SecondDiameters

{0, 1, 1}
{0, 0, 1}
Returns: 0

The three points from the problem statement. We have D( S[0] ) = D( S[2] ) = {0, 1} and D( S[1] ) = {0, sqrt(2)}. In all cases the second largest distance is zero.

{0, 0, 1, 1}
{0, 1, 0, 1}
Returns: 4

Four points in the corners of a unit square. Regardless of which one we remove, the other three will have diameter sqrt(2) and second diameter 1.

{0, 0, 1, 2, 2}
{0, 10, 5, 0, 10}
Returns: 500

For each of the five sets S[0] through S[4] here the second diameter is 10. Note that S[2] contains two pairs of points that are sqrt(104) apart, but that does not make the second diameter equal to the diameter.

{1, 2, 3, 4, 5}
{1, 3, 6, 10, 15}
Returns: 534

The return value is computed as 85 + 90 + 153 + 153 + 53.

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6553, 4384, 3021, 7928, 3609, 879, 1852, 292, 824, 2143, 4432, 9990, 9712, 5603, 9498, 2749, 572, 3972, 9564, 731, 8349, 270, 8091, 7957, 4030, 8451, 9110, 6146, 3580, 237, 4239, 2747, 667, 7244, 5913, 647, 4379, 5545, 5552, 6467, 4981, 9475, 4253, 4813, 7552, 6413, 7527, 2183, 9937, 6734, 7362, 2674, 7491, 5482, 4643, 2484, 4962, 5584, 3854, 9977, 5970, 9190, 7691, 9263, 3352, 3670, 9263, 5203, 2889, 5642, 4147, 3660, 4907, 5134, 8292, 2582, 8829, 8323, 3287, 2256, 2601, 5046, 1147, 834, 9058, 1791, 7337, 9434, 8271, 3064, 7641, 7307, 1682, 6636, 9694, 434, 2013, 3800, 7682, 3220, 7446, 1653, 5516, 7614, 4187, 3886, 3905, 6221, 1065, 5015, 6516, 3524, 5957, 5773, 1631, 430, 13, 4696, 620, 3277, 7679, 6335, 4739, 6603, 1096, 2988, 8473, 866, 5585, 8721, 3913, 4236, 6051, 339, 4282, 9983, 7762, 5099, 8426, 6939, 6712, 9974, 7448, 7366, 6464, 7937, 4391, 5655, 2493, 6114, 1458, 5451, 9027, 9666, 5909, 2894, 2843, 3305, 8082, 1252, 7158, 4004, 7334, 3533, 367, 7743, 7237, 9047, 683, 7150, 1927, 5864, 7080, 8968, 218, 8271, 6097, 2056, 854, 8005, 9344, 557, 9422, 4133, 3257, 535, 2787, 5262, 6732, 4835, 2573, 854, 6926, 2742, 4772, 7572, 4673, 3221, 6300, 8449, 1829, 7629, 849, 3124, 5510, 5241, 5301, 6020, 3398, 3984, 9842, 5745, 9351, 1230, 769, 5262, 8313, 8877, 3188, 302, 9548, 5664, 6560, 1602, 8255, 3801, 8293, 2790, 5996, 5183, 8959, 8709, 8664, 9475, 5020, 4305, 3619, 8373, 7003, 1476, 1243, 5795, 8511, 9465, 1109, 29, 9452, 9097, 9970, 2481, 706, 6359, 2169, 1354, 9202, 4735, 1035, 9294, 9203, 1037, 665, 4746, 2285, 9178, 8844, 9757, 2865, 3505, 1995, 1141, 9629, 5754, 4999, 565, 2957, 5213, 3729, 8159, 4736, 9535, 4797, 3015, 3917, 8440, 8256, 8629, 4924, 2155, 4433, 7431, 9284, 1539, 2008, 7635, 8333, 6886, 209, 8301, 141, 958, 934, 3434, 9792, 3753, 2499, 7170, 5601, 8461, 9921, 10, 8997, 6221, 1332, 