-------
(12, 118098, 9) ALL distance distributions for INTERNAL point
(9, 118098, 9) has 1 possible DDs: {[6, 108, 864, 4032, 12096, 24192, 32256, 27648, 13824, 3072]}
(10, 118098, 9) has 6 possible DDs: {[1, 50, 315, 2040, 6510, 16380, 26670, 30840, 22995, 10250, 2047], [2, 40, 360, 1920, 6720, 16128, 26880, 30720, 23040, 10240, 2048], [3, 30, 405, 1800, 6930, 15876, 27090, 30600, 23085, 10230, 2049], [4, 20, 450, 1680, 7140, 15624, 27300, 30480, 23130, 10220, 2050], [5, 10, 495, 1560, 7350, 15372, 27510, 30360, 23175, 10210, 2051], [6, 0, 540, 1440, 7560, 15120, 27720, 30240, 23220, 10200, 2052]}
(11, 118098, 9) has 87 possible DDs: {[1, 0, 275, 330, 4950, 7392, 22638, 25740, 29535, 18260, 7623, 1354], [1, 1, 265, 375, 4830, 7602, 22386, 25950, 29415, 18305, 7613, 1355], [1, 2, 255, 420, 4710, 7812, 22134, 26160, 29295, 18350, 7603, 1356], [1, 3, 245, 465, 4590, 8022, 21882, 26370, 29175, 18395, 7593, 1357], [1, 4, 235, 510, 4470, 8232, 21630, 26580, 29055, 18440, 7583, 1358], [1, 5, 225, 555, 4350, 8442, 21378, 26790, 28935, 18485, 7573, 1359], [1, 6, 215, 600, 4230, 8652, 21126, 27000, 28815, 18530, 7563, 1360], [1, 7, 205, 645, 4110, 8862, 20874, 27210, 28695, 18575, 7553, 1361], [1, 8, 195, 690, 3990, 9072, 20622, 27420, 28575, 18620, 7543, 1362], [1, 9, 185, 735, 3870, 9282, 20370, 27630, 28455, 18665, 7533, 1363], [1, 10, 175, 780, 3750, 9492, 20118, 27840, 28335, 18710, 7523, 1364], [1, 11, 165, 825, 3630, 9702, 19866, 28050, 28215, 18755, 7513, 1365], [1, 12, 155, 870, 3510, 9912, 19614, 28260, 28095, 18800, 7503, 1366], [1, 13, 145, 915, 3390, 10122, 19362, 28470, 27975, 18845, 7493, 1367], [1, 14, 135, 960, 3270, 10332, 19110, 28680, 27855, 18890, 7483, 1368], [1, 15, 125, 1005, 3150, 10542, 18858, 28890, 27735, 18935, 7473, 1369], [1, 16, 115, 1050, 3030, 10752, 18606, 29100, 27615, 18980, 7463, 1370], [1, 17, 105, 1095, 2910, 10962, 18354, 29310, 27495, 19025, 7453, 1371], [1, 18, 95, 1140, 2790, 11172, 18102, 29520, 27375, 19070, 7443, 1372], [1, 19, 85, 1185, 2670, 11382, 17850, 29730, 27255, 19115, 7433, 1373], [1, 20, 75, 1230, 2550, 11592, 17598, 29940, 27135, 19160, 7423, 1374], [1, 21, 65, 1275, 2430, 11802, 17346, 30150, 27015, 19205, 7413, 1375], [1, 22, 55, 1320, 2310, 12012, 17094, 30360, 26895, 19250, 7403, 1376], [1, 23, 45, 1365, 2190, 12222, 16842, 30570, 26775, 19295, 7393, 1377], [1, 24, 35, 1410, 2070, 12432, 16590, 30780, 26655, 19340, 7383, 1378], [1, 25, 25, 1455, 1950, 12642, 16338, 30990, 26535, 19385, 