Statistics

Problem Statement for "Springs"

Problem Statement

Consider a group of metal springs supporting a rigid rod. The rod's weight is uniformly distributed along its length at a rate of 1 pound per inch. Each of the springs exerts an upwards force when it is compressed. This force is given by Fi = ki*xi+1/(maxi-xi)2 where Fi is the force, xi is the amount the spring is compressed (xi may be negative, in which case the spring is extended and the force may be downward), and maxi and ki are inputs. Notice that as the compression approaches max, the force goes to infinity, so the spring will never be compressed by max or more. Given the positions, k's, and max's for the springs supporting the rod (corresponding elements of the inputs represent one spring), you are to determine how much each spring is compressed by the rod. You may assume that the leftmost spring supports the leftmost end of the rod, while the rightmost spring supports the rightmost end of the rod. Note that some of the springs may be negatively compressed (see examples).

There are three basic conditions that must be fulfilled by the compressions of the springs. First, the total force exerted upwards (the sum of the F's) must equal the weight of the rod. Second, since the rod is rigid, the compressions of the springs must be such that the tops of the springs are all in a line (with some constant slope). Third, the sum of the torques around every point where the rod touches a spring must be 0. The torques come from both the upward (or downward) forces exerted by the springs, and also from the weight of the rod. The torque around a point due to a spring is equal to the force exerted by the spring times the horizontal distance from the spring to the point. The torque around a point caused by the weight of the rod to the right of the point is equal to the weight of the portion of the rod to the right squared, and then divided by 2. The left side of the point is analogous. See examples for more information.

Definition

Class:
Springs
Method:
compression
Parameters:
int[], int[], int[]
Returns:
double[]
Method signature:
double[] compression(int[] positions, int[] ks, int[] maxs)
(be sure your method is public)

Notes

  • In reality, the rotation of the rod would result in some more complicated effects which we will ignore for this problem.
  • When none of the springs are compressed at all, their tops form a horizontal line.

Constraints

  • positions, ks and maxs will each contain between 2 and 50 elements, inclusive.
  • positions, ks and maxs will each contain the same number of elements.
  • positions will be sorted in strictly ascending order.
  • Each element of positions will be between 0 and 1000, inclusive.
  • Each element of maxs and ks will be between 1 and 1000, inclusive.

Examples

  1. {0,1,3}

    {1,1,1}

    {1000,1000,1000}

    Returns: {0.857141855426, 0.964284712354, 1.17857042621 }

    The image above shows the approximate setup of the springs and rod. The values in maxs are large enough that we can ignore them in this discussion and our results won't be far off. The first spring is compressed by 6/7, the second by 27/28, and the third by 33/28. You will note that the sum of these three compressions is 3. Furthermore, the slope of the rod (3/28) matches the compression of the springs. Finally, we can calculate the torque at each location (negative values indicate counterclockwise torque): Torque due to: Position | Spring 0 | Spring 1 | Spring 2 | Weight of Left | Weight of Right ---------+----------+----------+----------+----------------+---------------- 0 | 0 | -27/28*1 | -33/28*3 | 0 | 3*3/2 = 9/2 1 | 6/7 * 1 | 0 | -33/28*2 | -1*1/2=-1/2 | 2*2/2 = 2 3 | 6/7 * 3 | 27/28*2 | 0 | -3*3/2=-9/2 | 0 You can easily verify that the sum of the torques at each of the three positions is 0.When you solve the problem taking max into account, you find that each of the above values is approximately one millionth too high.

  2. {0,1,2,4}

    {2,1,1,1}

    {1,10,10,10}

    Returns: {0.066863594314, 0.421263093855, 0.775662593396, 1.484461592477 }

  3. {1,99,101}

    {1,100,100}

    {1000,1000,1000}

    Returns: {48.510296857713, 0.744851008845, -0.229954008478 }

  4. {0,1000}

    {1,1000}

    {1,1000}

    Returns: {0.955235859695, 0.499999998999 }

  5. {0,707,708,1000}

    {1,1000,1000,1}

    {1000,1000,1000,1000}

    Returns: {250.47392797967768, 0.6029503662014406, 0.24952606971845626, -102.95036850331559 }

  6. {0, 1, 1000}

    {70, 71, 140}

    {1000, 1000, 1000}

    Returns: {3.547874851643951, 3.5478966060661126, 3.569629273805603 }

  7. {0, 1, 2}

    {10, 10, 10}

    {1000, 1000, 1000}

    Returns: {0.06666656665333207, 0.06666656665333202, 0.06666656665333198 }

  8. {0, 499, 500, 501, 1000}

    {100, 100, 1, 100, 100}

    {1000, 1000, 10, 1000, 1000}

    Returns: {2.4937213165348435, 2.4937213165348426, 2.4937213165348426, 2.4937213165348426, 2.4937213165348417 }

