------- (14, 6144, 9) ALL distance distributions for EXTERNAL point (9, 6144, 9) has 0 possible DDs: {} (10, 6144, 9) has 1 possible DDs: {[0, 120, 0, 1440, 0, 3024, 0, 1440, 0, 120, 0]} (11, 6144, 9) has 7 possible DDs: {[0, 60, 60, 720, 720, 1512, 1512, 720, 720, 60, 60, 0], [0, 61, 50, 765, 600, 1722, 1260, 930, 600, 105, 50, 1], [0, 62, 40, 810, 480, 1932, 1008, 1140, 480, 150, 40, 2], [0, 63, 30, 855, 360, 2142, 756, 1350, 360, 195, 30, 3], [0, 64, 20, 900, 240, 2352, 504, 1560, 240, 240, 20, 4], [0, 65, 10, 945, 120, 2562, 252, 1770, 120, 285, 10, 5], [0, 66, 0, 990, 0, 2772, 0, 1980, 0, 330, 0, 6]} (12, 6144, 9) has 39 possible DDs: {[0, 25, 110, 165, 1320, 66, 2772, 66, 1320, 165, 110, 25, 0], [0, 26, 100, 210, 1200, 276, 2520, 276, 1200, 210, 100, 26, 0], [0, 26, 101, 200, 1245, 156, 2730, 24, 1410, 90, 145, 16, 1], [0, 27, 90, 255, 1080, 486, 2268, 486, 1080, 255, 90, 27, 0], [0, 27, 91, 245, 1125, 366, 2478, 234, 1290, 135, 135, 17, 1], [0, 28, 80, 300, 960, 696, 2016, 696, 960, 300, 80, 28, 0], [0, 28, 81, 290, 1005, 576, 2226, 444, 1170, 180, 125, 18, 1], [0, 28, 82, 280, 1050, 456, 2436, 192, 1380, 60, 170, 8, 2], [0, 29, 70, 345, 840, 906, 1764, 906, 840, 345, 70, 29, 0], [0, 29, 71, 335, 885, 786, 1974, 654, 1050, 225, 115, 19, 1], [0, 29, 72, 325, 930, 666, 2184, 402, 1260, 105, 160, 9, 2], [0, 30, 60, 390, 720, 1116, 1512, 1116, 720, 390, 60, 30, 0], [0, 30, 61, 380, 765, 996, 1722, 864, 930, 270, 105, 20, 1], [0, 30, 62, 370, 810, 876, 1932, 612, 1140, 150, 150, 10, 2], [0, 30, 63, 360, 855, 756, 2142, 360, 1350, 30, 195, 0, 3], [0, 31, 50, 435, 600, 1326, 1260, 1326, 600, 435, 50, 31, 0], [0, 31, 51, 425, 645, 1206, 1470, 1074, 810, 315, 95, 21, 1], [0, 31, 52, 415, 690, 1086, 1680, 822, 1020, 195, 140, 11, 2], [0, 31, 53, 405, 735, 966, 1890, 570, 1230, 75, 185, 1, 3], [0, 32, 40, 480, 480, 1536, 1008, 1536, 480, 480, 40, 32, 0], [0, 32, 41, 470, 525, 1416, 1218, 1284, 690, 360, 85, 22, 1], [0, 32, 42, 460, 570, 1296, 1428, 1032, 900, 240, 130, 12, 2], [0, 32, 43, 450, 615, 1176, 1638, 780, 1110, 120, 175, 2, 3], [0, 33, 30, 525, 360, 1746, 756, 1746, 360, 525, 30, 33, 0], [0, 33, 31, 515, 405, 1626, 966, 1494, 570, 405, 75, 23, 1], [0, 33, 32, 505, 450, 1506, 1176, 1242, 780, 285, 120, 13, 2], [0, 33, 33, 495, 495, 1386, 1386, 990, 990, 165, 165, 3, 3], [0, 34, 20, 570, 240, 1956, 504, 1956, 240, 570, 20, 34, 0], [0, 34, 21, 560, 285, 1836, 714, 1704, 450, 450, 65, 24, 1], [0, 34, 22, 550, 330, 1716, 924, 1452, 660, 330, 110, 14, 2], [0, 34, 23, 540, 375, 1596, 1134, 1200, 870, 210, 155, 4, 3], [0, 35, 10, 615, 120, 2166, 252, 2166, 120, 615, 10, 35, 0], [0, 35, 11, 605, 165, 2046, 462, 1914, 330, 495, 55, 25, 1], [0, 35, 12, 595, 210, 1926, 672, 1662, 540, 375, 100, 15, 2], [0, 35, 13, 585, 255, 1806, 882, 