, 312, 387, 396, 768, 216, 313, 58, 36, 0, 1], [0, 3, 42, 28, 313, 378, 432, 684, 342, 187, 142, 0, 9, 0], [0, 3, 42, 29, 304, 414, 348, 810, 216, 271, 106, 9, 8, 0], [0, 3, 42, 30, 295, 450, 264, 936, 90, 355, 70, 18, 7, 0], [0, 3, 43, 16, 375, 195, 774, 264, 678, 25, 175, 8, 3, 1], [0, 3, 43, 17, 366, 231, 690, 390, 552, 109, 139, 17, 2, 1], [0, 3, 43, 18, 357, 267, 606, 516, 426, 193, 103, 26, 1, 1], [0, 3, 43, 19, 348, 303, 522, 642, 300, 277, 67, 35, 0, 1], [0, 3, 43, 20, 340, 330, 474, 684, 300, 235, 115, 8, 8, 0], [0, 3, 43, 21, 331, 366, 390, 810, 174, 319, 79, 17, 7, 0], [0, 3, 43, 22, 322, 402, 306, 936, 48, 403, 43, 26, 6, 0], [0, 3, 44, 8, 402, 147, 816, 264, 636, 73, 148, 16, 2, 1], [0, 3, 44, 9, 393, 183, 732, 390, 510, 157, 112, 25, 1, 1], [0, 3, 44, 10, 384, 219, 648, 516, 384, 241, 76, 34, 0, 1], [0, 3, 44, 11, 376, 246, 600, 558, 384, 199, 124, 7, 8, 0], [0, 3, 44, 12, 367, 282, 516, 684, 258, 283, 88, 16, 7, 0], [0, 3, 44, 13, 358, 318, 432, 810, 132, 367, 52, 25, 6, 0], [0, 3, 44, 14, 349, 354, 348, 936, 6, 451, 16, 34, 5, 0], [0, 3, 45, 0, 429, 99, 858, 264, 594, 121, 121, 24, 1, 1], [0, 3, 45, 1, 420, 135, 774, 390, 468, 205, 85, 33, 0, 1], [0, 3, 45, 2, 412, 162, 726, 432, 468, 163, 133, 6, 8, 0], [0, 3, 45, 3, 403, 198, 642, 558, 342, 247, 97, 15, 7, 0], [0, 3, 45, 4, 394, 234, 558, 684, 216, 331, 61, 24, 6, 0], [0, 3, 45, 5, 385, 270, 474, 810, 90, 415, 25, 33, 5, 0], [0, 4, 29, 96, 120, 705, 102, 852, 348, 130, 165, 4, 4, 1], [0, 4, 29, 97, 111, 741, 18, 978, 222, 214, 129, 13, 3, 1], [0, 4, 30, 87, 156, 621, 228, 726, 432, 94, 174, 3, 4, 1], [0, 4, 30, 88, 147, 657, 144, 852, 306, 178, 138, 12, 3, 1], [0, 4, 30, 89, 138, 693, 60, 978, 180, 262, 102, 21, 2, 1], [0, 4, 31, 78, 192, 537, 354, 600, 516, 58, 183, 2, 4, 1], [0, 4, 31, 79, 183, 573, 270, 726, 390, 142, 147, 11, 3, 1], [0, 4, 31, 80, 174, 609, 186, 852, 264, 226, 111, 20, 2, 1], [0, 4, 31, 81, 165, 645, 102, 978, 138, 310, 75, 29, 1, 1], [0, 4, 31, 82, 156, 681, 18, 1104, 12, 394, 39, 38, 0, 1], [0, 4, 31, 82, 157, 672, 54, 1020, 138, 268, 123, 2, 9, 0], [0, 4, 32, 69, 228, 453, 480, 474, 600, 22, 192, 1, 4, 1], [0, 4, 32, 70, 219, 489, 396, 600, 474, 106, 156, 10, 3, 1], [0, 4, 32, 71, 210, 525, 312, 726, 348, 190, 120, 19, 2, 1], [0, 4, 32, 72, 201, 561, 228, 852, 222, 274, 84, 28, 1, 1], [0, 4, 32, 73, 192, 597, 144, 978, 96, 358, 48, 37, 0, 1], [0, 4, 32, 73, 193, 588, 180, 894, 222, 232, 132, 1, 9, 0], [0, 4, 32, 74, 184, 624, 96, 1020, 96, 316, 96, 10, 8, 0], [0, 4, 33, 61, 255, 405, 522, 474, 558, 70, 165, 9, 3, 1], [0, 4, 33, 62, 246, 441, 438, 600, 432, 154, 129, 18, 2, 1], [0, 4, 33, 63, 237, 477, 354, 726, 306, 238, 93, 27, 1, 1], [0, 4, 33, 64, 228, 513, 270, 852, 180, 322, 57, 36, 0, 1], [0, 4, 33, 64, 229, 504, 306, 768, 306, 196, 141, 0, 9, 0], [0, 4, 33, 65, 220, 540, 222, 894, 180, 280, 105, 9, 8, 0], [0, 4, 33, 66, 211, 576, 138, 1020, 54, 364, 69, 18, 7, 0], [0, 4, 34, 52, 291, 321, 648, 348, 642, 34, 174, 8, 3, 1], [0, 4, 34, 53, 282, 357, 564, 474, 516, 118, 138, 17, 2, 1], [0, 4, 34, 54, 273, 