  9. {0, 500, 1000}

    {100, 1, 100}

    {1000, 10, 1000}

    Returns: {4.97492734400514, 4.97492734400514, 4.97492734400514 }

  10. {0, 999, 1000}

    {100, 50, 50}

    {1000, 1000, 1000}

    Returns: {4.9974987405258595, 5.002498726676254, 5.002503731667396 }

  11. {38,48,55,73,170,212,242,346,462,470,549,563,577,626,639,698,723,835,875,956,961,980,984}

    {951,517,650,774,467,541,867,679,308,249,105,133,998,539,748,638,769,965,452,867,712,829,237}

    {400,186,92,792,30,126,92,48,487,819,26,8,95,609,408,431,411,509,343,756,646,808,747}

    Returns: {0.07143361138304566, 0.07135464602616691, 0.07129937027635178, 0.07115723263397003, 0.07039126867224613, 0.07005961417335536, 0.06982271810271912, 0.06900147839118008, 0.06808548025138655, 0.06802230796588356, 0.06739848164654141, 0.06728793014691116, 0.0671773786472809, 0.06679044839857502, 0.06668779343463264, 0.066221897829048, 0.06602448443685112, 0.0651400724398091, 0.06482421101229409, 0.06418459162157619, 0.06414510894313681, 0.06399507476506719, 0.06396348862231568 }

  12. {438,645,931}

    {682,882,30}

    {518,769,704}

    Returns: {-0.05341570962740011, 0.5529559649235833, 1.3907448486027199 }

  13. {152,289,393,919}

    {375,842,437,58}

    {765,60,1000,281}

    Returns: {-0.34521925092815287, 0.35643321657850113, 0.8890745057806329, 3.583010256937567 }

  14. {72,204,465,537,725}

    {741,965,131,142,41}

    {588,519,794,642,425}

    Returns: {-0.02300311715214045, 0.316861087485813, 0.9888653102926753, 1.1742457855497406, 1.6582948042765226 }

  15. {0,107,196,460}

    {351,277,548,7}

    {933,67,180,4}

    Returns: {-0.27973023455067236, 0.3233404254872815, 0.82495994645343, 2.312909986173241 }

  16. {55,185,214,339,408,489,874,889,946}

    {146,860,720,717,78,701,78,21,53}

    {198,879,786,558,977,281,638,772,749}

    Returns: {-0.13724852140536287, 0.06047239109008684, 0.1045793638775333, 0.29469562589238885, 0.399639802524589, 0.5228351403102154, 1.1083932273159702, 1.1312071787577531, 1.217900194236527 }

  17. {436,570,971}

    {166,381,20}

    {365,185,436}

    Returns: {-0.6387685989525544, 1.3080260201673963, 7.133881559474116 }

  18. {91,197,490,773}

    {589,818,200,4}

    {371,437,55,114}

    Returns: {-0.2497833498087797, 0.4294247101315315, 2.306858309777863, 4.120215677354354 }

  19. {101,263,269,724,756}

    {890,256,984,13,68}

    {194,715,203,184,778}

    Returns: {-0.12579175511414586, 0.4569103518629669, 0.47849191138063785, 2.1150935081373436, 2.2301951588982547 }

  20. {70,233,714,842}

    {652,628,45,26}

    {332,238,60,393}

    Returns: {-0.12824954684258777, 0.8893322161384023, 3.892134841867582, 4.691217453288237 }

  21. {46,56,260}

    {758,294,2}

    {145,715,815}

    Returns: {-0.44092989784954306, 1.5743315671673301, 42.68566545351155 }

  22. {210,245,318,465,998}

    {416,808,921,408,9}

    {134,185,255,185,254}

    Returns: {-0.7165157535889275, -0.33209695539564343, 0.469690823693206, 2.084249776104999, 7.93839890287701 }

  23. {471,477}

    {5,688}

    {693,817}

    Returns: {0.5999995828273035, 0.004360462938709286 }

  24. {5,103,121,317,501}

    {783,760,961,28,39}

    {637,796,980,536,947}

    Returns: {-0.26885356916834113, 0.27473632519279023, 0.37457936701422256, 1.4617591557364853, 2.4823769165777936 }

  25. {95,333,646,689,713,732}

    {98,711,78,488,725,105}

    {736,434,339,170,662,717}

    Returns: {0.773263935821183, 0.5233185630779049, 0.19460889220124067, 0.149450694604766, 0.1242461192020825, 0.10429249700829146 }