1410, 750, 255, 145, 5, 3], [0, 36, 0, 660, 0, 2376, 0, 2376, 0, 660, 0, 36, 0], [0, 36, 1, 650, 45, 2256, 210, 2124, 210, 540, 45, 26, 1], [0, 36, 2, 640, 90, 2136, 420, 1872, 420, 420, 90, 16, 2], [0, 36, 3, 630, 135, 2016, 630, 1620, 630, 300, 135, 6, 3]} (13, 6144, 9) has 182 possible DDs: {[0, 9, 99, 15, 1005, 378, 1566, 1566, 378, 1005, 15, 99, 9, 0], [0, 9, 100, 5, 1050, 258, 1776, 1314, 588, 885, 60, 89, 10, 0], [0, 10, 89, 60, 885, 588, 1314, 1776, 258, 1050, 5, 100, 9, 0], [0, 10, 90, 50, 930, 468, 1524, 1524, 468, 930, 50, 90, 10, 0], [0, 10, 91, 40, 975, 348, 1734, 1272, 678, 810, 95, 80, 11, 0], [0, 10, 92, 30, 1020, 228, 1944, 1020, 888, 690, 140, 70, 12, 0], [0, 10, 92, 31, 1010, 273, 1824, 1230, 636, 900, 20, 115, 2, 1], [0, 10, 93, 20, 1065, 108, 2154, 768, 1098, 570, 185, 60, 13, 0], [0, 10, 93, 21, 1055, 153, 2034, 978, 846, 780, 65, 105, 3, 1], [0, 10, 94, 11, 1100, 33, 2244, 726, 1056, 660, 110, 95, 4, 1], [0, 11, 80, 95, 810, 678, 1272, 1734, 348, 975, 40, 91, 10, 0], [0, 11, 81, 85, 855, 558, 1482, 1482, 558, 855, 85, 81, 11, 0], [0, 11, 82, 75, 900, 438, 1692, 1230, 768, 735, 130, 71, 12, 0], [0, 11, 82, 76, 890, 483, 1572, 1440, 516, 945, 10, 116, 2, 1], [0, 11, 83, 65, 945, 318, 1902, 978, 978, 615, 175, 61, 13, 0], [0, 11, 83, 66, 935, 363, 1782, 1188, 726, 825, 55, 106, 3, 1], [0, 11, 84, 55, 990, 198, 2112, 726, 1188, 495, 220, 51, 14, 0], [0, 11, 84, 56, 980, 243, 1992, 936, 936, 705, 100, 96, 4, 1], [0, 11, 85, 45, 1035, 78, 2322, 474, 1398, 375, 265, 41, 15, 0], [0, 11, 85, 46, 1025, 123, 2202, 684, 1146, 585, 145, 86, 5, 1], [0, 11, 86, 36, 1070, 3, 2412, 432, 1356, 465, 190, 76, 6, 1], [0, 12, 70, 140, 690, 888, 1020, 1944, 228, 1020, 30, 92, 10, 0], [0, 12, 71, 130, 735, 768, 1230, 1692, 438, 900, 75, 82, 11, 0], [0, 12, 72, 120, 780, 648, 1440, 1440, 648, 780, 120, 72, 12, 0], [0, 12, 72, 121, 770, 693, 1320, 1650, 396, 990, 0, 117, 2, 1], [0, 12, 73, 110, 825, 528, 1650, 1188, 858, 660, 165, 62, 13, 0], [0, 12, 73, 111, 815, 573, 1530, 1398, 606, 870, 45, 107, 3, 1], [0, 12, 74, 100, 870, 408, 1860, 936, 1068, 540, 210, 52, 14, 0], [0, 12, 74, 101, 860, 453, 1740, 1146, 816, 750, 90, 97, 4, 1], [0, 12, 75, 90, 915, 288, 2070, 684, 1278, 420, 255, 42, 15, 0], [0, 12, 75, 91, 905, 333, 1950, 894, 1026, 630, 135, 87, 5, 1], [0, 12, 76, 80, 960, 168, 2280, 432, 1488, 300, 300, 32, 16, 0], [0, 12, 76, 81, 950, 213, 2160, 642, 1236, 510, 180, 77, 6, 1], [0, 12, 77, 70, 1005, 48, 2490, 180, 1698, 180, 345, 22, 17, 0], [0, 12, 77, 71, 995, 93, 2370, 390, 1446, 390, 225, 67, 7, 1], [0, 13, 60, 185, 570, 1098, 768, 2154, 108, 1065, 20, 93, 10, 0], [0, 13, 61, 175, 615, 978, 978, 1902, 318, 945, 65, 83, 11, 0], [0, 13, 62, 165, 660, 858, 1188, 1650, 528, 825, 110, 73, 12, 0], [0, 13, 63, 155, 705, 738, 1398, 