7373, 1379], [1, 26, 15, 1500, 1830, 12852, 16086, 31200, 26415, 19430, 7363, 1380], [1, 27, 5, 1545, 1710, 13062, 15834, 31410, 26295, 19475, 7353, 1381], [2, 0, 220, 660, 3960, 9240, 20328, 27720, 28380, 18700, 7524, 1364], [2, 1, 210, 705, 3840, 9450, 20076, 27930, 28260, 18745, 7514, 1365], [2, 2, 200, 750, 3720, 9660, 19824, 28140, 28140, 18790, 7504, 1366], [2, 3, 190, 795, 3600, 9870, 19572, 28350, 28020, 18835, 7494, 1367], [2, 4, 180, 840, 3480, 10080, 19320, 28560, 27900, 18880, 7484, 1368], [2, 5, 170, 885, 3360, 10290, 19068, 28770, 27780, 18925, 7474, 1369], [2, 6, 160, 930, 3240, 10500, 18816, 28980, 27660, 18970, 7464, 1370], [2, 7, 150, 975, 3120, 10710, 18564, 29190, 27540, 19015, 7454, 1371], [2, 8, 140, 1020, 3000, 10920, 18312, 29400, 27420, 19060, 7444, 1372], [2, 9, 130, 1065, 2880, 11130, 18060, 29610, 27300, 19105, 7434, 1373], [2, 10, 120, 1110, 2760, 11340, 17808, 29820, 27180, 19150, 7424, 1374], [2, 11, 110, 1155, 2640, 11550, 17556, 30030, 27060, 19195, 7414, 1375], [2, 12, 100, 1200, 2520, 11760, 17304, 30240, 26940, 19240, 7404, 1376], [2, 13, 90, 1245, 2400, 11970, 17052, 30450, 26820, 19285, 7394, 1377], [2, 14, 80, 1290, 2280, 12180, 16800, 30660, 26700, 19330, 7384, 1378], [2, 15, 70, 1335, 2160, 12390, 16548, 30870, 26580, 19375, 7374, 1379], [2, 16, 60, 1380, 2040, 12600, 16296, 31080, 26460, 19420, 7364, 1380], [2, 17, 50, 1425, 1920, 12810, 16044, 31290, 26340, 19465, 7354, 1381], [2, 18, 40, 1470, 1800, 13020, 15792, 31500, 26220, 19510, 7344, 1382], [2, 19, 30, 1515, 1680, 13230, 15540, 31710, 26100, 19555, 7334, 1383], [2, 20, 20, 1560, 1560, 13440, 15288, 31920, 25980, 19600, 7324, 1384], [2, 21, 10, 1605, 1440, 13650, 15036, 32130, 25860, 19645, 7314, 1385], [2, 22, 0, 1650, 1320, 13860, 14784, 32340, 25740, 19690, 7304, 1386], [3, 0, 165, 990, 2970, 11088, 18018, 29700, 27225, 19140, 7425, 1374], [3, 1, 155, 1035, 2850, 11298, 17766, 29910, 27105, 19185, 7415, 1375], [3, 2, 145, 1080, 2730, 11508, 17514, 30120, 26985, 19230, 7405, 1376], [3, 3, 135, 1125, 2610, 11718, 17262, 30330, 26865, 19275, 7395, 1377], [3, 4, 125, 1170, 2490, 11928, 17010, 30540, 26745, 19320, 7385, 1378], [3, 5, 115, 1215, 2370, 12138, 16758, 30750, 26625, 19365, 7375, 1379], [3, 6, 105, 1260, 2250, 12348, 16506, 30960, 26505, 19410, 7365, 1380], [3, 7, 95, 1305, 2130, 12558, 16254, 31170, 26385, 19455, 7355, 1381], [3, 8, 85, 1350, 2010, 12768, 16002, 31380, 26265, 19500, 7345, 1382], [3, 9, 75, 1395, 1890, 12978, 