  26. {57,455,509}

    {107,570,871}

    {256,751,477}

    Returns: {1.918898649172696, 0.30365102774683583, 0.08449682785488499 }

  27. {176,369}

    {2,190}

    {570,916}

    Returns: {48.249998163271, 0.5078947305624268 }

  28. {28,730,917}

    {15,864,839}

    {441,105,101}

    Returns: {10.402224402596818, 1.5872376665589254, -0.7609140708186892 }

  29. {322,809}

    {3,872}

    {206,318}

    Returns: {81.16664527633782, 0.2792431079056854 }

  30. {576,603}

    {1,893}

    {452,504}

    Returns: {13.499994799312077, 0.015117576778280295 }

  31. {280,312}

    {125,64}

    {422,422}

    Returns: {0.12799995505011524, 0.24999991215645706 }

  32. {22,162}

    {103,76}

    {3,5}

    Returns: {0.6778112557103275, 0.9202620951626639 }

  33. {11,123,179,202,279,314,330,338,388}

    {20,27,3,10,24,15,30,11,20}

    {8,8,10,6,10,9,7,7,10}

    Returns: {3.973773698577615, 3.191935926370664, 2.801017040267189, 2.6404610691889756, 2.102947600796697, 1.8586232969820253, 1.7469321866667467, 1.691086631509107, 1.3420519117738614 }

  34. {79,367}

    {326,322}

    {41,38}

    Returns: {0.44171592664971326, 0.44720276672997505 }

  35. {20,112,181,274,413}

    {304,306,275,245,314}

    {147,207,50,184,95}

    Returns: {0.22738588034383483, 0.25043558586712605, 0.2677228650095944, 0.2910231108103127, 0.32584820937267656 }

  36. {1,12,14,15,17}

    {61,49,27,29,29}

    {316,415,437,303,390}

    Returns: {0.10124951903234314, 0.0778514268254131, 0.07359722824233492, 0.07147012895079582, 0.06721593036771764 }

  37. {37,48,107,116,156}

    {83,68,66,66,76}

    {274,243,273,313,140}

    Returns: {0.2893906125351897, 0.2978587320061806, 0.3432786455324046, 0.3502071069177608, 0.381000268630455 }

  38. {17,98,103,377,532,631,640,665,705,708,734,756,765,769,777}

    {136,89,145,115,129,134,124,100,42,70,57,116,24,81,81}

    {55,61,58,29,54,38,34,31,37,31,59,33,24,57,21}

    Returns: {0.875759187568633, 0.8171455964097888, 0.813527473498749, 0.6152543379737696, 0.5030925277315368, 0.4314536940929494, 0.42494107285307775, 0.40685045829787897, 0.3779054750095608, 0.375734601262937, 0.35692036212553013, 0.3410006213169552, 0.33448800007708357, 0.33159350174825175, 0.3258045050905881 }

  39. {4,9,33,35,41,54,55,71,82,84,91,93}

    {60,209,93,206,140,99,69,146,155,60,116,47}

    {144,254,125,67,56,145,324,206,65,209,252,363}

    Returns: {0.06981742023890475, 0.06914182671205608, 0.06589897778318252, 0.06562874037244305, 0.06481802814022466, 0.06306148497041815, 0.06292636626504841, 0.06076446697913271, 0.059278161220065656, 0.05900792380932619, 0.058062092871738066, 0.057791855460998603 }

  40. {2,7,11,15,17,19,35,37,40,52,71,77,84,93}

    {600,185,129,518,272,468,503,622,380,99,534,189,71,252}

    {52,51,55,42,44,59,58,47,41,55,45,53,43,51}

    Returns: {0.007655115906566749, 0.009362329738421143, 0.010728100803904655, 0.012093871869388172, 0.012776757402129928, 0.013459642934871684, 0.018922727196805742, 0.0196056127295475, 0.020629941028660136, 0.024727254225110677, 0.031214666786157374, 0.03326332338438264, 0.03565342274897879, 0.0387264076463167 }

  41. {9,39,111,112,117,152,168,194,214,265,267,268,320,428,451}

    {5,8,7,6,6,5,5,6,7,5,6,7,5,6,5}

    {10,7,4,25,9,31,32,8,3,25,28,11,12,11,13}

    Returns: {1.3733832159084098, 1.600778737429716, 2.146527989080851, 2.1541078397982276, 2.192007093385112, 2.4573018684933023, 2.5785794799713324, 2.775655598623131, 2.927252612970668, 3.3138249995568887, 3.3289847009916427, 3.3365645517090194, 3.7307167890126167, 4.549340666489318, 4.723677232988987 }