1398, 738, 705, 155, 63, 13, 0], [0, 13, 63, 156, 695, 783, 1278, 1608, 486, 915, 35, 108, 3, 1], [0, 13, 64, 145, 750, 618, 1608, 1146, 948, 585, 200, 53, 14, 0], [0, 13, 64, 146, 740, 663, 1488, 1356, 696, 795, 80, 98, 4, 1], [0, 13, 65, 135, 795, 498, 1818, 894, 1158, 465, 245, 43, 15, 0], [0, 13, 65, 136, 785, 543, 1698, 1104, 906, 675, 125, 88, 5, 1], [0, 13, 66, 125, 840, 378, 2028, 642, 1368, 345, 290, 33, 16, 0], [0, 13, 66, 126, 830, 423, 1908, 852, 1116, 555, 170, 78, 6, 1], [0, 13, 67, 115, 885, 258, 2238, 390, 1578, 225, 335, 23, 17, 0], [0, 13, 67, 116, 875, 303, 2118, 600, 1326, 435, 215, 68, 7, 1], [0, 13, 68, 105, 930, 138, 2448, 138, 1788, 105, 380, 13, 18, 0], [0, 13, 68, 106, 920, 183, 2328, 348, 1536, 315, 260, 58, 8, 1], [0, 13, 69, 96, 965, 63, 2538, 96, 1746, 195, 305, 48, 9, 1], [0, 14, 51, 220, 495, 1188, 726, 2112, 198, 990, 55, 84, 11, 0], [0, 14, 52, 210, 540, 1068, 936, 1860, 408, 870, 100, 74, 12, 0], [0, 14, 53, 200, 585, 948, 1146, 1608, 618, 750, 145, 64, 13, 0], [0, 14, 53, 201, 575, 993, 1026, 1818, 366, 960, 25, 109, 3, 1], [0, 14, 54, 190, 630, 828, 1356, 1356, 828, 630, 190, 54, 14, 0], [0, 14, 54, 191, 620, 873, 1236, 1566, 576, 840, 70, 99, 4, 1], [0, 14, 55, 180, 675, 708, 1566, 1104, 1038, 510, 235, 44, 15, 0], [0, 14, 55, 181, 665, 753, 1446, 1314, 786, 720, 115, 89, 5, 1], [0, 14, 56, 170, 720, 588, 1776, 852, 1248, 390, 280, 34, 16, 0], [0, 14, 56, 171, 710, 633, 1656, 1062, 996, 600, 160, 79, 6, 1], [0, 14, 57, 160, 765, 468, 1986, 600, 1458, 270, 325, 24, 17, 0], [0, 14, 57, 161, 755, 513, 1866, 810, 1206, 480, 205, 69, 7, 1], [0, 14, 58, 150, 810, 348, 2196, 348, 1668, 150, 370, 14, 18, 0], [0, 14, 58, 151, 800, 393, 2076, 558, 1416, 360, 250, 59, 8, 1], [0, 14, 59, 140, 855, 228, 2406, 96, 1878, 30, 415, 4, 19, 0], [0, 14, 59, 141, 845, 273, 2286, 306, 1626, 240, 295, 49, 9, 1], [0, 14, 60, 131, 890, 153, 2496, 54, 1836, 120, 340, 39, 10, 1], [0, 14, 60, 132, 880, 198, 2376, 264, 1584, 330, 220, 84, 0, 2], [0, 14, 61, 122, 925, 78, 2586, 12, 1794, 210, 265, 74, 1, 2], [0, 15, 41, 265, 375, 1398, 474, 2322, 78, 1035, 45, 85, 11, 0], [0, 15, 42, 255, 420, 1278, 684, 2070, 288, 915, 90, 75, 12, 0], [0, 15, 43, 245, 465, 1158, 894, 1818, 498, 795, 135, 65, 13, 0], [0, 15, 43, 246, 455, 1203, 774, 2028, 246, 1005, 15, 110, 3, 1], [0, 15, 44, 235, 510, 1038, 1104, 1566, 708, 675, 180, 55, 14, 0], [0, 15, 44, 236, 500, 1083, 984, 1776, 456, 885, 60, 100, 4, 1], [0, 15, 45, 225, 555, 918, 1314, 1314, 918, 555, 225, 45, 15, 0], [0, 15, 45, 226, 545, 963, 1194, 1524, 666, 765, 105, 90, 5, 1], [0, 15, 46, 215, 600, 798, 1524, 1062, 1128, 435, 270, 35, 16, 0], [0, 15, 46, 216, 590, 843, 1404, 1272, 876, 645, 150, 80, 6, 1], [0, 15, 47, 205, 645, 678, 1734, 810, 1338, 315, 315, 25, 17, 0], [0, 