Statistics

Problem Statement for "CakeForSix"

Problem Statement

Time limit is 4 seconds.

You have a cake. Seen from above, the cake is a (strictly) convex polygon. You are given the coordinates of its vertices in the int[]s x and y.

You have five friends. You now want to cut the cake into six pieces of equal area (but not necessarily equal shape). Of course, anyone can do that in five cuts -- but only a true pro can do it in three!

Find three straight-line cuts passing through the same point that cut the cake into six equally large parts. Return {x, y, d1, d2, d3}, where (x, y) is the common point of the three cuts, and d1, d2, d3 are their directions in radians.

Definition

Class:
CakeForSix
Method:
cut
Parameters:
int[], int[]
Returns:
double[]
Method signature:
double[] cut(int[] x, int[] y)
(be sure your method is public)

Notes

  • The positive direction along the x axis is 0 (radians), the positive direction along the y axis is pi/2 (radians).
  • A cut in direction d is the same as a cut in direction pi*k+d for any integer k.
  • You may return any directions, they do not have to be from [0,pi).
  • The grader will compute the areas of your six cake pieces in doubles. The answer will be accepted if the relative or absolute difference between them is less than 10^(-4).
  • More precisely, let X and Y be the smallest and the largest of your six areas, as computed by the grader. Then, your answer will be accepted if Y < max( X + 10^(-4), X * (1+10^(-4)) ).
  • (The original version of the problem used 1e-7 precision instead of 1e-4. For upsolving this problem in the archive the precision limit was lowered due to the existence of challenge cases that most likely make the task unsolvable with 1e-7 precision. In an ideal world the constraints would not allow such cases and still require high precision, so that it isn't easy to solve the problem via some general numeric optimization.)

Constraints

  • x will have between 3 and 50 elements, inclusive.
  • y will have the same number of elements as x.
  • All coordinates will be between 0 and 10,000, inclusive.
  • x and y will describe a convex polygon in counterclockwise order.

Examples

  1. {0, 20, 30, 50, 30, 20}

    {10, 0, 0, 10, 20, 20}

    Returns: {24.999999999437453, 9.999999999500002, 0.0, 0.7266423406817211, 2.4149503129080787 }

    A symmetric but not regular hexagon. The example answer corresponds to cutting it into halves horizontally and making two other cuts through its center that cut each part into thirds.

  2. {0, 1000, 0}

    {0, 0, 1000}

    Returns: {333.3333333331763, 333.3333333332546, 0.7853981633986264, 2.0344439357948154, 2.6779450445891753 }

    A right triangle. Again, we can start by making one of the three cuts along its axis of symmetry.

  3. {40, 70, 90, 90, 50}

    {30, 20, 40, 100, 60}

    Returns: {69.79517771922892, 52.77575974637605, 2.0616329654335885, 3.637826104091601, 4.32123485812475 }

    An irregular pentagon.

  4. {0, 0, 10000, 10000}

    {10000, 0, 0, 10000}

    Returns: {5000.000000000911, 5000.0, 0.0, 0.9827937232470758, 2.158798930342717 }

  5. {136, 7540, 8392}

    {5135, 172, 9154}

    Returns: {5355.999999999865, 4820.333333334152, 0.959693619341629, 2.0100309250510993, 3.0813845404188718 }

  6. {9000, 8968, 8874, 8719, 8505, 8236, 7915, 7549, 7143, 6703, 6236, 5749, 5251, 4748, 4250, 3763, 3296, 2856, 2450, 2084, 1763, 1494, 1280, 1125, 1031, 1000, 1031, 1125, 1280, 1494, 1763, 2084, 2450, 2856, 3296, 3763, 4250, 4748, 5251, 5749, 6236, 6703, 7143, 7549, 7915, 8236, 8505, 8719, 8874, 8968}

    {5000, 5501, 5994, 6472, 6927, 7351, 7738, 8082, 8377, 8619, 8804, 8929, 8992, 8992, 8929, 8804, 8619, 8377, 8082, 7738, 7351, 6927, 6472, 5994, 5501, 4999, 4498, 4005, 3527, 3072, 2648, 2261, 1917, 1622, 1380, 1195, 1070, 1007, 1007, 1070, 1195, 1380, 1622, 1917, 2261, 2648, 3072, 3527, 4005, 4498}

    Returns: {4999.536271697201, 4999.50003121912, 0.0, 1.0471950764730034, 2.094395603698658 }

  7. {3375, 3376, 3376}

    {7125, 7125, 7126}

    Returns: {3375.666666668073, 7125.333333331, 2.3561944967876194, 3.605240264355624, 4.248741401010673 }

  8. {69, 113, 189, 1600, 6508, 9610, 9796, 9720, 9583, 9281, 2785, 1131, 336}

    {2212, 1749, 1427, 338, 91, 2204, 4974, 8714, 9110, 9898, 9679, 9477, 9300}

    Returns: {4941.73175166328, 5139.976674378074, 2.457476460579188, 3.5799839635194046, 4.488071376887452 }

  9. {45, 241, 4205, 9421, 9592, 9182, 3490}

    {9111, 1102, 253, 503, 3876, 9875, 9490}

    Returns: {4884.435149828806, 5007.2444788618795, 0.946877644343644, 2.1155663761086596, 3.0664291917519817 }

  10. {91, 135, 957, 2513, 3704, 6562, 9349, 9843, 9875, 9730, 9291, 8750, 4878, 572, 185, 93}

    {1574, 795, 511, 40, 71, 242, 476, 4450, 4771, 9253, 9588, 9851, 9971, 9912, 6414, 3588}

    Returns: {4953.596834257813, 5064.09672603099, 2.2160853629110795, 3.2776523709814804, 4.22670743345617 }

  11. {47, 113, 966, 6652, 9195, 9865, 9992, 9742, 9479, 9050, 7207, 2146, 224}

    {6950, 685, 91, 15, 369, 732, 4286, 6581, 8906, 9099, 9719, 9793, 9260}

    Returns: {4919.258316805511, 4844.187446626415, 0.7921396090797101, 1.9133756644991256, 2.843409653824802 }

  12. {49, 68, 1514, 3872, 4797, 8443, 9885, 9966, 9951, 9772, 2232, 1696}

    {6198, 3140, 1377, 280, 104, 78, 1830, 3279, 8435, 9845, 9855, 9789}

    Returns: {5279.132041312909, 5097.809404820765, 0.8956477911174654, 2.0214173440966277, 3.0094560006034876 }

  13. {1771, 3857, 5211, 8006, 7351, 4239}

    {8719, 3548, 1843, 1548, 6570, 9881}

    Returns: {5144.82636575789, 5569.446161696193, 0.6865230464710954, 1.8313241511011078, 2.359222578961263 }