4076, 2219, 61, 8829, 6143, 4562, 9770, 3016, 7970, 6625, 9218, 7054, 4248, 4149, 1926, 4861, 8440, 8000, 1049, 4064, 8048, 1880, 4225, 4478, 9577, 1124, 1157, 9549, 3467, 5921, 8989, 791, 5300, 5205, 9563, 211, 4260, 7953, 4082, 8733, 8292, 620, 1921, 4965, 3363, 9483, 3855, 5991, 6347, 4383, 3965, 6929, 6716, 8467, 656, 3756, 7951, 75, 9306, 8328, 4222, 4489, 5589, 6295, 4048, 4303, 6918, 5758, 9912, 1356, 7450, 592, 8231, 2222, 6137, 5024, 4142, 9089, 8399, 3072, 2875, 553, 2302, 1867, 4135, 5106, 9020, 8610, 3047, 7805, 6867, 3420, 1306, 6003, 1977, 4769, 8589, 4263, 4659, 7977, 5062, 4970, 7795, 8589, 9877, 7983, 9250, 1669, 2321, 5848, 3288, 4874, 5007, 4959, 1440, 1135, 3969, 7057, 4114, 9582, 1152, 2811, 7079, 8093, 2031, 5814, 3644, 7303, 7242, 4221, 2564, 92, 3372, 7308, 8183, 6394, 1909, 3283, 9921, 2506, 5379, 17, 5656, 1287, 8945, 9941, 6990, 3356, 521, 1197, 5512, 608, 9496, 1713, 8347, 8646, 4395, 1191, 103, 8135, 7120, 310, 4389, 855, 9548, 66, 5311, 8300, 9728, 572, 9269, 1572, 2697, 1616, 9848, 4766, 2655, 2679, 2282, 8348, 3510, 235, 3054, 8529, 1005, 3441, 7740, 2131, 8304, 3726, 1362, 9921, 2349, 4045, 7608, 5670, 5822, 3137, 3634, 332, 7251, 7244, 6705, 7273, 3208, 8719, 9725, 1548, 6730, 6301, 1065, 8350, 5495, 2427, 3216, 4727, 1717, 1124, 9514, 3371, 7649, 8376, 5547, 7649, 8667, 1717, 6563, 3563, 3573, 1802, 4016, 1942, 8549, 1682, 7971, 6715, 6423, 2757, 1245, 8042, 1817, 4946, 2906, 8778, 2507, 7043, 619, 7002, 6479, 5383, 1480, 6767, 2982, 2477, 5578, 5912, 669, 8065, 3493, 9494, 729, 878, 1628, 8469, 5047, 5158, 887, 3556, 596, 3670, 1096, 2729, 8522, 7434, 7376, 5851, 8141, 5268, 9122, 683, 4496, 5654, 3107, 4219, 9635, 6179, 468, 4831, 3031, 9251, 846, 2625, 8833, 3734, 5892, 8642, 2601, 1489, 6668, 3436, 7989, 8178, 7274, 2658, 3886, 358, 2850, 4761, 8027, 7867, 6820, 2542, 7009, 2398, 527, 9515, 8362, 8180, 938, 5449, 8295, 6861, 1305, 7165, 453, 9083, 9539, 6954, 2132, 2767, 9435, 2606, 2040, 9025, 1413, 2907, 5451, 7003, 7898, 3880, 5571, 4266, 2278, 8730, 8651, 9096, 3325, 1174, 165, 3920, 4043, 5517, 3909, 393, 12, 9178, 9726, 7879, 4830, 8772, 4208, 4208, 8450, 4338, 8784, 5789, 7373, 6031, 6697, 4996, 8554, 6886, 432, 3965, 9141, 381, 6053, 8805, 8096, 1487, 2806, 7962, 7569, 1861, 971, 6661, 2770, 8284, 2059, 5528, 5959, 754, 1128, 2784, 8062, 785, 2932, 7015, 3207, 5654, 6119, 5521, 5671, 3965, 9550, 2120, 2416, 9500, 9450, 4712, 2860, 9927, 8392, 4762, 322, 5106, 1072, 6404, 431, 474, 6236, 9753, 3269, 5312, 7435, 1276, 2585, 2914, 7578, 4472, 7539, 6926, 9699, 3489, 86, 3603, 9271, 6433, 2575, 4750, 2183, 3391, 1762, 9366, 5790, 3306, 8015, 5900, 1565, 9437, 6543, 