15750, 31590, 26145, 19545, 7335, 1383], [3, 10, 65, 1440, 1770, 13188, 15498, 31800, 26025, 19590, 7325, 1384], [3, 11, 55, 1485, 1650, 13398, 15246, 32010, 25905, 19635, 7315, 1385], [3, 12, 45, 1530, 1530, 13608, 14994, 32220, 25785, 19680, 7305, 1386], [3, 13, 35, 1575, 1410, 13818, 14742, 32430, 25665, 19725, 7295, 1387], [3, 14, 25, 1620, 1290, 14028, 14490, 32640, 25545, 19770, 7285, 1388], [3, 15, 15, 1665, 1170, 14238, 14238, 32850, 25425, 19815, 7275, 1389], [3, 16, 5, 1710, 1050, 14448, 13986, 33060, 25305, 19860, 7265, 1390], [4, 0, 110, 1320, 1980, 12936, 15708, 31680, 26070, 19580, 7326, 1384], [4, 1, 100, 1365, 1860, 13146, 15456, 31890, 25950, 19625, 7316, 1385], [4, 2, 90, 1410, 1740, 13356, 15204, 32100, 25830, 19670, 7306, 1386], [4, 3, 80, 1455, 1620, 13566, 14952, 32310, 25710, 19715, 7296, 1387], [4, 4, 70, 1500, 1500, 13776, 14700, 32520, 25590, 19760, 7286, 1388], [4, 5, 60, 1545, 1380, 13986, 14448, 32730, 25470, 19805, 7276, 1389], [4, 6, 50, 1590, 1260, 14196, 14196, 32940, 25350, 19850, 7266, 1390], [4, 7, 40, 1635, 1140, 14406, 13944, 33150, 25230, 19895, 7256, 1391], [4, 8, 30, 1680, 1020, 14616, 13692, 33360, 25110, 19940, 7246, 1392], [4, 9, 20, 1725, 900, 14826, 13440, 33570, 24990, 19985, 7236, 1393], [4, 10, 10, 1770, 780, 15036, 13188, 33780, 24870, 20030, 7226, 1394], [4, 11, 0, 1815, 660, 15246, 12936, 33990, 24750, 20075, 7216, 1395], [5, 0, 55, 1650, 990, 14784, 13398, 33660, 24915, 20020, 7227, 1394], [5, 1, 45, 1695, 870, 14994, 13146, 33870, 24795, 20065, 7217, 1395], [5, 2, 35, 1740, 750, 15204, 12894, 34080, 24675, 20110, 7207, 1396], [5, 3, 25, 1785, 630, 15414, 12642, 34290, 24555, 20155, 7197, 1397], [5, 4, 15, 1830, 510, 15624, 12390, 34500, 24435, 20200, 7187, 1398], [5, 5, 5, 1875, 390, 15834, 12138, 34710, 24315, 20245, 7177, 1399], [6, 0, 0, 1980, 0, 16632, 11088, 35640, 23760, 20460, 7128, 1404]}
(12, 118098, 9) has 1357 possible DDs: {[1, 0, 33, 770, 0, 10296, 5082, 32076, 20295, 29480, 13365, 5826, 874], [1, 0, 34, 760, 45, 10176, 5292, 31824, 20505, 29360, 13410, 5816, 875], [1, 0, 35, 750, 90, 10056, 5502, 31572, 20715, 29240, 13455, 5806, 876], [1, 0, 36, 740, 135, 9936, 5712, 31320, 20925, 29120, 13500, 5796, 877], [1, 0, 37, 730, 180, 9816, 5922, 31068, 21135, 29000, 13545, 5786, 878], [1, 0, 38, 720, 225, 9696, 6132, 30816, 21345, 28880, 13590, 5776, 879], [1, 0, 39, 710, 270, 9576, 6342, 30564, 21555, 28760, 13635, 5766, 880], [1, 0, 40, 700, 315, 9456, 6552, 30312, 21765, 