  14. {578, 918, 1350, 5080, 7724, 8724, 9593, 9678, 3813}

    {9548, 1207, 195, 380, 963, 1341, 2489, 8640, 9475}

    Returns: {5003.572013019831, 4973.064463183953, 2.266271673061211, 3.310540637299611, 4.269317950846101 }

  15. {85, 89, 191, 1361, 4649, 7954, 9892, 9997, 9972, 9645, 5298, 668}

    {6252, 2168, 671, 163, 59, 195, 607, 6058, 8016, 9334, 9949, 9815}

    Returns: {5022.726812759395, 4938.659714481821, 0.7925047779306549, 1.9153381376882503, 2.8693202461984826 }

  16. {19, 177, 1279, 2598, 6341, 8129, 9510, 9772, 9841, 4816, 1302}

    {7879, 1715, 812, 275, 12, 215, 460, 564, 9926, 9743, 9381}

    Returns: {5108.51509874214, 4980.2161564124535, 0.8915822249326666, 2.033266368375299, 3.007208921327793 }

  17. {118, 225, 6203, 9903, 9955, 9974, 9618, 9562, 7746, 5885, 3928, 3235, 1130, 294, 132}

    {1337, 68, 5, 126, 3106, 7734, 8723, 8779, 9346, 9776, 9881, 9859, 9765, 8294, 7150}

    Returns: {5013.641639303471, 4777.417531597691, 0.7611511243793851, 1.883442098215748, 2.812229863103877 }

  18. {68, 231, 647, 2924, 4484, 6570, 8622, 8820, 9140, 9747, 9337, 9185, 7930, 1846, 1495}

    {6776, 3916, 1123, 693, 573, 448, 777, 1119, 2003, 4720, 7842, 8146, 9453, 9741, 9401}

    Returns: {4879.695969004862, 5049.166146304411, 2.5411552088629854, 3.6305453815944406, 4.662363874492706 }

  19. {265, 667, 3862, 7375, 9753, 9971, 9969, 9079, 5997, 3663}

    {6263, 2895, 1073, 70, 2592, 7362, 7600, 9234, 9426, 8891}

    Returns: {5531.143719728228, 4998.423826632774, 0.9161326159211101, 2.041104047185316, 3.096050743076537 }

  20. {47, 67, 244, 4186, 7009, 8907, 9879, 9815, 9744, 8747, 8098, 2651, 1193, 419}

    {8035, 3642, 482, 71, 139, 690, 1500, 6703, 7369, 9040, 9849, 9893, 9128, 8498}

    Returns: {4918.117644097556, 4919.902036273653, 0.6776796420414679, 1.7197793086063178, 2.7043651248279597 }

  21. {239, 281, 851, 7119, 8875, 9948, 8964, 6776, 5891, 2389, 448}

    {1475, 324, 222, 10, 657, 5889, 7415, 9955, 9974, 9977, 9969}

    Returns: {4685.202655920897, 4957.696660553217, 0.9036349131994557, 1.9695459902536476, 2.9207832844896386 }

  22. {101, 265, 824, 3613, 5572, 9109, 9676, 9932, 9984, 9477, 8190, 5942, 2479, 298, 139}

    {3072, 1651, 103, 39, 34, 95, 285, 4378, 9280, 9513, 9663, 9847, 9817, 9178, 7063}

    Returns: {5063.499778346833, 4916.005394837003, 0.7353497711096677, 1.8085498091497394, 2.7651879681513503 }

  23. {4, 24, 77, 241, 533, 1927, 4311, 7010, 8463, 9091, 9718, 9977, 9970, 9949, 9919, 9469, 301}

    {8038, 3868, 2720, 1576, 553, 212, 81, 22, 194, 886, 2891, 5095, 6815, 6970, 7164, 9921, 9821}

    Returns: {4935.734762812468, 5082.68459671136, 2.541175542197408, 3.6817890092027907, 4.665062689793753 }

  24. {82, 640, 3063, 9430, 8208, 3940}

    {7637, 3713, 392, 453, 9108, 9847}

    Returns: {4936.752941706138, 4947.1757670972565, 1.1632191366454734, 2.175906769588589, 3.1068134889518633 }

  25. {50, 178, 330, 1527, 4487, 6796, 8992, 9362, 9989, 9877, 9704, 8201, 4596, 1669, 383, 211, 179}

    {5241, 2126, 1071, 334, 214, 329, 899, 1249, 5846, 7967, 9556, 9816, 9896, 9901, 9851, 8273, 7905}

    Returns: {4931.362379585722, 5177.171575195851, 2.406044371332735, 3.521267418322056, 4.458714039111242 }

  26. {91, 733, 2841, 7130, 8513, 9350, 9413, 9967, 9883, 9776, 9493, 6682, 5090, 3258, 872, 611, 114, 96}

    {525, 302, 94, 233, 290, 674, 1055, 4853, 7713, 8567, 9529, 9745, 9819, 9648, 9058, 8618, 5650, 3870}

    Returns: {5007.2487960508915, 4888.184132601525, 2.5180158079223034, 3.653101979887871, 4.581924658462527 }

  27. {159, 173, 280, 349, 601, 772, 836, 1327, 1801, 3667, 8507, 9492, 9917, 9917, 9853, 9572, 8517, 6208, 5572, 5053, 2982, 1494, 584, 222}

    {7238, 6718, 4639, 4052, 2183, 1632, 1490, 800, 586, 507, 402, 1160, 3885, 4857, 8298, 8691, 9284, 9771, 9872, 9867, 9732, 9528, 8936, 8449}

    Returns: {5077.722465306972, 5102.357363701174, 0.5382495294305747, 1.5888438791539934, 2.580330633883062 }

  28. {138, 169, 296, 368, 1892, 5320, 6806, 8069, 8238, 9033, 9353, 9566, 9806, 9808, 9093, 8503, 4501, 4105, 3770, 2068, 658, 554, 461, 162}

    {3358, 1791, 984, 582, 454, 215, 229, 273, 388, 1089, 1533, 2890, 4731, 6892, 9354, 9379, 9505, 9514, 9516, 8927, 7129, 6800, 6255, 3609}

    Returns: {5065.142707271173, 4760.051699188007, 2.4189314761962954, 3.532107225656307, 4.4377576615323875 }

  29. {351, 400, 532, 1044, 1506, 3360, 4197, 5600, 7673, 8645, 9599, 9669, 9684, 9643, 9479, 8700, 7224, 4204, 3051, 2122, 1113, 799, 568, 373}

    {4228, 3538, 2779, 1502, 1263, 415, 217, 224, 352, 430, 2201, 5974, 6810, 8752, 9222, 9442, 9752, 9740, 9582, 9089, 8359, 7655, 6821, 5848}