2800, 2524, 8174, 4185, 9174, 3255, 9507, 3548, 216, 410, 1452, 6663, 4714, 4350, 3524, 9308, 7383, 4148, 1080, 8937, 1336, 1645, 3854, 9697, 3940, 8373, 8126, 8066, 8976, 6832, 3846, 3013, 1909, 8317, 5348, 50, 5910, 5597, 973, 9766, 411, 8964, 4907, 4562, 8310, 5691, 8676, 3374, 3121, 5063, 3582, 9098, 6773, 2573, 6421, 4371, 9997, 8109, 4625, 3662, 8290, 7170, 4624, 8003, 8531, 8621, 7225, 1005, 743, 7832, 5308, 4633, 4558, 6071, 9184, 2063, 1668, 3971, 4911, 2457, 1127, 9416, 3638, 4646, 387, 4036, 5594, 3967, 2653, 10, 7853, 9994, 3728, 4349, 1360, 7580, 5691, 8316, 9064, 5354, 7502, 9068, 4726, 5932, 9918, 6406, 9980, 8060, 5134, 2616, 115, 5667, 9699, 5928, 5335, 5924, 9710, 7820, 4694, 9528, 6321, 6275, 6996, 9252, 4777, 3663, 5057, 480, 3154, 2641, 4245, 1654, 8359, 6367, 3450, 826, 9175, 4783, 7840, 2793, 7066, 8720, 3319, 1841, 3226, 7612, 1237, 381, 5883, 7838, 7592, 8879, 3310, 6186, 1458, 6787, 5673, 3545, 8058, 5176, 6067, 6365, 4187, 1153, 6994, 6256, 8328, 9328, 8537, 4417, 4710, 6129, 9966, 467, 7149, 8288, 5269, 8384, 2466, 6596, 2269, 2872, 4091, 9072, 7014, 9931, 5769, 880, 2098, 192, 7603, 5588, 3214, 6861, 1633, 3076, 3759, 1471, 4965, 3255, 1612, 3784, 5110, 1505, 4211, 1644, 6381, 3917, 4926, 5730, 9971, 9332, 774, 4580, 7451, 6942, 5468, 1526, 7552, 1344, 9874, 4310, 4165, 8884, 4020, 9205, 8341, 7999, 5611, 7876, 8114, 509, 8352, 4290, 49, 5448, 9500, 6697, 3877, 4095, 4774, 6840, 6126, 1870, 1446, 5769, 9008, 6209, 6668, 8516, 4700, 9586, 9440, 6204, 5030, 3447, 2922, 6689, 4312, 1395, 6566, 2010, 3667, 3798, 371, 2937, 7855, 2232, 2817, 1268, 9742, 1866, 5531, 4534, 9211, 1749, 2228, 8949, 4604, 9283, 2377, 8942, 7972, 7902, 4418, 2346, 6933, 3535, 400, 7984, 6849, 2106, 8376, 5906, 939, 338, 3461, 2497, 3200, 6021, 6543, 320, 5889, 8233, 665, 528, 9208, 6272, 2397, 1100, 1076, 2557, 3861, 9824, 4691, 2580, 9147, 3489, 2637, 9480, 9745, 7754, 2625, 4006, 4484, 4481, 9437, 2628, 7272, 8702, 5456, 3530, 9645, 404, 9276, 6249, 3396, 8564, 7139, 122, 3336, 8645, 4263, 2864, 6114, 2093, 9091, 7874, 4947, 8204, 3696, 642, 5424, 5181, 4606, 3834, 3586, 4730, 1879, 386, 7148, 6227, 6464, 1137, 6685, 9080, 5552, 2758, 7690, 6897, 2914, 1763, 9667, 572, 5956, 1987, 1189, 6986, 6526, 5348, 7330, 9726, 605, 4640, 5969, 312, 1997, 849, 4162, 5873, 4340, 3199, 6150, 5386, 4092, 7216, 4661, 5382, 4542, 632, 7889, 6732, 70, 2466, 827, 6858, 8048, 2005, 76, 495, 8123, 6958, 8853, 3776, 5468, 3009, 5647, 3451, 6652, 2914, 5240, 4057, 3842, 5094, 6070, 149, 7484, 8556, 543, 6119, 6023, 3168, 1786, 4712, 9219, 4431, 4268, 5623, 8637, 3223, 6271, 2593, 8559, 9056, 5564, 115, 7889, 5305, 771, 5721, 7657, 