  42. {17,35,73,157,256}

    {130,155,120,196,116}

    {59,141,185,108,149}

    Returns: {0.2085169533733739, 0.2334245079500617, 0.28600712316751375, 0.4022423778587235, 0.5392339280305065 }

  43. {1,60,76,93,221,261,284,286,336,389,449,503}

    {21,13,16,24,18,13,10,13,5,23,6,22}

    {440,376,47,158,433,239,323,393,201,133,443,48}

    Returns: {2.245998226465338, 2.3695293666715895, 2.4030293368970135, 2.4386230552615262, 2.7066228170649187, 2.790372742628479, 2.838528949827526, 2.8427164461057037, 2.947403853060154, 3.0583725044318713, 3.1839973927772114, 3.2970597922880174 }

  44. {127,130,159,166,190,217,251,264,425,435,486,583,608,672,729,730,751,792,808}

    {317,318,317,313,314,316,312,312,316,318,315,314,316,315,318,314,312,313,318}

    {123,141,107,46,190,50,130,152,124,51,84,60,124,105,133,44,178,33,59}

    Returns: {0.10229900581256857, 0.10240563920645192, 0.10343642868065764, 0.10368523993305212, 0.10453830708411893, 0.1054980076290691, 0.10670651942641372, 0.10716859746657491, 0.11289125627164806, 0.11324670091792591, 0.11505946861394287, 0.11850728168283786, 0.11939589329853245, 0.12167073903471061, 0.12369677351849427, 0.12373231798312205, 0.12447875174030551, 0.12593607479004462, 0.12650478622408917 }

  45. {104,383,399,526,614,764}

    {121,78,68,154,158,64}

    {68,63,47,59,67,63}

    Returns: {1.2687530996035146, 1.0794442705024048, 1.068587850195531, 0.9824150140097212, 0.9227047023219159, 0.8209257619449752 }

  46. {309,646}

    {8,3}

    {119,196}

    Returns: {21.062486967976042, 56.1666496193033 }

  47. {30,66,90}

    {288,245,179}

    {101,88,99}

    Returns: {0.07445445674442452, 0.08731598497717538, 0.09589033713234263 }

  48. {62,78,97}

    {380,348,256}

    {21,401,57}

    Returns: {0.028052349315393632, 0.03619541112894382, 0.04586529703253467 }

  49. {34,63}

    {152,151}

    {6,22}

    Returns: {0.09520604769691202, 0.09601268696432233 }

  50. {5,11,153,392,487,626,903,919}

    {263,263,263,264,260,262,260,263}

    {63,123,48,136,87,148,115,56}

    Returns: {0.39426496181734494, 0.3948409188907944, 0.40847190296243285, 0.4314141930548383, 0.44053351338445557, 0.4538765189193692, 0.48046653714362153, 0.48200242267282023 }

  51. {49,130}

    {195,88}

    {126,166}

    Returns: {0.20769198360858604, 0.4602268580477248 }

  52. {25,26,153,199,218,299,307,317,393,423,459,522,604,678,687,779,862}

    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {76,76,79,88,95,24,29,46,69,57,110,69,121,59,15,125,21}

    Returns: {30.279217789340713, 30.256045379586386, 27.313149340787017, 26.24721849208803, 25.80694270675584, 23.929977516655455, 23.74459823862085, 23.512874141077592, 21.751770999748835, 21.056598707119065, 20.222391955963335, 18.762530141440813, 16.862392541586104, 15.147634219765997, 14.939082531977064, 12.807220834579098, 10.883910824970059 }

  53. {69,161,174,209,252,309,391,404,455,702,745,752,764}

    {290,290,272,264,286,294,270,277,288,261,277,267,273}

    {28,30,33,29,32,31,30,29,33,32,32,33,31}

    Returns: {0.1850995221845182, 0.18711527188394297, 0.18740010608060084, 0.18816696737929503, 0.18910911126054794, 0.1903579996612785, 0.19215464613250494, 0.1924394803291628, 0.19355690679297435, 0.19896875652947352, 0.1999109004107264, 0.20006427267046523, 0.20032719654430325 }

  54. {6,46,90,189,211,223,255}

    {103,103,101,102,101,102,106}

    {2,13,11,12,14,2,15}

    Returns: {0.4372511874491116, 0.4110898201870431, 0.3823123161987677, 0.3175629322251482, 0.3031741802310105, 0.2953257700523899, 0.2743966762427351 }

  55. {231,445,457,739}

    {180,7,47,87}

    {90,31,21,118}

    Returns: {1.124705159630976, 1.6831723142465962, 1.714488229458687, 2.450412236942822 }