    Returns: {5217.018419680675, 5021.568906022683, 0.9833262294591427, 2.0749372093482354, 3.1133633198098574 }

  30. {509, 517, 559, 708, 1061, 1715, 2004, 3007, 3518, 7874, 8197, 8454, 9731, 9788, 9789, 9773, 9670, 9245, 8781, 8657, 7627, 4596, 2143, 1645, 610, 521}

    {4431, 3585, 1672, 1346, 669, 498, 433, 297, 296, 1119, 1193, 1302, 3120, 3759, 5384, 5866, 6469, 7930, 8910, 9162, 9475, 9700, 9387, 9139, 8480, 6038}

    Returns: {4957.735815066397, 5064.558779828557, 0.9572956105295056, 2.080518604204855, 3.1086041246311056 }

  31. {370, 489, 705, 733, 960, 1391, 1941, 2407, 3964, 7464, 8844, 9437, 9453, 9711, 9916, 9910, 9606, 8343, 8057, 6965, 2935, 763, 503, 406}

    {5766, 4540, 2819, 2601, 1234, 869, 471, 138, 184, 353, 606, 1303, 1335, 2160, 4775, 7893, 8614, 9413, 9477, 9530, 9586, 9075, 7185, 6187}

    Returns: {5171.023876715833, 4954.907316800462, 2.4582904045854868, 3.568889846801177, 4.545081948219925 }

  32. {138, 175, 567, 713, 1516, 3222, 4762, 6863, 7828, 9176, 9244, 9904, 9857, 9735, 9590, 9514, 9299, 9137, 8198, 7456, 5051, 2112, 772, 566, 287}

    {7331, 5607, 2334, 1731, 789, 348, 228, 130, 108, 487, 626, 2767, 4599, 6682, 8293, 8608, 9204, 9270, 9467, 9573, 9845, 9874, 9819, 9347, 8317}

    Returns: {5047.0811881413465, 5079.739195071939, 0.5951758192938748, 1.6727771695222284, 2.5988106757625107 }

  33. {128, 191, 864, 3593, 5321, 8127, 9056, 9532, 9891, 9944, 9981, 9932, 9799, 9476, 7598, 5421, 3869, 2673, 1942, 1680, 1256, 501, 332, 224}

    {1692, 319, 232, 166, 199, 330, 569, 1730, 3145, 3972, 6615, 6995, 7488, 8251, 9437, 9708, 9874, 9904, 9572, 9247, 8603, 6067, 4604, 3490}

    Returns: {5051.693712365185, 4785.371734204609, 0.7304825307755696, 1.7994919591177918, 2.8149176719460853 }

  34. {150, 160, 197, 241, 300, 657, 1331, 2664, 3813, 5754, 8357, 9417, 9905, 9789, 9002, 7889, 6751, 6266, 4671, 3354, 2455, 1050, 674, 284, 190}

    {4996, 4147, 3412, 3080, 2890, 1911, 665, 352, 242, 362, 820, 1531, 4797, 7984, 9481, 9856, 9892, 9891, 9814, 9593, 9436, 9184, 9060, 6382, 5446}

    Returns: {5048.725957764429, 5114.099842085515, 0.6909640209934849, 1.7140648318026706, 2.748039500398049 }

  35. {231, 251, 423, 459, 539, 865, 3156, 6786, 7130, 7665, 8411, 8497, 9083, 9419, 9812, 9640, 9546, 8701, 8340, 8054, 5435, 3691, 1898, 1075, 441}

    {5745, 5341, 1874, 1184, 1070, 820, 329, 228, 264, 447, 827, 900, 1851, 2732, 3792, 6774, 7808, 9567, 9682, 9738, 9744, 9660, 8564, 7967, 6468}

    Returns: {5066.846882852365, 4912.02897681343, 2.2701023009556884, 3.384729832730273, 4.300443917953122 }

  36. {203, 418, 1782, 2111, 3067, 5472, 8974, 9728, 9799, 9839, 9830, 9496, 9374, 8669, 7996, 7104, 5844, 5172, 2926, 1755, 836, 283, 259, 220}

    {4690, 2199, 1040, 777, 475, 218, 130, 345, 1301, 5209, 7752, 8843, 9033, 9608, 9746, 9910, 9945, 9933, 9755, 9522, 9080, 7960, 7836, 6706}

    Returns: {5189.690866673371, 5071.243334778122, 1.0194960154598034, 2.1468583512215984, 3.1079644341234123 }

  37. {101, 154, 490, 1322, 2247, 2791, 4354, 6127, 8514, 8949, 9396, 9542, 9697, 9715, 9308, 9158, 8133, 7538, 6635, 5451, 1725, 903, 511, 470}

    {5761, 4220, 2981, 504, 199, 106, 126, 306, 969, 1252, 2053, 2399, 3020, 4142, 7579, 7906, 9267, 9458, 9703, 9804, 9786, 9535, 9375, 9292}

    Returns: {4814.063794887768, 5039.5104892499085, 2.20098873446221, 3.1948494444004183, 4.255669380059161 }

  38. {90, 287, 382, 950, 2281, 2885, 7406, 8064, 9101, 9621, 9761, 9638, 9444, 9323, 8775, 8105, 7478, 5477, 4381, 2108, 1455, 923, 347, 144}

    {4707, 2133, 1365, 625, 291, 244, 334, 457, 896, 1164, 4427, 6086, 7596, 8181, 8812, 9173, 9428, 9801, 9919, 9741, 9132, 8333, 7138, 5758}

    Returns: {4921.637861750829, 4887.734525866479, 0.6226219133127133, 1.6617567192967746, 2.6519485494163417 }

  39. {6204, 6665, 8087, 9247, 9254, 8738, 7284, 6278}

    {3080, 2783, 1973, 3235, 3927, 5008, 5146, 4388}

    Returns: {7735.437489047611, 3700.475621464043, 0.8470938567042583, 1.9198640999766805, 2.9658399113200438 }

  40. {1211, 1692, 3036, 5870, 7850, 7336, 5583, 4594, 2991, 1809}

    {7361, 5260, 3398, 3481, 6261, 7400, 9614, 9778, 9312, 8500}

    Returns: {4379.748113528124, 6505.03345092812, 2.271142160918605, 3.296067728970034, 4.400774518075659 }

  41. {6411, 6716, 7539, 8710, 9927, 9278, 8785, 6749}

    {5118, 3941, 3132, 3128, 4807, 5736, 6218, 5861}

    Returns: {8097.156562666994, 4695.560697416204, 2.6284847783929184, 3.614545421747519, 4.671304300783179 }