15, 47, 206, 635, 723, 1614, 1020, 1086, 525, 195, 70, 7, 1], [0, 15, 48, 195, 690, 558, 1944, 558, 1548, 195, 360, 15, 18, 0], [0, 15, 48, 196, 680, 603, 1824, 768, 1296, 405, 240, 60, 8, 1], [0, 15, 49, 185, 735, 438, 2154, 306, 1758, 75, 405, 5, 19, 0], [0, 15, 49, 186, 725, 483, 2034, 516, 1506, 285, 285, 50, 9, 1], [0, 15, 50, 176, 770, 363, 2244, 264, 1716, 165, 330, 40, 10, 1], [0, 15, 50, 177, 760, 408, 2124, 474, 1464, 375, 210, 85, 0, 2], [0, 15, 51, 166, 815, 243, 2454, 12, 1926, 45, 375, 30, 11, 1], [0, 15, 51, 167, 805, 288, 2334, 222, 1674, 255, 255, 75, 1, 2], [0, 16, 32, 300, 300, 1488, 432, 2280, 168, 960, 80, 76, 12, 0], [0, 16, 33, 290, 345, 1368, 642, 2028, 378, 840, 125, 66, 13, 0], [0, 16, 33, 291, 335, 1413, 522, 2238, 126, 1050, 5, 111, 3, 1], [0, 16, 34, 280, 390, 1248, 852, 1776, 588, 720, 170, 56, 14, 0], [0, 16, 34, 281, 380, 1293, 732, 1986, 336, 930, 50, 101, 4, 1], [0, 16, 35, 270, 435, 1128, 1062, 1524, 798, 600, 215, 46, 15, 0], [0, 16, 35, 271, 425, 1173, 942, 1734, 546, 810, 95, 91, 5, 1], [0, 16, 36, 260, 480, 1008, 1272, 1272, 1008, 480, 260, 36, 16, 0], [0, 16, 36, 261, 470, 1053, 1152, 1482, 756, 690, 140, 81, 6, 1], [0, 16, 37, 250, 525, 888, 1482, 1020, 1218, 360, 305, 26, 17, 0], [0, 16, 37, 251, 515, 933, 1362, 1230, 966, 570, 185, 71, 7, 1], [0, 16, 38, 240, 570, 768, 1692, 768, 1428, 240, 350, 16, 18, 0], [0, 16, 38, 241, 560, 813, 1572, 978, 1176, 450, 230, 61, 8, 1], [0, 16, 39, 230, 615, 648, 1902, 516, 1638, 120, 395, 6, 19, 0], [0, 16, 39, 231, 605, 693, 1782, 726, 1386, 330, 275, 51, 9, 1], [0, 16, 40, 221, 650, 573, 1992, 474, 1596, 210, 320, 41, 10, 1], [0, 16, 40, 222, 640, 618, 1872, 684, 1344, 420, 200, 86, 0, 2], [0, 16, 41, 211, 695, 453, 2202, 222, 1806, 90, 365, 31, 11, 1], [0, 16, 41, 212, 685, 498, 2082, 432, 1554, 300, 245, 76, 1, 2], [0, 16, 42, 202, 730, 378, 2292, 180, 1764, 180, 290, 66, 2, 2], [0, 17, 22, 345, 180, 1698, 180, 2490, 48, 1005, 70, 77, 12, 0], [0, 17, 23, 335, 225, 1578, 390, 2238, 258, 885, 115, 67, 13, 0], [0, 17, 24, 325, 270, 1458, 600, 1986, 468, 765, 160, 57, 14, 0], [0, 17, 24, 326, 260, 1503, 480, 2196, 216, 975, 40, 102, 4, 1], [0, 17, 25, 315, 315, 1338, 810, 1734, 678, 645, 205, 47, 15, 0], [0, 17, 25, 316, 305, 1383, 690, 1944, 426, 855, 85, 92, 5, 1], [0, 17, 26, 305, 360, 1218, 1020, 1482, 888, 525, 250, 37, 16, 0], [0, 17, 26, 306, 350, 1263, 900, 1692, 636, 735, 130, 82, 6, 1], [0, 17, 27, 295, 405, 1098, 1230, 1230, 1098, 405, 295, 27, 17, 0], [0, 17, 27, 296, 395, 1143, 1110, 1440, 846, 615, 175, 72, 7, 1], [0, 17, 28, 285, 450, 978, 1440, 978, 1308, 285, 340, 17, 18, 0], [0, 17, 28, 286, 440, 1023, 1320, 1188, 1056, 495, 220, 62, 8, 1], [0, 17, 29, 275, 495, 858, 1650, 726, 1518, 165, 385, 7, 19, 0], [0, 17, 29, 276, 485, 903, 1530, 