28640, 13680, 5756, 881], [1, 0, 41, 690, 360, 9336, 6762, 30060, 21975, 28520, 13725, 5746, 882], [1, 0, 42, 680, 405, 9216, 6972, 29808, 22185, 28400, 13770, 5736, 883], [1, 0, 43, 670, 450, 9096, 7182, 29556, 22395, 28280, 13815, 5726, 884], [1, 0, 44, 660, 495, 8976, 7392, 29304, 22605, 28160, 13860, 5716, 885], [1, 0, 45, 650, 540, 8856, 7602, 29052, 22815, 28040, 13905, 5706, 886], [1, 0, 46, 640, 585, 8736, 7812, 28800, 23025, 27920, 13950, 5696, 887], [1, 0, 47, 630, 630, 8616, 8022, 28548, 23235, 27800, 13995, 5686, 888], [1, 0, 48, 620, 675, 8496, 8232, 28296, 23445, 27680, 14040, 5676, 889], [1, 0, 49, 610, 720, 8376, 8442, 28044, 23655, 27560, 14085, 5666, 890], [1, 0, 50, 600, 765, 8256, 8652, 27792, 23865, 27440, 14130, 5656, 891], [1, 0, 51, 590, 810, 8136, 8862, 27540, 24075, 27320, 14175, 5646, 892], [1, 0, 52, 580, 855, 8016, 9072, 27288, 24285, 27200, 14220, 5636, 893], [1, 0, 53, 570, 900, 7896, 9282, 27036, 24495, 27080, 14265, 5626, 894], [1, 0, 54, 560, 945, 7776, 9492, 26784, 24705, 26960, 14310, 5616, 895], [1, 0, 55, 550, 990, 7656, 9702, 26532, 24915, 26840, 14355, 5606, 896], [1, 0, 56, 540, 1035, 7536, 9912, 26280, 25125, 26720, 14400, 5596, 897], [1, 0, 57, 530, 1080, 7416, 10122, 26028, 25335, 26600, 14445, 5586, 898], [1, 0, 58, 520, 1125, 7296, 10332, 25776, 25545, 26480, 14490, 5576, 899], [1, 0, 59, 510, 1170, 7176, 10542, 25524, 25755, 26360, 14535, 5566, 900], [1, 0, 60, 500, 1215, 7056, 10752, 25272, 25965, 26240, 14580, 5556, 901], [1, 0, 61, 490, 1260, 6936, 10962, 25020, 26175, 26120, 14625, 5546, 902], [1, 0, 62, 480, 1305, 6816, 11172, 24768, 26385, 26000, 14670, 5536, 903], [1, 0, 63, 470, 1350, 6696, 11382, 24516, 26595, 25880, 14715, 5526, 904], [1, 0, 64, 460, 1395, 6576, 11592, 24264, 26805, 25760, 14760, 5516, 905], [1, 0, 65, 450, 1440, 6456, 11802, 24012, 27015, 25640, 14805, 5506, 906], [1, 0, 66, 440, 1485, 6336, 12012, 23760, 27225, 25520, 14850, 5496, 907], [1, 0, 67, 430, 1530, 6216, 12222, 23508, 27435, 25400, 14895, 5486, 908], [1, 0, 68, 420, 1575, 6096, 12432, 23256, 27645, 25280, 14940, 5476, 909], [1, 0, 69, 410, 1620, 5976, 12642, 23004, 27855, 25160, 14985, 5466, 910], [1, 0, 70, 400, 1665, 5856, 12852, 22752, 28065, 25040, 15030, 5456, 911], [1, 0, 71, 390, 1710, 5736, 13062, 22500, 28275, 24920, 15075, 5446, 912], [1, 0, 72, 380, 1755, 5616, 13272, 22248, 28485, 24800, 15120, 5436, 913], [1, 0, 73, 370, 1800, 5496, 13482, 21996, 28695, 24680, 15165, 5426, 914], [1, 0, 74, 360, 