  42. {2202, 4542, 7342, 8291, 9509, 7199, 3962, 3400}

    {4334, 810, 1149, 1317, 5221, 7280, 7275, 6927}

    Returns: {5869.6421433694795, 4195.785268337613, 2.561791988959407, 3.5861443440987952, 4.6975090259765 }

  43. {86, 1091, 2290, 2514, 3327, 3428, 2496, 547}

    {4746, 3944, 3706, 3831, 4818, 5514, 6823, 6471}

    Returns: {1763.4052408211246, 5265.932676802058, 0.9785279158500235, 2.0767093257946314, 3.107608964232112 }

  44. {3276, 3726, 4424, 4861, 6779, 7553, 9363, 9333, 8760, 7051, 6486, 4862}

    {8055, 6368, 5256, 4881, 3711, 3865, 6611, 6984, 7905, 8610, 8733, 8497}

    Returns: {6398.195605818857, 6502.804590439093, 0.4551416412378153, 1.7092986308877214, 2.699722019840641 }

  45. {7183, 7590, 9314, 9434, 9559, 9749, 9862, 9213, 8681, 7768}

    {8521, 7401, 7194, 7324, 7600, 8180, 8542, 9496, 9772, 9509}

    Returns: {8532.717776061505, 8417.819785229965, 2.476295829915763, 3.5249246871847433, 4.608014080219966 }

  46. {4914, 5359, 5595, 6023, 6192, 6327, 6356, 5823, 5302, 4967, 4934, 4925}

    {445, 136, 37, 106, 144, 453, 1099, 1658, 1880, 1629, 1131, 975}

    Returns: {5600.587824622224, 905.499293001104, 0.9000304494009785, 1.9050649404656876, 2.7715278969431507 }

  47. {205, 517, 1406, 2528, 3414, 4639, 5014, 5028, 4966, 3797, 3329, 1570, 408, 247}

    {3773, 3169, 2409, 2513, 2844, 3474, 4276, 4406, 4793, 6415, 6850, 6178, 4735, 4150}

    Returns: {2592.1001325817742, 4473.8375937024875, 2.786931255038792, 3.7005722566204353, 4.65435386240642 }

  48. {4889, 4901, 5047, 5170, 5382, 6019, 6213, 6575, 7019, 7530, 8074, 8272, 8850, 8955, 9251, 9354, 9441, 9423, 9405, 9294, 9138, 8945, 8493, 8476, 8125, 7476, 7246, 6939, 6125, 5902, 5486, 5434, 5042, 4976}

    {2612, 1981, 1453, 1170, 832, 324, 243, 108, 5, 49, 220, 313, 769, 944, 1533, 1912, 2343, 2566, 2707, 3048, 3353, 3658, 4154, 4169, 4399, 4562, 4583, 4605, 4305, 4198, 3927, 3866, 3288, 3071}

    Returns: {7141.091437728823, 2310.7090224633703, 0.7196673499345836, 1.7619856809770609, 2.8090351047252526 }

  49. {5383, 5390, 5439, 5567, 5583, 5963, 6238, 7023, 7991, 8292, 8849, 9071, 9113, 9142, 9302, 9748, 9966, 9912, 9610, 9507, 9152, 8293, 7930, 7797, 7526, 6887, 6499, 6235, 5853, 5729, 5409}

    {5459, 5303, 4997, 4635, 4596, 3960, 3797, 3342, 3219, 3271, 3546, 3696, 3727, 3751, 3934, 4566, 5190, 6094, 6698, 6870, 7271, 7727, 7769, 7775, 7763, 7647, 7469, 7289, 6892, 6678, 5838}

    Returns: {7677.719600772402, 5511.017487281011, 1.0287977094414065, 2.081133724364212, 3.127269891893888 }

  50. {7186, 7239, 7321, 7549, 7732, 7899, 8028, 8269, 8418, 8690, 9088, 9396, 9476, 9585, 9829, 9940, 9971, 9983, 9881, 9800, 9662, 9239, 9128, 8664, 8409, 8187, 7796, 7733, 7401, 7254, 7201, 7194, 7186}

    {2770, 2571, 2384, 2016, 1818, 1741, 1684, 1597, 1570, 1533, 1657, 1822, 1888, 2000, 2296, 2558, 2685, 3004, 3492, 3638, 3852, 4211, 4250, 4330, 4362, 4312, 4105, 4067, 3771, 3506, 3339, 3188, 2796}

    Returns: {8577.46315808969, 2957.237827346674, 2.5678951835758763, 3.6049278366878994, 4.662181722191505 }

  51. {3185, 3192, 3287, 3777, 4251, 5269, 5475, 6144, 6931, 7202, 7514, 8796, 9518, 9887, 9980, 9997, 9571, 9537, 9129, 8847, 8746, 8523, 7038, 6565, 5610, 4747, 4453, 3817, 3321, 3213, 3199}

    {4165, 4067, 3567, 2805, 2091, 1529, 1469, 1334, 1261, 1298, 1438, 2045, 2905, 3952, 4363, 4592, 6023, 6094, 6932, 7211, 7286, 7438, 8054, 8063, 7894, 7573, 7365, 6712, 5858, 5424, 5314}

    Returns: {6540.851883721997, 4662.695900523669, 2.44558191369713, 3.484994293732111, 4.54071441899747 }

  52. {224, 248, 379, 873, 960, 1099, 1742, 1834, 2286, 3061, 3243, 4488, 4644, 5842, 6391, 7185, 7480, 7568, 7577, 7612, 7469, 7086, 6734, 6523, 5979, 5492, 4724, 4281, 3388, 2460, 2092, 1714, 1150, 772, 294}

    {3964, 3711, 3132, 1803, 1594, 1320, 721, 644, 451, 126, 63, 72, 86, 542, 955, 2003, 2837, 3135, 3232, 3954, 4451, 5602, 6074, 6330, 6679, 6991, 7262, 7384, 7275, 7067, 6897, 6667, 6107, 5642, 4481}

    Returns: {3927.442883444379, 3700.8292562445636, 2.4835859717130955, 3.532661991148538, 4.581306479234366 }

  53. {3165, 3170, 3252, 3363, 3472, 3842, 4170, 4694, 5419, 5553, 6505, 7225, 7642, 7950, 8196, 8298, 8477, 8594, 8577, 8481, 8284, 8056, 7949, 7849, 7581, 6637, 5930, 5575, 5164, 4558, 4031, 3620, 3269, 3166}

    {2832, 2624, 2151, 1673, 1427, 905, 648, 299, 41, 21, 75, 400, 698, 969, 1360, 1537, 1955, 2500, 2831, 3486, 3967, 4339, 4483, 4604, 4851, 5353, 5448, 5454, 5379, 5085, 4724, 4262, 3550, 2892}