936, 1266, 375, 265, 52, 9, 1], [0, 17, 30, 266, 530, 783, 1740, 684, 1476, 255, 310, 42, 10, 1], [0, 17, 30, 267, 520, 828, 1620, 894, 1224, 465, 190, 87, 0, 2], [0, 17, 31, 256, 575, 663, 1950, 432, 1686, 135, 355, 32, 11, 1], [0, 17, 31, 257, 565, 708, 1830, 642, 1434, 345, 235, 77, 1, 2], [0, 17, 32, 246, 620, 543, 2160, 180, 1896, 15, 400, 22, 12, 1], [0, 17, 32, 247, 610, 588, 2040, 390, 1644, 225, 280, 67, 2, 2], [0, 17, 33, 237, 655, 468, 2250, 138, 1854, 105, 325, 57, 3, 2], [0, 18, 13, 380, 105, 1788, 138, 2448, 138, 930, 105, 68, 13, 0], [0, 18, 14, 370, 150, 1668, 348, 2196, 348, 810, 150, 58, 14, 0], [0, 18, 14, 371, 140, 1713, 228, 2406, 96, 1020, 30, 103, 4, 1], [0, 18, 15, 360, 195, 1548, 558, 1944, 558, 690, 195, 48, 15, 0], [0, 18, 15, 361, 185, 1593, 438, 2154, 306, 900, 75, 93, 5, 1], [0, 18, 16, 350, 240, 1428, 768, 1692, 768, 570, 240, 38, 16, 0], [0, 18, 16, 351, 230, 1473, 648, 1902, 516, 780, 120, 83, 6, 1], [0, 18, 17, 340, 285, 1308, 978, 1440, 978, 450, 285, 28, 17, 0], [0, 18, 17, 341, 275, 1353, 858, 1650, 726, 660, 165, 73, 7, 1], [0, 18, 18, 330, 330, 1188, 1188, 1188, 1188, 330, 330, 18, 18, 0], [0, 18, 18, 331, 320, 1233, 1068, 1398, 936, 540, 210, 63, 8, 1], [0, 18, 19, 320, 375, 1068, 1398, 936, 1398, 210, 375, 8, 19, 0], [0, 18, 19, 321, 365, 1113, 1278, 1146, 1146, 420, 255, 53, 9, 1], [0, 18, 20, 311, 410, 993, 1488, 894, 1356, 300, 300, 43, 10, 1], [0, 18, 20, 312, 400, 1038, 1368, 1104, 1104, 510, 180, 88, 0, 2], [0, 18, 21, 301, 455, 873, 1698, 642, 1566, 180, 345, 33, 11, 1], [0, 18, 21, 302, 445, 918, 1578, 852, 1314, 390, 225, 78, 1, 2], [0, 18, 22, 291, 500, 753, 1908, 390, 1776, 60, 390, 23, 12, 1], [0, 18, 22, 292, 490, 798, 1788, 600, 1524, 270, 270, 68, 2, 2], [0, 18, 23, 282, 535, 678, 1998, 348, 1734, 150, 315, 58, 3, 2], [0, 18, 24, 272, 580, 558, 2208, 96, 1944, 30, 360, 48, 4, 2], [0, 19, 4, 415, 30, 1878, 96, 2406, 228, 855, 140, 59, 14, 0], [0, 19, 5, 405, 75, 1758, 306, 2154, 438, 735, 185, 49, 15, 0], [0, 19, 5, 406, 65, 1803, 186, 2364, 186, 945, 65, 94, 5, 1], [0, 19, 6, 395, 120, 1638, 516, 1902, 648, 615, 230, 39, 16, 0], [0, 19, 6, 396, 110, 1683, 396, 2112, 396, 825, 110, 84, 6, 1], [0, 19, 7, 385, 165, 1518, 726, 1650, 858, 495, 275, 29, 17, 0], [0, 19, 7, 386, 155, 1563, 606, 1860, 606, 705, 155, 74, 7, 1], [0, 19, 8, 375, 210, 1398, 936, 1398, 1068, 375, 320, 19, 18, 0], [0, 19, 8, 376, 200, 1443, 816, 1608, 816, 585, 200, 64, 8, 1], [0, 19, 9, 365, 255, 1278, 1146, 1146, 1278, 255, 365, 9, 19, 0], [0, 19, 9, 366, 245, 1323, 1026, 1356, 1026, 465, 245, 54, 9, 1], [0, 19, 10, 356, 290, 1203, 1236, 1104, 1236, 345, 290, 44, 10, 1], [0, 19, 10, 357, 280, 1248, 1116, 1314, 984, 555, 170, 89, 0, 2], [0, 19, 11, 346, 335, 1083, 1446, 852, 1446, 225, 335, 34, 11, 1], [0, 