  56. {14,63,69,70,74,75,98,113,174,233,274,329,381,388,390,422,466,473,511,611,699,727,739,772,850,873}

    {60,89,52,68,56,65,44,17,78,38,32,36,15,87,55,31,73,13,53,16,83,55,95,49,44,63}

    {6,33,15,9,48,63,45,30,12,43,11,67,39,7,67,57,70,9,55,53,49,26,38,17,24,17}

    Returns: {0.45446443918881174, 0.47759362834691527, 0.48042577395811165, 0.48089779822664436, 0.48278589530077526, 0.483257919569308, 0.4941144777455607, 0.5011948417735516, 0.5299883221540478, 0.5578377539974786, 0.5771907490073204, 0.6031520837766202, 0.627697345740322, 0.631001515620051, 0.6319455641571166, 0.6470503407501638, 0.6678194085656037, 0.6711235784453328, 0.6890605006495764, 0.7362629275028489, 0.7778010631337287, 0.791017742652645, 0.7966820338750378, 0.8122588347366178, 0.8490767276821702, 0.859933285858423 }

  57. {12,38,41,44,55,123,173,182,236,278,302}

    {29,83,69,40,84,56,30,22,30,44,23}

    {50,19,24,48,54,52,66,68,67,22,38}

    Returns: {0.24911045955797356, 0.33569231095444385, 0.34568252457711346, 0.3556727381997831, 0.39230352148290515, 0.6187483635967506, 0.7852519239745781, 0.8152225648425868, 0.9950464100506407, 1.1349094007680156, 1.2148311097493727 }

  58. {114,156,288}

    {194,128,48}

    {56,141,65}

    Returns: {0.1948721028181939, 0.5066190066830498, 1.4863949902583116 }

  59. {5,12,20,22,34,44,53,56}

    {394,308,389,316,312,296,364,462}

    {118,241,285,49,186,209,230,124}

    Returns: {0.019196753017625752, 0.01886643250522254, 0.0184889233481903, 0.01839454605893224, 0.017828282323383876, 0.017356395877093575, 0.0169316980754323, 0.016790132141545212 }

  60. {1,59,136,142}

    {109,31,27,93}

    {17,21,12,23}

    Returns: {0.5500713958096961, 0.543713033125255, 0.5352717585269451, 0.5346139968699339 }

  61. {732,786}

    {60,149}

    {97,55}

    Returns: {0.44999821209607715, 0.18120582035163263 }

  62. {194,257}

    {46,44}

    {4,2}

    Returns: {0.6828070010960754, 0.7024109797760594 }

  63. {4,11,12,15,16,26,27,37,63,69,72,76,89,97}

    {19,20,21,19,21,23,21,18,20,24,25,19,20,19}

    {151,290,570,236,133,135,683,652,313,123,284,153,523,593}

    Returns: {0.2367199393909662, 0.2515228325678412, 0.2536375315931091, 0.2599816286689126, 0.2620963276941805, 0.2832433179468591, 0.2853580169721269, 0.3065050072248055, 0.36148718188176987, 0.374175376033377, 0.38051947310918055, 0.388978269210252, 0.4164693565387342, 0.433386948740877 }

  64. {68,77,194,255,313,466,658,753}

    {112,83,80,100,108,106,103,83}

    {37,331,382,398,92,200,41,43}

    Returns: {0.5981514999003879, 0.6073863197597249, 0.727438977931106, 0.7900305347555014, 0.849543818293451, 1.0065357559021804, 1.2035452462347034, 1.3010239003054829 }

  65. {17,23,30,55,96,122,123,127,148,150,152,194,206,211,255,280,283}

    {181,144,10,113,60,114,217,239,262,136,20,71,187,244,189,217,188}

    {90,78,96,86,46,48,73,67,62,43,30,90,49,83,80,51,57}

    Returns: {0.12694507339898087, 0.12593283202831232, 0.12475188376253235, 0.12053421138474674, 0.11361722868517835, 0.10923084941228131, 0.10906214251716989, 0.10838731493672418, 0.10484447013938428, 0.10450705634916142, 0.10416964255893857, 0.09708395296425876, 0.09505947022292166, 0.09421593574736453, 0.08679283236246187, 0.08257515998467625, 0.08206903929934198 }

  66. {1,87,160,362,370,466}

    {114,120,100,90,112,129}

    {72,233,205,229,82,96}

    Returns: {0.7452726624515917, 0.7288238502679594, 0.7148614864376667, 0.6762259043319254, 0.6746957822683317, 0.6563343175052072 }

  67. {22,88,133,134,139,147,187,201,264,268,278,293,319,332,333,342,419,420,456,462,473,490}