    Returns: {5872.338721544515, 2735.8511534114714, 0.6618561538779091, 1.709629121928768, 2.758178459762499 }

  54. {7681, 7730, 7819, 7844, 8023, 8117, 8175, 8591, 8760, 9058, 9190, 9484, 9652, 9894, 9972, 9984, 9973, 9970, 9957, 9858, 9799, 9531, 9391, 9208, 9025, 8900, 8856, 8647, 8617, 8259, 8135, 8055, 7912, 7858, 7746, 7682}

    {6887, 6522, 6309, 6265, 6065, 5966, 5925, 5729, 5711, 5760, 5782, 5899, 6037, 6382, 6642, 6737, 7081, 7110, 7149, 7402, 7508, 7791, 7874, 7948, 8002, 8011, 8011, 8000, 7987, 7823, 7755, 7691, 7549, 7474, 7162, 6948}

    Returns: {8841.317648988172, 6861.351000241386, 2.2186218768362975, 3.2631801610695135, 4.303308760128685 }

  55. {2218, 2308, 2498, 2719, 2983, 3213, 3760, 4094, 4151, 4435, 4717, 5316, 5669, 6259, 6468, 6607, 6877, 6915, 7087, 7148, 7167, 6997, 6903, 6528, 6319, 5914, 5463, 4771, 4298, 4141, 3903, 3449, 3319, 2871, 2616, 2482, 2345, 2234, 2218}

    {7328, 6786, 6337, 5984, 5741, 5545, 5224, 5095, 5076, 5014, 5016, 5082, 5206, 5576, 5756, 5931, 6326, 6404, 6761, 7104, 7691, 8393, 8679, 9162, 9354, 9639, 9877, 9980, 9954, 9926, 9851, 9629, 9546, 9204, 8858, 8594, 8310, 7943, 7713}

    Returns: {4692.99813143012, 7498.834339232511, 1.0391217875992038, 2.085287271752904, 3.129332643933128 }

  56. {1, 64, 151, 325, 790, 983, 1098, 1411, 1946, 2547, 2961, 3194, 3314, 3496, 3735, 4096, 4763, 5132, 5189, 5164, 5127, 5027, 4564, 4493, 4312, 3760, 3014, 2126, 1820, 1542, 1169, 343, 216, 6}

    {4757, 4339, 3918, 3505, 2866, 2706, 2647, 2495, 2236, 2175, 2180, 2201, 2232, 2286, 2434, 2715, 3336, 4354, 4835, 5154, 5320, 5601, 6365, 6447, 6612, 7058, 7284, 7269, 7196, 7095, 6845, 6004, 5640, 4825}

    Returns: {2595.69350788411, 4729.786510184894, 2.54720618887064, 3.590566225639286, 4.635299273533469 }

  57. {4956, 4969, 5052, 5147, 5346, 5660, 5834, 6199, 6670, 7072, 7181, 7458, 7499, 7602, 7779, 7740, 7633, 7600, 7546, 7425, 7313, 6961, 6603, 6317, 6235, 6111, 5916, 5846, 5409, 5147, 4987}

    {8853, 8190, 7873, 7731, 7516, 7259, 7184, 7101, 7131, 7351, 7429, 7634, 7675, 7885, 8396, 8780, 9202, 9260, 9349, 9497, 9583, 9834, 9964, 9987, 9990, 9969, 9919, 9877, 9581, 9354, 9041}

    Returns: {6344.647055915358, 8541.631102361724, 1.0435486661744422, 2.0778217488509747, 3.139520096611894 }

  58. {6622, 6624, 6638, 6685, 6773, 6841, 6896, 7161, 7262, 7512, 7676, 7986, 8162, 8248, 8266, 8516, 8770, 8813, 9044, 9207, 9212, 9347, 9476, 9677, 9941, 9963, 9917, 9854, 9783, 9751, 9734, 9711, 9566, 9509, 9078, 8710, 8473, 8089, 7953, 7740, 7471, 7454, 7116, 7001, 6773, 6769, 6689, 6624}

    {3725, 3627, 3366, 3164, 2871, 2744, 2668, 2345, 2254, 2105, 2032, 1926, 1901, 1895, 1896, 1910, 1978, 1993, 2087, 2162, 2165, 2271, 2374, 2606, 3203, 3765, 4067, 4245, 4415, 4461, 4484, 4514, 4696, 4758, 5089, 5228, 5263, 5261, 5240, 5179, 5023, 5012, 4791, 4622, 4230, 4221, 4040, 3747}

    Returns: {8303.053602730404, 3585.9169347916486, 2.172711054730665, 3.228851808540364, 4.272433212206433 }

  59. {2558, 2603, 2622, 2635, 2794, 2812, 2986, 3355, 3828, 3940, 4482, 4644, 5291, 5963, 6072, 6685, 7198, 7415, 7694, 8320, 8490, 8978, 9259, 9405, 9704, 9880, 9980, 9969, 9675, 9286, 9128, 8985, 8610, 8271, 7824, 7047, 6784, 6212, 5626, 5518, 5104, 4487, 4042, 3573, 3378, 3265, 3225, 3090, 2863, 2642}

    {6109, 5468, 5357, 5302, 4699, 4636, 4251, 3780, 3264, 3151, 2761, 2662, 2400, 2301, 2295, 2317, 2432, 2492, 2570, 2874, 3026, 3477, 3792, 4009, 4590, 5198, 5908, 6303, 7489, 8130, 8357, 8512, 8852, 9075, 9306, 9619, 9657, 9660, 9610, 9598, 9504, 9165, 8854, 8495, 8295, 8151, 8100, 7898, 7458, 6644}

    Returns: {6279.69595824689, 5980.749149261229, 0.9534964030438873, 2.0019978638167957, 3.0496754548634195 }

  60. {2515, 2519, 2576, 2624, 2705, 2978, 3155, 3497, 3689, 4061, 4443, 4933, 5587, 5743, 5865, 6537, 7052, 7293, 7602, 8078, 8302, 8433, 8443, 8425, 8386, 8307, 8260, 7993, 7645, 7430, 7295, 6598, 6344, 5956, 5659, 5538, 5376, 5225, 4593, 4133, 3829, 3380, 3194, 2941, 2736, 2693, 2659, 2530}

    {7059, 6956, 6440, 6271, 6004, 5426, 5213, 4811, 4672, 4419, 4266, 4161, 4064, 4068, 4092, 4266, 4509, 4736, 5039, 5621, 6252, 6772, 6993, 7205, 7623, 7938, 8071, 8545, 9048, 9227, 9321, 9772, 9858, 9925, 9953, 9964, 9962, 9942, 9815, 9588, 9417, 9100, 8888, 8533, 8165, 8030, 7889, 7214}