19, 11, 347, 325, 1128, 1326, 1062, 1194, 435, 215, 79, 1, 2], [0, 19, 12, 336, 380, 963, 1656, 600, 1656, 105, 380, 24, 12, 1], [0, 19, 12, 337, 370, 1008, 1536, 810, 1404, 315, 260, 69, 2, 2], [0, 19, 13, 327, 415, 888, 1746, 558, 1614, 195, 305, 59, 3, 2], [0, 19, 14, 317, 460, 768, 1956, 306, 1824, 75, 350, 49, 4, 2], [0, 20, 0, 400, 180, 1368, 1104, 1104, 1368, 180, 400, 0, 20, 0], [0, 20, 0, 401, 170, 1413, 984, 1314, 1116, 390, 280, 45, 10, 1], [0, 20, 0, 402, 160, 1458, 864, 1524, 864, 600, 160, 90, 0, 2], [0, 20, 1, 391, 215, 1293, 1194, 1062, 1326, 270, 325, 35, 11, 1], [0, 20, 1, 392, 205, 1338, 1074, 1272, 1074, 480, 205, 80, 1, 2], [0, 20, 2, 381, 260, 1173, 1404, 810, 1536, 150, 370, 25, 12, 1], [0, 20, 2, 382, 250, 1218, 1284, 1020, 1284, 360, 250, 70, 2, 2], [0, 20, 3, 371, 305, 1053, 1614, 558, 1746, 30, 415, 15, 13, 1], [0, 20, 3, 372, 295, 1098, 1494, 768, 1494, 240, 295, 60, 3, 2], [0, 20, 4, 362, 340, 978, 1704, 516, 1704, 120, 340, 50, 4, 2], [0, 20, 5, 352, 385, 858, 1914, 264, 1914, 0, 385, 40, 5, 2]} (14, 6144, 9) has 779 possible DDs: {[0, 2, 70, 32, 430, 1134, 12, 2784, 12, 1134, 430, 32, 70, 2, 0], [0, 2, 71, 22, 475, 1014, 222, 2532, 222, 1014, 475, 22, 71, 2, 0], [0, 2, 72, 12, 520, 894, 432, 2280, 432, 894, 520, 12, 72, 2, 0], [0, 2, 72, 13, 510, 939, 312, 2490, 180, 1104, 400, 57, 62, 3, 0], [0, 2, 73, 2, 565, 774, 642, 2028, 642, 774, 565, 2, 73, 2, 0], [0, 2, 73, 3, 555, 819, 522, 2238, 390, 984, 445, 47, 63, 3, 0], [0, 2, 73, 4, 545, 864, 402, 2448, 138, 1194, 325, 92, 53, 4, 0], [0, 3, 62, 57, 400, 1104, 180, 2490, 312, 939, 510, 13, 72, 2, 0], [0, 3, 62, 58, 390, 1149, 60, 2700, 60, 1149, 390, 58, 62, 3, 0], [0, 3, 63, 47, 445, 984, 390, 2238, 522, 819, 555, 3, 73, 2, 0], [0, 3, 63, 48, 435, 1029, 270, 2448, 270, 1029, 435, 48, 63, 3, 0], [0, 3, 63, 49, 425, 1074, 150, 2658, 18, 1239, 315, 93, 53, 4, 0], [0, 3, 64, 38, 480, 909, 480, 2196, 480, 909, 480, 38, 64, 3, 0], [0, 3, 64, 39, 470, 954, 360, 2406, 228, 1119, 360, 83, 54, 4, 0], [0, 3, 65, 28, 525, 789, 690, 1944, 690, 789, 525, 28, 65, 3, 0], [0, 3, 65, 29, 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0], [0, 4, 60, 30, 561, 704, 693, 2244, 66, 1452, 110, 174, 45, 0, 1], [0, 4, 61, 14, 665, 324, 1578, 852, 1578, 324, 665, 14, 61, 4, 0], [0, 4, 61, 15, 655, 369, 1458, 1062, 1326, 534, 545, 59, 51, 5, 0], [0, 4, 61, 16, 645, 414, 1338, 1272, 1074, 744, 425, 104, 41, 6, 0], [0, 4, 61, 17, 635, 459, 1218, 1482, 822, 954, 305, 149, 31, 7, 0], [0, 4, 61, 18, 625, 504, 1098, 1692, 570, 1164, 185, 194, 21, 8, 0], [0, 4, 61, 19, 615, 549, 978, 1902, 318, 1374, 65, 239, 11, 9, 0], [0, 4, 61, 20, 606, 584, 903, 1992, 276, 1332, 155, 164, 46, 0, 1], [0, 4, 61, 21, 596, 629, 783, 2202, 24, 1542, 35, 209, 36, 1, 1], [0, 4, 62, 4, 710, 204, 1788, 