1845, 5376, 13692, 21744, 28905, 24560, 15210, 5416, 915], [1, 0, 75, 350, 1890, 5256, 13902, 21492, 29115, 24440, 15255, 5406, 916], [1, 0, 76, 340, 1935, 5136, 14112, 21240, 29325, 24320, 15300, 5396, 917], [1, 0, 77, 330, 1980, 5016, 14322, 20988, 29535, 24200, 15345, 5386, 918], [1, 0, 78, 320, 2025, 4896, 14532, 20736, 29745, 24080, 15390, 5376, 919], [1, 0, 79, 310, 2070, 4776, 14742, 20484, 29955, 23960, 15435, 5366, 920], [1, 0, 80, 300, 2115, 4656, 14952, 20232, 30165, 23840, 15480, 5356, 921], [1, 0, 81, 290, 2160, 4536, 15162, 19980, 30375, 23720, 15525, 5346, 922], [1, 0, 82, 280, 2205, 4416, 15372, 19728, 30585, 23600, 15570, 5336, 923], [1, 0, 83, 270, 2250, 4296, 15582, 19476, 30795, 23480, 15615, 5326, 924], [1, 0, 84, 260, 2295, 4176, 15792, 19224, 31005, 23360, 15660, 5316, 925], [1, 0, 85, 250, 2340, 4056, 16002, 18972, 31215, 23240, 15705, 5306, 926], [1, 0, 86, 240, 2385, 3936, 16212, 18720, 31425, 23120, 15750, 5296, 927], [1, 0, 87, 230, 2430, 3816, 16422, 18468, 31635, 23000, 15795, 5286, 928], [1, 0, 88, 220, 2475, 3696, 16632, 18216, 31845, 22880, 15840, 5276, 929], [1, 0, 89, 210, 2520, 3576, 16842, 17964, 32055, 22760, 15885, 5266, 930], [1, 0, 90, 200, 2565, 3456, 17052, 17712, 32265, 22640, 15930, 5256, 931], [1, 0, 91, 190, 2610, 3336, 17262, 17460, 32475, 22520, 15975, 5246, 932], [1, 0, 92, 180, 2655, 3216, 17472, 17208, 32685, 22400, 16020, 5236, 933], [1, 0, 93, 170, 2700, 3096, 17682, 16956, 32895, 22280, 16065, 5226, 934], [1, 0, 94, 160, 2745, 2976, 17892, 16704, 33105, 22160, 16110, 5216, 935], [1, 0, 95, 150, 2790, 2856, 18102, 16452, 33315, 22040, 16155, 5206, 936], [1, 0, 96, 140, 2835, 2736, 18312, 16200, 33525, 21920, 16200, 5196, 937], [1, 0, 97, 130, 2880, 2616, 18522, 15948, 33735, 21800, 16245, 5186, 938], [1, 0, 98, 120, 2925, 2496, 18732, 15696, 33945, 21680, 16290, 5176, 939], [1, 0, 99, 110, 2970, 2376, 18942, 15444, 34155, 21560, 16335, 5166, 940], [1, 0, 100, 100, 3015, 2256, 19152, 15192, 34365, 21440, 16380, 5156, 941], [1, 0, 101, 90, 3060, 2136, 19362, 14940, 34575, 21320, 16425, 5146, 942], [1, 0, 102, 80, 3105, 2016, 19572, 14688, 34785, 21200, 16470, 5136, 943], [1, 0, 103, 70, 3150, 1896, 19782, 14436, 34995, 21080, 16515, 5126, 944], [1, 0, 104, 60, 3195, 1776, 19992, 14184, 35205, 20960, 16560, 5116, 945], [1, 0, 105, 50, 3240, 1656, 20202, 13932, 35415, 20840, 16605, 5106, 946], [1, 0, 106, 40, 3285, 1536, 20412, 13680, 35625, 20720, 16650, 5096, 947], [1, 0, 107, 30, 