    Returns: {5478.099557674676, 7021.512475493041, 0.6886667467471557, 1.7346934258372062, 2.7896677522862814 }

  61. {2007, 2027, 2050, 2063, 2078, 2108, 2172, 2219, 2408, 2589, 2729, 2972, 3088, 3201, 3266, 3394, 3602, 3687, 3903, 4063, 4169, 4192, 4185, 4171, 4059, 4026, 3934, 3906, 3796, 3754, 3661, 3547, 3507, 3378, 3259, 3189, 2928, 2859, 2692, 2586, 2439, 2401, 2294, 2197, 2167, 2089, 2073, 2051, 2015}

    {8904, 8771, 8624, 8558, 8508, 8436, 8336, 8279, 8064, 7941, 7877, 7831, 7815, 7813, 7820, 7855, 7940, 7984, 8147, 8362, 8617, 8923, 9057, 9138, 9400, 9452, 9577, 9615, 9737, 9778, 9843, 9905, 9923, 9953, 9979, 9991, 9965, 9958, 9905, 9865, 9757, 9726, 9622, 9517, 9466, 9311, 9255, 9177, 9033}

    Returns: {3103.421162132932, 8900.056257149687, 2.4556925716139775, 3.49465595251392, 4.546685996712138 }

  62. {1378, 1534, 1571, 1717, 1846, 2036, 2533, 2775, 3608, 4432, 5120, 5383, 6257, 6304, 6534, 6854, 7218, 8043, 8149, 8276, 8531, 9035, 9252, 9540, 9567, 9631, 9624, 9586, 9563, 9451, 9424, 9204, 8536, 8382, 6880, 6049, 5955, 5682, 5067, 4513, 4270, 3878, 3380, 2726, 2212, 2141, 1878, 1504, 1407}

    {4186, 3423, 3254, 2599, 2234, 1878, 1306, 1113, 553, 145, 68, 52, 75, 83, 137, 238, 421, 916, 997, 1098, 1310, 2036, 2381, 3558, 3672, 4144, 4412, 4672, 4809, 5418, 5532, 6041, 6943, 7108, 8080, 8255, 8263, 8283, 8220, 8150, 8090, 7926, 7670, 7211, 6590, 6503, 6159, 5241, 4765}

    Returns: {5509.306752598299, 4155.166584027512, 0.7492644777455206, 1.8003976257142802, 2.8440908830798173 }

  63. {2159, 2236, 2278, 2493, 2582, 2889, 3226, 3407, 3759, 3839, 4249, 4439, 4536, 5386, 6033, 6653, 7112, 7188, 7495, 7846, 7931, 8126, 8265, 8352, 8337, 8314, 8278, 8188, 8103, 7783, 7419, 6721, 6626, 6245, 5982, 5346, 5115, 4937, 4876, 4591, 4276, 4186, 3610, 3193, 2703, 2494, 2264, 2174}

    {6802, 6138, 5950, 5450, 5283, 4816, 4502, 4347, 4120, 4079, 3913, 3840, 3813, 3769, 3859, 4120, 4357, 4402, 4663, 5108, 5288, 5788, 6280, 6588, 6912, 7362, 7627, 7925, 8073, 8624, 9135, 9626, 9675, 9822, 9872, 9908, 9906, 9899, 9894, 9854, 9781, 9755, 9445, 9129, 8625, 8315, 7630, 7275}

    Returns: {5257.656474982892, 6851.623039732825, 2.1146274679532713, 3.1634541354846504, 4.204157679513648 }

  64. {1040, 1069, 1073, 1108, 1173, 1246, 1320, 1474, 1731, 1831, 2203, 2513, 2804, 3017, 3633, 3793, 3973, 4211, 4455, 5090, 5310, 5650, 5669, 5705, 5761, 5748, 5738, 5696, 5434, 5243, 5130, 4733, 4578, 4451, 3906, 3548, 3268, 3228, 3046, 2762, 2241, 2062, 1663, 1458, 1276, 1138, 1053}

    {7711, 7216, 7178, 6948, 6783, 6628, 6506, 6273, 5971, 5875, 5581, 5423, 5324, 5300, 5258, 5276, 5316, 5393, 5510, 5951, 6206, 6931, 6987, 7213, 7575, 7876, 7937, 8148, 8747, 9059, 9234, 9543, 9663, 9736, 9932, 9979, 9994, 9989, 9961, 9904, 9695, 9573, 9249, 8987, 8658, 8293, 7866}

    Returns: {3390.699885328585, 7620.834726859304, 2.5086512780180614, 3.5574920244267565, 4.609716229065054 }

  65. {1929, 2017, 2063, 2482, 2718, 3353, 3755, 4745, 5128, 5326, 5962, 6327, 6416, 6552, 7132, 7336, 7830, 8083, 8966, 9101, 9397, 9579, 9699, 9758, 9747, 9612, 9518, 9196, 9000, 8765, 8267, 7871, 7515, 6365, 5785, 5608, 5309, 4657, 3909, 3696, 3552, 3252, 3043, 2865, 2419, 2142, 2002, 1950}

    {5858, 5156, 5005, 3997, 3679, 3014, 2726, 2301, 2204, 2159, 2176, 2188, 2196, 2210, 2335, 2431, 2705, 2864, 3723, 3887, 4484, 5017, 5370, 5719, 6373, 7158, 7385, 7998, 8327, 8626, 9072, 9367, 9591, 9888, 9953, 9946, 9890, 9698, 9410, 9320, 9217, 8994, 8822, 8603, 7928, 7284, 6845, 6490}

    Returns: {5835.251759484703, 6039.945015319619, 2.4002558127679485, 3.442759946361183, 4.4898855719132955 }

  66. {3164, 3222, 3225, 3294, 3604, 3705, 4128, 4395, 4462, 4507, 4561, 5190, 5319, 5742, 6096, 6422, 6913, 7477, 7760, 8140, 8303, 8725, 9047, 9146, 9330, 9303, 9295, 9225, 8918, 8582, 7777, 7412, 6973, 5855, 5631, 5154, 4990, 4838, 4781, 4485, 3992, 3759, 3639, 3609, 3521, 3317, 3197}

    {6818, 6250, 6237, 6025, 5366, 5157, 4694, 4418, 4371, 4344, 4317, 4006, 3957, 3845, 3802, 3832, 3888, 4067, 4229, 4454, 4609, 5164, 5591, 5893, 6509, 7141, 7312, 7714, 8463, 8903, 9505, 9716, 9888, 9945, 9892, 9750, 9684, 9602, 9565, 9337, 8922, 8710, 8447, 8380, 8182, 7671, 7116}