600, 1788, 204, 710, 4, 62, 4, 0], [0, 4, 62, 5, 700, 249, 1668, 810, 1536, 414, 590, 49, 52, 5, 0], [0, 4, 62, 6, 690, 294, 1548, 1020, 1284, 624, 470, 94, 42, 6, 0], [0, 4, 62, 7, 680, 339, 1428, 1230, 1032, 834, 350, 139, 32, 7, 0], [0, 4, 62, 8, 670, 384, 1308, 1440, 780, 1044, 230, 184, 22, 8, 0], [0, 4, 62, 9, 660, 429, 1188, 1650, 528, 1254, 110, 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2490, 114, 1269, 235, 145, 37, 6, 0], [0, 5, 48, 88, 420, 849, 816, 1608, 1080, 519, 640, 0, 68, 3, 0], [0, 5, 48, 89, 410, 894, 696, 1818, 828, 729, 520, 45, 58, 4, 0], [0, 5, 48, 90, 400, 939, 576, 2028, 576, 939, 400, 90, 48, 5, 0], [0, 5, 48, 91, 390, 984, 456, 2238, 324, 1149, 280, 135, 38, 6, 0], [0, 5, 48, 92, 380, 1029, 336, 2448, 72, 1359, 160, 180, 28, 7, 0], [0, 5, 49, 79, 455, 774, 906, 1566, 1038, 609, 565, 35, 59, 4, 0], [0, 5, 49, 80, 445, 819, 786, 1776, 786, 819, 445, 80, 49, 5, 0], [0, 5, 49, 81, 435, 864, 666, 1986, 534, 1029, 325, 125, 39, 6, 0], [0, 5, 49, 82, 425, 909, 546, 2196, 282, 1239, 205, 170, 29, 7, 0], [0, 5, 49, 83, 415, 954, 426, 2406, 30, 1449, 85, 215, 19, 8, 0], [0, 5, 50, 69, 500, 654, 1116, 1314, 1248, 489, 610, 25, 60, 4, 0], [0, 5, 50, 70, 490, 699, 996, 1524, 996, 699, 490, 70, 50, 5, 0], [0, 5, 50, 71, 480, 744, 876, 1734, 744, 909, 370, 115, 40, 6, 0], [0, 5, 50, 72, 470, 789, 756, 1944, 492, 1119, 250, 160, 30, 7, 0], [0, 5, 50, 73, 460, 834, 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52, 56, 521, 719, 741, 2160, 114, 1467, 70, 200, 37, 1, 1], [0, 5, 53, 40, 625, 339, 1626, 768, 1626, 339, 625, 40, 53, 5, 0], [0, 5, 53, 41, 615, 384, 1506, 978, 1374, 549, 505, 85, 43, 6, 0], [0, 5, 53, 42, 605, 429, 1386, 1188, 1122, 759, 385, 130, 33, 7, 0], [0, 5, 53, 43, 595, 474, 1266, 1398, 870, 969, 265, 175, 23, 8, 0], [0, 5, 53, 44, 585, 519, 1146, 1608, 618, 1179, 145, 220, 13, 9, 0], [0, 5, 53, 45, 575, 564, 1026, 1818, 366, 1389, 25, 265, 3, 10, 0], [0, 5, 53, 45, 576, 554, 1071, 1698, 576, 1137, 235, 145, 48, 0, 1], [0, 5, 53, 46, 566, 599, 951, 1908, 324, 1347, 115, 190, 38, 1, 1], [0, 5, 54, 30, 670, 219, 1836, 516, 1836, 219, 670, 30, 54, 5, 0], [0, 5, 54, 31, 660, 264, 1716, 726, 1584, 429, 550, 75, 44, 6, 0], [0, 5, 54, 32, 650, 309, 1596, 936, 1332, 639, 430, 120, 34, 7, 0], [0, 5, 54, 33, 640, 354, 1476, 1146, 1080, 849, 310, 165, 24, 8, 0], [0, 5, 54, 34, 630, 399, 1356, 1356, 828, 1059, 190, 210, 14, 9, 0], [0, 5, 54, 35, 620, 444, 1236, 1566, 576, 1269, 70, 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642, 1500, 609, 400, 145, 26, 8, 0], [0, 5, 56, 14, 720, 159, 1776, 852, 1248, 819, 280, 190, 16, 9, 0], [0, 5, 56, 15, 710, 204, 1656, 1062, 996, 1029, 160, 235, 6, 10, 0], [0, 5, 56, 15, 711, 194, 1701, 942, 1206, 777, 370, 115, 51, 0, 1], [0, 5, 56, 16, 701, 239, 