    {48,47,11,50,30,36,40,12,49,49,38,22,36,30,47,33,48,20,39,31,42,25}

    {37,28,20,15,36,24,39,70,72,23,82,70,43,34,73,51,71,56,22,86,65,85}

    Returns: {0.7704019928722894, 0.7256984759724547, 0.695218805358931, 0.6945414793452972, 0.6911548492771279, 0.685736241168057, 0.6586432006227027, 0.6491606364318286, 0.6064890975728955, 0.60377979351836, 0.5970065333820215, 0.5868466431775136, 0.5692361668230332, 0.560430928645793, 0.5597536026321592, 0.5536576685094545, 0.5015035654596474, 0.5008262394460135, 0.4764425029551945, 0.47237854687339137, 0.4649279607234189, 0.4534134184916433 }

  68. {7,20,56,69,75,78,80,98,123,149,152,162,164,180,207,217,218,219,225,256,283,290,299,306,307,348,365,374,378,419,428,445,450,461,496,500,501,507,518}

    {484,305,450,524,290,510,87,317,74,399,473,525,398,512,462,194,365,310,224,269,246,461,488,321,518,457,195,135,445,532,526,435,341,276,441,382,180,267,468}

    {47,54,28,28,31,91,96,74,60,83,65,20,90,91,90,35,38,41,95,24,81,96,89,56,83,55,35,70,70,73,88,59,50,47,84,44,26,36,23}

    Returns: {0.037501349044095786, 0.03741464468481807, 0.03717454030527977, 0.037087835946002054, 0.03704781854941234, 0.037027809851117484, 0.03701447071892091, 0.03689441852915176, 0.03672767937669461, 0.03655427065813918, 0.03653426195984432, 0.03646756629886146, 0.03645422716666489, 0.036347514109092316, 0.03616743582443859, 0.036100740163455734, 0.03609407059735745, 0.03608740103125916, 0.036047383634669444, 0.03584062708562258, 0.03566054880096886, 0.03561386183828086, 0.03555383574339629, 0.035507148780708285, 0.03550047921461, 0.035227027004580275, 0.035113644380909415, 0.03505361828602484, 0.035026940021631696, 0.03475348781160197, 0.034693461716717396, 0.034580079093046535, 0.03454673126255511, 0.03447336603547396, 0.03423993122203395, 0.034213252957640806, 0.03420658339154252, 0.034166565994952804, 0.03409320076787166 }

  69. {21,59,63,72,132,325,341,349,519,549,585,603,609,684,718}

    {261,281,293,223,204,228,212,242,281,289,277,288,259,249,270}

    {10,8,9,10,6,6,5,5,7,10,6,8,6,9,7}

    Returns: {0.19496125923321556, 0.19345532628314205, 0.19329680702523958, 0.19294013869495902, 0.19056234982642192, 0.1829137956326276, 0.18227971860101772, 0.18196268008521277, 0.17522561162435765, 0.1740367171900891, 0.17261004386896683, 0.17189670720840572, 0.171658928321552, 0.16868669223588062, 0.1673392785437096 }

  70. {59,200,294,354,440,562,597}

    {316,454,325,332,147,218,370}

    {68,80,72,82,68,68,61}

    Returns: {0.2697620895095064, 0.2591874839521354, 0.25213774691388813, 0.24763791476181538, 0.2411881553438444, 0.2320384966346298, 0.2294135945459207 }

  71. {13,41,76,80,84,124,134,139,142,148,158,159}

    {18,24,19,18,19,19,20,22,18,24,19,22}

    {49,58,65,65,132,64,120,91,86,89,53,141}

    Returns: {1.228833581239134, 1.0465576866709172, 0.8187128184606463, 0.792673404950901, 0.7666339914411556, 0.506239856343703, 0.4411413225693399, 0.4085920556821584, 0.3890624955498495, 0.3500033752852315, 0.28490484151086837, 0.278394988133432 }

  72. {73,294}

    {87,110}

    {21,12}

    Returns: {1.2700854147799623, 1.0044702619631387 }

  73. {58,199,206,223,417,561}

    {266,637,161,183,121,558}

    {36,70,67,103,122,91}

    Returns: {0.24492911334611017, 0.2543496523173654, 0.2548173386492717, 0.2559531483124727, 0.2689147409395898, 0.2785357169102334 }

  74. {35,315}

    {19,27}

    {183,217}

    Returns: {7.368419346387416, 5.1851843596728475 }

  75. {28,98,142,257,335,356,359,398,423,576,609,622,720,783}

    {216,229,221,218,214,226,226,229,227,216,221,223,222,226}

    {333,260,198,254,251,299,345,254,140,144,130,134,167,154}

    Returns: {0.2472892813771444, 0.24639869795409908, 0.24583890265961345, 0.2443758013217533, 0.24338343693607423, 0.24311626190916064, 0.243078094048173, 0.24258191185533345, 0.242263846347103, 0.2403172854367325, 0.2398974389658683, 0.23973204490158845, 0.238485228109325, 0.23768370302858421 }