    Returns: {6255.694815600098, 6877.811606587113, 0.9283518141923166, 1.9737395539963627, 3.0288605831644895 }

  67. {27, 102, 118, 139, 231, 260, 376, 450, 568, 677, 859, 1118, 1271, 1321, 1667, 1851, 2181, 2241, 2515, 2896, 2988, 3223, 3352, 3502, 3520, 3534, 3445, 3344, 3324, 3159, 2624, 2518, 2484, 2246, 2073, 1730, 1486, 1375, 1066, 826, 658, 573, 444, 391, 361, 216, 182, 108}

    {3102, 2440, 2374, 2288, 2102, 2054, 1883, 1798, 1698, 1608, 1463, 1329, 1273, 1255, 1198, 1207, 1256, 1268, 1390, 1630, 1693, 1964, 2189, 2581, 2772, 3123, 3464, 3756, 3810, 4061, 4482, 4554, 4573, 4640, 4681, 4709, 4685, 4661, 4576, 4446, 4333, 4262, 4120, 4061, 4013, 3753, 3669, 3424}

    Returns: {1773.803846453955, 2959.5398484278107, 2.115413249593474, 3.161780614303853, 4.210518378266528 }

  68. {873, 916, 948, 992, 1019, 1163, 1352, 1432, 1590, 1744, 1870, 1927, 2103, 2255, 2503, 3003, 3205, 3554, 3636, 4161, 4267, 4402, 4484, 4562, 4646, 4675, 4681, 4674, 4604, 4586, 4457, 4244, 4054, 3724, 3520, 3205, 2837, 2663, 2103, 1970, 1652, 1395, 1347, 1128, 945, 901, 889}

    {8224, 7725, 7553, 7422, 7354, 7081, 6854, 6760, 6579, 6481, 6401, 6373, 6294, 6264, 6225, 6195, 6216, 6333, 6382, 6751, 6874, 7070, 7212, 7437, 7692, 8030, 8125, 8326, 8641, 8700, 9010, 9295, 9514, 9743, 9819, 9925, 9984, 9973, 9862, 9816, 9606, 9400, 9338, 8996, 8632, 8428, 8344}

    Returns: {2782.7791487728227, 8081.948936636673, 0.13911529072353324, 1.1818690254469473, 2.2359664879318 }

  69. {6703, 6712, 6754, 6776, 6847, 6961, 7040, 7108, 7203, 7290, 7322, 7669, 7961, 8091, 8254, 8517, 8840, 9205, 9441, 9534, 9792, 9962, 9966, 9961, 9951, 9881, 9862, 9744, 9536, 9478, 9341, 8975, 8869, 8657, 8512, 8489, 8208, 7798, 7772, 7509, 7230, 6939, 6852, 6818, 6757, 6745, 6708}

    {2934, 2876, 2640, 2571, 2393, 2188, 2065, 1975, 1854, 1768, 1743, 1558, 1425, 1398, 1393, 1400, 1480, 1627, 1811, 1904, 2251, 2697, 2961, 3150, 3367, 3552, 3600, 3897, 4153, 4212, 4319, 4527, 4576, 4636, 4671, 4671, 4654, 4578, 4566, 4422, 4213, 3864, 3715, 3630, 3434, 3385, 2988}

    Returns: {8346.043973929936, 3028.139671740008, 2.1878801053278396, 3.2345760056600104, 4.284275397419407 }

  70. {6, 22, 39, 158, 219, 443, 553, 798, 1175, 1411, 2006, 2150, 2339, 2794, 2974, 3317, 3448, 3553, 3742, 3839, 3895, 3912, 3918, 3946, 4110, 4127, 4130, 4083, 4049, 4027, 3993, 3728, 3647, 3590, 3385, 2952, 2693, 2507, 2065, 1637, 1247, 1045, 935, 509, 382, 318, 144, 115, 19}

    {2874, 2587, 2447, 2089, 1921, 1580, 1467, 1228, 1023, 899, 812, 806, 829, 925, 983, 1199, 1323, 1425, 1646, 1777, 1898, 1935, 1954, 2057, 2685, 2816, 2864, 3225, 3424, 3497, 3567, 4031, 4152, 4220, 4412, 4665, 4776, 4851, 4876, 4861, 4724, 4633, 4555, 4121, 3982, 3886, 3567, 3482, 3014}

    Returns: {2066.402056849183, 2839.578050521363, 2.4394892191347015, 3.4824252324858866, 4.531944523522003 }

  71. {3108, 3118, 3131, 3251, 3476, 3649, 3858, 4189, 4674, 5372, 5418, 5705, 5905, 6294, 6442, 6677, 7045, 7470, 7610, 7710, 8165, 8674, 9200, 9387, 9430, 9419, 9387, 9308, 9041, 8646, 8475, 8195, 7883, 7698, 6891, 6536, 6081, 5739, 5638, 5237, 4523, 4075, 3998, 3636, 3382, 3267, 3129}

    {6811, 6656, 6480, 5896, 5399, 5117, 4786, 4441, 4155, 3768, 3749, 3697, 3674, 3639, 3637, 3683, 3768, 3882, 3959, 4025, 4327, 4735, 5570, 6261, 6472, 7067, 7487, 7698, 8348, 8918, 9095, 9339, 9562, 9634, 9904, 9972, 9988, 9928, 9910, 9780, 9341, 9041, 8984, 8561, 8148, 7823, 7244}

    Returns: {6281.462647071446, 6815.175622433919, 0.9578725330192368, 2.0036871162443446, 3.055077165667218 }

  72. {5, 44, 129, 170, 353, 370, 451, 602, 748, 929, 1084, 1255, 1529, 1673, 1787, 1891, 1986, 2060, 2225, 2367, 2397, 2636, 2739, 2775, 2789, 2788, 2784, 2775, 2736, 2661, 2553, 2334, 2149, 1919, 1736, 1570, 1253, 1034, 926, 644, 566, 343, 271, 145, 73, 45, 14}

    {4147, 3864, 3642, 3543, 3306, 3286, 3202, 3092, 3010, 2918, 2844, 2823, 2839, 2867, 2892, 2917, 2941, 2979, 3079, 3220, 3261, 3590, 3841, 3974, 4167, 4208, 4283, 4367, 4596, 4767, 4992, 5243, 5363, 5501, 5560, 5586, 5592, 5537, 5500, 5372, 5316, 5118, 5027, 4775, 4594, 4521, 4305}

    Returns: {1398.739271406578, 4209.323310766935, 2.127054652889629, 3.173715189128533, 4.219244964398643 }