1581, 1152, 954, 987, 250, 160, 41, 1, 1], [0, 5, 56, 17, 691, 284, 1461, 1362, 702, 1197, 130, 205, 31, 2, 1], [0, 5, 56, 18, 681, 329, 1341, 1572, 450, 1407, 10, 250, 21, 3, 1], [0, 5, 57, 4, 765, 39, 1986, 600, 1458, 699, 325, 180, 17, 9, 0], [0, 5, 57, 5, 755, 84, 1866, 810, 1206, 909, 205, 225, 7, 10, 0], [0, 5, 57, 5, 756, 74, 1911, 690, 1416, 657, 415, 105, 52, 0, 1], [0, 5, 57, 6, 746, 119, 1791, 900, 1164, 867, 295, 150, 42, 1, 1], [0, 5, 57, 7, 736, 164, 1671, 1110, 912, 1077, 175, 195, 32, 2, 1], [0, 5, 57, 8, 726, 209, 1551, 1320, 660, 1287, 55, 240, 22, 3, 1], [0, 6, 36, 153, 210, 1299, 144, 2322, 540, 804, 540, 21, 66, 3, 0], [0, 6, 36, 154, 200, 1344, 24, 2532, 288, 1014, 420, 66, 56, 4, 0], [0, 6, 37, 143, 255, 1179, 354, 2070, 750, 684, 585, 11, 67, 3, 0], [0, 6, 37, 144, 245, 1224, 234, 2280, 498, 894, 465, 56, 57, 4, 0], [0, 6, 37, 145, 235, 1269, 114, 2490, 246, 1104, 345, 101, 47, 5, 0], [0, 6, 38, 133, 300, 1059, 564, 1818, 960, 564, 630, 1, 68, 3, 0], [0, 6, 38, 134, 290, 1104, 444, 2028, 708, 774, 510, 46, 58, 4, 0], [0, 6, 38, 135, 280, 1149, 324, 2238, 456, 984, 390, 91, 48, 5, 0], [0, 6, 38, 136, 270, 1194, 204, 2448, 204, 1194, 270, 136, 38, 6, 0], [0, 6, 39, 124, 335, 984, 654, 1776, 918, 654, 555, 36, 59, 4, 0], [0, 6, 39, 125, 325, 1029, 534, 1986, 666, 864, 435, 81, 49, 5, 0], [0, 6, 39, 126, 315, 1074, 414, 2196, 414, 1074, 315, 126, 39, 6, 0], [0, 6, 39, 127, 305, 1119, 294, 2406, 162, 1284, 195, 171, 29, 7, 0], [0, 6, 40, 114, 380, 864, 864, 1524, 1128, 534, 600, 26, 60, 4, 0], [0, 6, 40, 115, 370, 909, 744, 1734, 876, 744, 480, 71, 50, 5, 0], [0, 6, 40, 116, 360, 954, 624, 1944, 624, 954, 360, 116, 40, 6, 0], [0, 6, 40, 117, 350, 999, 504, 2154, 372, 1164, 240, 161, 30, 7, 0], [0, 6, 40, 118, 340, 1044, 384, 2364, 120, 1374, 120, 206, 20, 8, 0], [0, 6, 41, 104, 425, 744, 1074, 1272, 1338, 414, 645, 16, 61, 4, 0], [0, 6, 41, 105, 415, 789, 954, 1482, 1086, 624, 525, 61, 51, 5, 0], [0, 6, 41, 106, 405, 834, 834, 1692, 834, 834, 405, 106, 41, 6, 0], [0, 6, 41, 107, 395, 879, 714, 1902, 582, 1044, 285, 151, 31, 7, 0], [0, 6, 41, 108, 385, 924, 594, 2112, 330, 1254, 165, 196, 21, 8, 0], [0, 6, 41, 109, 375, 969, 474, 2322, 78, 1464, 45, 241, 11, 9, 0], [0, 6, 41, 110, 366, 1004, 399, 2412, 36, 1422, 135, 166, 46, 0, 1], [0, 6, 42, 94, 470, 624, 1284, 1020, 1548, 294, 690, 6, 62, 4, 0], [0, 6, 42, 95, 460, 669, 1164, 1230, 1296, 504, 570, 51, 52, 5, 0], [0, 6, 42, 96, 450, 714, 1044, 1440, 1044, 714, 450, 96, 42, 6, 0], [0, 6, 42, 97, 440, 759, 924, 1650, 792, 924, 330, 141, 32, 7, 0], [0, 6, 42, 98, 430, 804, 804, 1860, 540, 1134, 210, 186, 22, 8, 0], [0, 6, 42, 99, 420, 849, 684, 2070, 288, 1344, 90, 231, 12, 9, 0], [0, 6, 42, 100, 411, 884, 609, 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