  76. {164,191,319,359,419,425,482,598,664,804}

    {95,97,86,95,103,88,92,94,104,95}

    {13,25,12,22,20,14,17,22,8,26}

    Returns: {0.4762208492646489, 0.49526487452110446, 0.585547660922079, 0.6137610316723836, 0.6560810877978404, 0.660313093410386, 0.70051714672957, 0.7823359219054532, 0.8288879836434557, 0.9276347812695216 }

  77. {31,65,130,214,216,222,253,262}

    {23,36,28,35,21,24,29,32}

    {197,274,238,257,159,150,63,301}

    Returns: {1.6180117448599467, 1.4746220953911142, 1.2004948243477578, 0.8462380433071127, 0.8378033580442401, 0.8124993022556226, 0.681761680681099, 0.6438055969981726 }

  78. {3,7,21,23,26,33,40,42,50,63,65,68,73,78,83}

    {18,22,25,25,31,18,33,16,19,20,33,29,21,15,29}

    {63,54,59,96,86,97,96,103,75,55,54,108,120,78,123}

    Returns: {0.2669688740982241, 0.26311887824389957, 0.24964389275376375, 0.24771889482660148, 0.2448313979358581, 0.23809390519079016, 0.23135641244572225, 0.22943141451855997, 0.22173142280991093, 0.2092189362833562, 0.20729393835619392, 0.20440644146545053, 0.19959394664754487, 0.1947814518296392, 0.18996895701173355 }

  79. {10,105,163,234,337,538}

    {340,367,326,248,46,540}

    {12,34,16,10,16,32}

    Returns: {0.2361061818702208, 0.2549057185982042, 0.26638333049528884, 0.2804335105762028, 0.3008161661865427, 0.34059202810574973 }

  80. {95,188,212,274,277,281,310,401}

    {26,25,25,27,25,27,27,25}

    {40,27,22,18,12,15,33,19}

    Returns: {1.7082959075032087, 1.5744721908208978, 1.5399370381286885, 1.450721227007148, 1.4464043329206218, 1.440648474138587, 1.3989184979688343, 1.2679727106775407 }

  81. {34,60,113,190,228,283,406,506,523,543,553,593,612,639,664,685,718,724,727,732,859,936}

    {24,16,16,11,32,24,16,21,18,16,10,27,32,2,3,3,33,29,14,10,28,18}

    {279,307,126,299,261,303,112,169,289,111,146,299,245,229,82,44,75,262,47,278,141,60}

    Returns: {2.58623245270088, 2.5671224890192788, 2.528167563052937, 2.4715726706112706, 2.4436427236920064, 2.403217800519388, 2.3128129723333495, 2.239313112019497, 2.226818135766142, 2.2121181637033716, 2.2047681776719865, 2.1753682335464455, 2.1614032600868134, 2.1415582978020735, 2.1231833327236105, 2.107748362057701, 2.08349340815413, 2.079083416535299, 2.0768784207258832, 2.0732034277101907, 1.9798586051115983, 1.923263712669932 }

  82. {42,122,140,147,204,238,302,525,556}

    {61,45,21,53,22,23,35,62,31}

    {43,104,38,144,62,70,93,36,168}

    Returns: {1.0336113656861579, 1.1942384741903391, 1.23037957360378, 1.244434445597896, 1.358881260407125, 1.4271477815214022, 1.5556494683247473, 2.0033975332801526, 2.065640537825523 }

  83. {10,36,48,76,183,198,228,295,356,436,501,594,633,653,666,715,719,759,764,797,897}

    {95,96,90,125,18,19,76,9,14,20,2,98,108,5,53,12,64,42,12,50,26}

    {64,55,13,97,78,45,110,66,125,54,120,101,1,115,31,29,86,66,24,62,40}

    Returns: {0.5874517794441148, 0.6003648077277601, 0.6063246669355965, 0.6202310050872147, 0.6733730830237555, 0.680822907033551, 0.6957225550531418, 0.7289984356302281, 0.7592943866033962, 0.7990267813223053, 0.8313093520314189, 0.8774982608921506, 0.8968678033176187, 0.906800901997346, 0.9132574161391687, 0.9375935079045005, 0.9395801276404459, 0.9594463249999003, 0.9619295996698323, 0.9783192124913822, 1.0279847058900184 }