  73. {11, 13, 44, 91, 118, 180, 429, 491, 507, 730, 954, 1033, 1224, 1231, 1529, 1613, 1698, 1761, 1951, 2059, 2176, 2265, 2361, 2448, 2484, 2495, 2468, 2394, 2356, 2314, 2289, 1989, 1918, 1810, 1653, 1605, 1410, 1107, 942, 859, 704, 536, 433, 222, 145, 85, 28, 11}

    {5954, 5869, 5528, 5355, 5306, 5205, 4875, 4827, 4817, 4694, 4607, 4594, 4592, 4592, 4599, 4625, 4656, 4685, 4785, 4880, 4987, 5091, 5263, 5479, 5647, 5840, 6038, 6286, 6373, 6457, 6492, 6807, 6863, 6922, 6993, 7007, 7048, 7047, 7022, 6997, 6935, 6825, 6757, 6522, 6389, 6216, 6041, 5973}

    Returns: {1251.0202807447472, 5816.066731960782, 0.7729050484886568, 1.8220523142824423, 2.8639588721916778 }

  74. {0,9999,10000,1}

    {9999,0,1,10000}

    Returns: {5000.000000002029, 4999.99999999814, 0.0, 2.3561278068567493, 2.3562611535238602 }

  75. {0,9147,10000,1}

    {9999,0,135,10000}

    Returns: {6376.137355044992, 3384.774175562365, 2.4105646465365442, 5.398384064354671, 5.479382739491042 }

  76. {0,0,1,2,4,5,8,10,13,14,9935}

    {14,13,10,8,5,4,2,1,0,0,9897}

    Returns: {3315.2240684849257, 3302.5616459859125, 0.7855999988943303, 3.922954103892864, 3.925073370675385 }

  77. {10000, 10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9991, 9990, 9988, 9987, 9984, 9982, 9979, 9978, 9974, 9971, 9969, 9964, 9961, 9957, 9952, 9951, 9945, 9940, 9936, 9929, 9926, 9921, 9914, 9912, 9905, 9900, 9892, 9889, 9882, 9878, 9869, 9864, 9858, 9851, 9843, 9834, 9824, 9813, 9812, 0, 1}

    {9624, 9625, 9637, 9648, 9658, 9667, 9675, 9682, 9688, 9699, 9704, 9713, 9717, 9728, 9735, 9745, 9748, 9759, 9767, 9772, 9784, 9791, 9800, 9811, 9813, 9824, 9833, 9840, 9852, 9857, 9865, 9876, 9879, 9889, 9896, 9907, 9911, 9920, 9925, 9936, 9942, 9949, 9957, 9966, 9976, 9987, 9999, 10000, 1, 0}

    Returns: {6605.819767837449, 6543.050325061955, 0.822887791901096, 3.8788736877229337, 3.922216451725043 }

  78. {9624, 9625, 9637, 9648, 9658, 9667, 9675, 9682, 9688, 9699, 9704, 9713, 9717, 9728, 9735, 9745, 9748, 9759, 9767, 9772, 9784, 9791, 9800, 9811, 9813, 9824, 9833, 9840, 9852, 9857, 9865, 9876, 9879, 9889, 9896, 9907, 9911, 9920, 9925, 9936, 9942, 9949, 9957, 9966, 9976, 9987, 9999, 10000, 1, 0}

    {0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 16, 18, 21, 22, 26, 29, 31, 36, 39, 43, 48, 49, 55, 60, 64, 71, 74, 79, 86, 88, 95, 100, 108, 111, 118, 122, 131, 136, 142, 149, 157, 166, 176, 187, 188, 10000, 9999}

    Returns: {6543.050325069824, 3394.1802321537907, 2.3936841186964193, 5.449670014517932, 5.493012778520248 }

  79. {0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 16, 18, 21, 22, 26, 29, 31, 36, 39, 43, 48, 49, 55, 60, 64, 71, 74, 79, 86, 88, 95, 100, 108, 111, 118, 122, 131, 136, 142, 149, 157, 166, 176, 187, 188, 10000, 9999}

    {376, 375, 363, 352, 342, 333, 325, 318, 312, 301, 296, 287, 283, 272, 265, 255, 252, 241, 233, 228, 216, 209, 200, 189, 187, 176, 167, 160, 148, 143, 135, 124, 121, 111, 104, 93, 89, 80, 75, 64, 58, 51, 43, 34, 24, 13, 1, 0, 9999, 10000}

    Returns: {3394.1802321628943, 3456.9496749396726, 0.8228877919016371, 3.878873687723343, 3.922216451725363 }

  80. {376, 375, 363, 352, 342, 333, 325, 318, 312, 301, 296, 287, 283, 272, 265, 255, 252, 241, 233, 228, 216, 209, 200, 189, 187, 176, 167, 160, 148, 143, 135, 124, 121, 111, 104, 93, 89, 80, 75, 64, 58, 51, 43, 34, 24, 13, 1, 0, 9999, 10000}

    {10000, 10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9991, 9990, 9988, 9987, 9984, 9982, 9979, 9978, 9974, 9971, 9969, 9964, 9961, 9957, 9952, 9951, 9945, 9940, 9936, 9929, 9926, 9921, 9914, 9912, 9905, 9900, 9892, 9889, 9882, 9878, 9869, 9864, 9858, 9851, 9843, 9834, 9824, 9813, 9812, 0, 1}

    Returns: {3456.9496749455707, 6605.819767828778, 2.393684118696325, 5.449670014517626, 5.493012778520259 }

  81. {300, 400, 300, 200}

    {500, 600, 700, 600}

    Returns: {299.99999999974995, 599.9999999995, 0.0, 1.107148717794088, 2.034443935795705 }

    A square, rotated by 45 degrees.

  82. {0, 4999, 9999 }

    {0, 4998, 9997 }

    Returns: {4999.352657600016, 4998.352653735224, 0.7853793604626449, 3.926890793648608, 3.926890800317779 }

  83. {10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981, 9980, 9979, 9978, 9977, 9976, 9975, 9974, 9973, 9972, 9971, 9970, 9969, 9968, 9967, 9966, 9965, 9964, 9963, 9962, 9961, 9960, 9959, 9958, 9957, 9956, 9955, 9954, 9953, 9952, 9951 }

    {0, 100, 199, 297, 394, 490, 585, 679, 772, 864, 955, 1045, 1134, 1222, 1309, 1395, 1480, 1564, 1647, 1729, 1810, 1890, 1969, 2047, 2124, 2200, 2275, 2349, 2422, 2494, 2565, 2635, 2704, 2772, 2839, 2905, 2970, 3034, 3097, 3159, 3220, 3280, 3339, 3397, 3454, 3510, 3565, 3619, 3672, 3724 }

    Returns: {9975.499999998734, 1982.6876830628732, 1.570796326813996, 1.5832341889144286, 1.5847610262081973 }

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