3330, 1416, 20622, 13428, 35835, 20600, 16695, 5086, 948], [1, 0, 108, 20, 3375, 1296, 20832, 13176, 36045, 20480, 16740, 5076, 949], [1, 0, 109, 10, 3420, 1176, 21042, 12924, 36255, 20360, 16785, 5066, 950], [1, 0, 110, 0, 3465, 1056, 21252, 12672, 36465, 20240, 16830, 5056, 951], [1, 1, 26, 785, 15, 10146, 5460, 31530, 20805, 29165, 13490, 5797, 877], [1, 1, 27, 775, 60, 10026, 5670, 31278, 21015, 29045, 13535, 5787, 878], [1, 1, 28, 765, 105, 9906, 5880, 31026, 21225, 28925, 13580, 5777, 879], [1, 1, 29, 755, 150, 9786, 6090, 30774, 21435, 28805, 13625, 5767, 880], [1, 1, 30, 745, 195, 9666, 6300, 30522, 21645, 28685, 13670, 5757, 881], [1, 1, 31, 735, 240, 9546, 6510, 30270, 21855, 28565, 13715, 5747, 882], [1, 1, 32, 725, 285, 9426, 6720, 30018, 22065, 28445, 13760, 5737, 883], [1, 1, 33, 715, 330, 9306, 6930, 29766, 22275, 28325, 13805, 5727, 884], [1, 1, 34, 705, 375, 9186, 7140, 29514, 22485, 28205, 13850, 5717, 885], [1, 1, 35, 695, 420, 9066, 7350, 29262, 22695, 28085, 13895, 5707, 886], [1, 1, 36, 685, 465, 8946, 7560, 29010, 22905, 27965, 13940, 5697, 887], [1, 1, 37, 675, 510, 8826, 7770, 28758, 23115, 27845, 13985, 5687, 888], [1, 1, 38, 665, 555, 8706, 7980, 28506, 23325, 27725, 14030, 5677, 889], [1, 1, 39, 655, 600, 8586, 8190, 28254, 23535, 27605, 14075, 5667, 890], [1, 1, 40, 645, 645, 8466, 8400, 28002, 23745, 27485, 14120, 5657, 891], [1, 1, 41, 635, 690, 8346, 8610, 27750, 23955, 27365, 14165, 5647, 892], [1, 1, 42, 625, 735, 8226, 8820, 27498, 24165, 27245, 14210, 5637, 893], [1, 1, 43, 615, 780, 8106, 9030, 27246, 24375, 27125, 14255, 5627, 894], [1, 1, 44, 605, 825, 7986, 9240, 26994, 24585, 27005, 14300, 5617, 895], [1, 1, 45, 595, 870, 7866, 9450, 26742, 24795, 26885, 14345, 5607, 896], [1, 1, 46, 585, 915, 7746, 9660, 26490, 25005, 26765, 14390, 5597, 897], [1, 1, 47, 575, 960, 7626, 9870, 26238, 25215, 26645, 14435, 5587, 898], [1, 1, 48, 565, 1005, 7506, 10080, 25986, 25425, 26525, 14480, 5577, 899], [1, 1, 49, 555, 1050, 7386, 10290, 25734, 25635, 26405, 14525, 5567, 900], [1, 1, 50, 545, 1095, 7266, 10500, 25482, 25845, 26285, 14570, 5557, 901], [1, 1, 51, 535, 1140, 7146, 10710, 25230, 26055, 26165, 14615, 5547, 902], [1, 1, 52, 525, 1185, 7026, 10920, 24978, 26265, 26045, 14660, 5537, 903], [1, 1, 53, 515, 1230, 6906, 11130, 24726, 26475, 25925, 14705, 5527, 904], [1, 1, 54, 505, 1275, 6786, 11340, 24474, 26685, 25805, 14750, 5517, 905], [1, 1, 55, 495, 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