393, 480, 600, 390, 202, 102, 26, 1, 1], [0, 4, 34, 55, 264, 429, 396, 726, 264, 286, 66, 35, 0, 1], [0, 4, 34, 56, 256, 456, 348, 768, 264, 244, 114, 8, 8, 0], [0, 4, 34, 57, 247, 492, 264, 894, 138, 328, 78, 17, 7, 0], [0, 4, 34, 58, 238, 528, 180, 1020, 12, 412, 42, 26, 6, 0], [0, 4, 35, 44, 318, 273, 690, 348, 600, 82, 147, 16, 2, 1], [0, 4, 35, 45, 309, 309, 606, 474, 474, 166, 111, 25, 1, 1], [0, 4, 35, 46, 300, 345, 522, 600, 348, 250, 75, 34, 0, 1], [0, 4, 35, 47, 292, 372, 474, 642, 348, 208, 123, 7, 8, 0], [0, 4, 35, 48, 283, 408, 390, 768, 222, 292, 87, 16, 7, 0], [0, 4, 35, 49, 274, 444, 306, 894, 96, 376, 51, 25, 6, 0], [0, 4, 36, 35, 354, 189, 816, 222, 684, 46, 156, 15, 2, 1], [0, 4, 36, 36, 345, 225, 732, 348, 558, 130, 120, 24, 1, 1], [0, 4, 36, 37, 336, 261, 648, 474, 432, 214, 84, 33, 0, 1], [0, 4, 36, 38, 328, 288, 600, 516, 432, 172, 132, 6, 8, 0], [0, 4, 36, 39, 319, 324, 516, 642, 306, 256, 96, 15, 7, 0], [0, 4, 36, 40, 310, 360, 432, 768, 180, 340, 60, 24, 6, 0], [0, 4, 36, 41, 301, 396, 348, 894, 54, 424, 24, 33, 5, 0], [0, 4, 37, 26, 390, 105, 942, 96, 768, 10, 165, 14, 2, 1], [0, 4, 37, 27, 381, 141, 858, 222, 642, 94, 129, 23, 1, 1], [0, 4, 37, 28, 372, 177, 774, 348, 516, 178, 93, 32, 0, 1], [0, 4, 37, 29, 364, 204, 726, 390, 516, 136, 141, 5, 8, 0], [0, 4, 37, 30, 355, 240, 642, 516, 390, 220, 105, 14, 7, 0], [0, 4, 37, 31, 346, 276, 558, 642, 264, 304, 69, 23, 6, 0], [0, 4, 37, 32, 337, 312, 474, 768, 138, 388, 33, 32, 5, 0], [0, 4, 38, 18, 417, 57, 984, 96, 726, 58, 138, 22, 1, 1], [0, 4, 38, 19, 408, 93, 900, 222, 600, 142, 102, 31, 0, 1], [0, 4, 38, 20, 400, 120, 852, 264, 600, 100, 150, 4, 8, 0], [0, 4, 38, 21, 391, 156, 768, 390, 474, 184, 114, 13, 7, 0], [0, 4, 38, 22, 382, 192, 684, 516, 348, 268, 78, 22, 6, 0], [0, 4, 38, 23, 373, 228, 600, 642, 222, 352, 42, 31, 5, 0], [0, 4, 38, 24, 364, 264, 516, 768, 96, 436, 6, 40, 4, 0], [0, 4, 39, 10, 444, 9, 1026, 96, 684, 106, 111, 30, 0, 1], [0, 4, 39, 11, 436, 36, 978, 138, 684, 64, 159, 3, 8, 0], [0, 4, 39, 12, 427, 72, 894, 264, 558, 148, 123, 12, 7, 0], [0, 4, 39, 13, 418, 108, 810, 390, 432, 232, 87, 21, 6, 0], [0, 4, 39, 14, 409, 144, 726, 516, 306, 316, 51, 30, 5, 0], [0, 4, 39, 15, 400, 180, 642, 642, 180, 400, 15, 39, 4, 0], [0, 4, 40, 4, 454, 24, 936, 264, 516, 196, 96, 20, 6, 0], [0, 4, 40, 5, 445, 60, 852, 390, 390, 280, 60, 29, 5, 0], [0, 4, 40, 6, 436, 96, 768, 516, 264, 364, 24, 38, 4, 0], [0, 5, 21, 123, 72, 747, 102, 810, 396, 103, 173, 3, 4, 1], [0, 5, 21, 124, 63, 783, 18, 936, 270, 187, 137, 12, 3, 1], [0, 5, 22, 114, 108, 663, 228, 684, 480, 67, 182, 2, 4, 1], [0, 5, 22, 115, 99, 699, 144, 810, 354, 151, 146, 11, 3, 1], [0, 5, 22, 116, 90, 735, 60, 936, 228, 235, 110, 20, 2, 1], [0, 5, 23, 105, 144, 579, 354, 558, 564, 31, 191, 1, 4, 1], [0, 5, 23, 106, 135, 615, 270, 684, 438, 115, 155, 10, 3, 1], [0, 5, 23, 107, 126, 651, 186, 810, 312, 199, 119, 19, 2, 1], [0, 5, 23, 108, 117, 687, 102, 936, 186, 283, 83, 28, 1, 1], [0, 5, 23, 109, 108, 723, 18, 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