5404, 8523, 1310, 5294, 6860, 4558, 5360, 6370, 8450, 1908, 5148, 4972, 2189, 1462, 2399, 4346, 2609, 1871, 2223, 5853, 4217, 7053, 6333, 9590, 7637, 4552, 8014, 2919, 8137, 2411, 4341, 779, 8806, 6106, 4402, 8028, 3923, 8147, 6105, 8290, 4241, 6581, 1782, 8040, 6205, 7417, 7221, 9224, 9422, 3272, 3113, 1966, 9883, 1604, 3977, 363, 2371, 9182, 3513, 1024, 724, 2672, 45, 8909, 469, 5254, 6174, 2116, 4647, 285, 1734, 9611, 3366, 2882, 7654, 9630, 8377, 7272, 8486, 3356, 6519, 6774, 9246, 6194, 7870, 6552, 9299, 9183, 8358, 1738, 6628, 6333, 2755, 5218, 9425, 8442, 638, 721, 3313, 9437, 4061, 9072, 5860, 1384, 663, 2349, 2572, 4303, 4433, 3796, 5323, 3873, 6548, 9755, 3706, 7524, 7517, 2020, 5624, 5467, 2231, 3609, 5428, 6751, 9333, 9352, 7914, 6313, 1289, 3088, 5407, 935, 1761, 993, 7481, 6472, 9755, 5772, 6025, 827, 4828, 5244, 517, 2170, 4811, 9498, 6286, 682, 3842, 1521, 4807, 3321, 8041, 6981, 399, 1770, 7850, 9038, 258, 2144, 6224, 878, 7204, 8044, 8370, 7087, 3248, 2619, 4657, 829, 4818, 9293, 6391, 8965, 3489, 3357, 8920, 8506, 7702, 5116, 8495, 5988, 8791, 2712, 7228, 6365, 5851, 4786, 9142, 7479, 6987, 4570, 4354, 854, 415, 8341, 2105, 7228, 5941, 6440, 6283, 7922, 7949, 9893, 925, 2654, 6907, 393, 9636, 2624, 4046, 8255, 5615, 2977, 9698, 1682, 8790, 7957, 4656, 3472, 9543, 8979, 5535, 5984, 1209, 6451, 2021, 9284, 6535, 653, 3173, 9882, 2904, 5891, 2975, 2389, 6282, 1660, 3601, 6768, 9886, 8587, 7209, 582, 6832, 1222, 619, 616, 6498, 5072, 9419, 3339, 488, 9245, 8821, 1814, 2792, 7194, 7496, 9333, 5441, 9070, 8480, 8293, 4495, 1790, 6884, 4158, 9367, 9293, 4052, 5301, 9247, 7632, 4184, 920, 3180, 6364, 2336, 6805, 3936, 3946, 5022, 9185, 6931, 3101, 5250, 4417, 769, 7221, 2950, 1512, 9525, 6738, 3018, 5787, 9913, 7120, 7915, 9259, 3918, 4494, 7637, 1918, 46, 2754, 2689, 6157, 3991, 7595, 2456, 1179, 6362, 6132, 1265, 5101, 1579, 664, 2086, 4895, 1916, 2136, 2326, 7538, 8594, 2522, 1465, 5689, 3462, 2183, 3608, 9223, 3925, 9564, 2978, 3632, 6875, 7921, 2847, 3948, 4392, 1963, 8912, 6049, 1753, 8780, 8217, 9906, 3509, 2968, 2569, 670, 6183, 2794, 5764, 6832, 1406, 3256, 106, 2689, 4833, 5332, 395, 1991, 7104, 1660, 3301, 8839, 9019, 5485, 1672, 3769, 3317, 1154, 5396, 9016, 5981, 2771, 224, 6703, 7918, 389, 3427, 7137, 9779, 7440, 458, 4183, 3740, 6307, 18, 2487, 8029, 1848, 8075, 9855, 8972, 7494, 5277, 4597, 777, 485, 1330, 3597, 3123, 6880, 4032, 3625, 7406, 2653, 6463, 2139, 5848, 8181, 2838, 1679, 4846, 4987, 1323, 9388, 2272, 9673, 3968, 3661, 7760, 972, 4522, 8743, 5475, 7779, 5225, 8649, 9664, 8319, 8573, 651, 503, 481, 4552, 1800, 1252, 6696, 4196, 3128, 6592, 3041, 8105}
Returns: 380956862978