  84. {134,147}

    {561,509}

    {12,10}

    Returns: {0.011574050160888812, 0.012750440963188413 }

  85. {1,18,55,89,123,161,186,258,260,332,381,386,394,444,448,506,521,580,649,669,710,802}

    {76,16,62,36,60,114,29,50,53,61,95,118,46,30,117,75,4,83,123,49,92,77}

    {220,145,169,297,183,240,72,244,98,155,53,175,248,42,47,149,62,238,167,296,85,13}

    Returns: {0.5179778251973841, 0.5192044561198927, 0.5218741822453529, 0.5243274440903702, 0.5267807059353876, 0.5295225868209952, 0.5313264558246844, 0.5365215985553095, 0.5366659080756045, 0.5418610508062296, 0.5453966340534604, 0.5457574078541982, 0.5463346459353788, 0.5499423839427573, 0.5502310029833476, 0.5544159790719065, 0.5554983004741201, 0.5597554313228267, 0.564734109773009, 0.5661772049759604, 0.5691355501420108, 0.5757737880755871 }

  86. {25,43,85,89,157,165,168,179,231,244,264,457,504,526,533,534,554,617,644,737,738,739,743}

    {232,367,247,194,123,162,197,258,163,65,300,150,98,331,67,232,371,189,289,334,310,237,217}

    {7,8,9,7,8,9,8,8,7,7,8,7,9,7,10,8,7,9,8,7,7,8,9}

    Returns: {0.15797852206234114, 0.15712203551779283, 0.15512356691384677, 0.1549332365706138, 0.1516976207356535, 0.15131696004918757, 0.15117421229176287, 0.15065080384787222, 0.14817650938584376, 0.14755793577033666, 0.14660628405417186, 0.13742284499318158, 0.1351864634601943, 0.13413964657241303, 0.13380656847175537, 0.13375898588594712, 0.13280733416978233, 0.12980963126386325, 0.12852490144704076, 0.12409972096687447, 0.12405213838106623, 0.12400455579525799, 0.12381422545202503 }

  87. {37,50,92}

    {126,154,153}

    {94,10,96}

    Returns: {0.1078671820746733, 0.11820409421248272, 0.1516002718884824 }

  88. {0,51,68,140,187,200,296,311,360,385,424,595,644,682,685,759,802,822,849,891,919,933,955,973}

    {126,125,126,127,125,127,127,125,127,125,125,127,126,127,125,127,125,126,127,125,127,125,125,125}

    {24,41,51,43,27,46,46,33,50,51,20,54,40,28,55,45,47,50,36,34,48,50,35,18}

    Returns: {0.40999609988965546, 0.40165976147514637, 0.39888098200364336, 0.38711203365374813, 0.3794295257031221, 0.37730457669550216, 0.36161264556230854, 0.35916078132274704, 0.3511513581401795, 0.3470649177409103, 0.34069007071805046, 0.31273881838704937, 0.3047293952044818, 0.2985180057975927, 0.2980276329496804, 0.28593176936784365, 0.2789030918811007, 0.27563393956168536, 0.27122058393047466, 0.26435536405970245, 0.259778550812521, 0.25749014418893024, 0.25389407663757335, 0.2509518395500996 }

  89. {554,589,837}

    {64,81,75}

    {115,110,165}

    Returns: {1.00010955151855, 1.091720087519208, 1.7408461711810124 }

  90. {16,17,19,23,42,55,108,146,167,170,197,208,243,260,283,287,368,371,372,404,425,485,535,540,553,571,611,638,675,703}

    {51,19,63,71,43,65,12,142,113,51,79,32,16,119,147,11,30,116,120,142,93,19,50,153,84,95,70,41,123,19}

    {195,226,122,111,405,71,360,255,379,407,326,34,132,199,417,450,450,143,184,329,81,450,372,332,445,183,247,288,28,66}

    Returns: {0.2611520840136008, 0.2613154706560094, 0.26164224394082664, 0.26229579051046104, 0.26540013671622464, 0.26752416306753657, 0.2761836551151929, 0.28239234752672004, 0.2858234670173008, 0.28631362694452667, 0.2907250662895591, 0.29252231935605383, 0.29824085184035515, 0.3010184247613015, 0.30477631753669954, 0.30542986410633394, 0.31866418214143133, 0.3191543420686571, 0.3193177287110658, 0.32454610126814126, 0.32797722075872204, 0.33778041930323865, 0.3459497514236691, 0.34676668463571214, 0.34889071098702407, 0.351831670550379, 0.3583671362467234, 0.36277857559175586, 0.3688238813608744, 0.3733987073483155 }

  91. {103,126,144,155,187,352,511,568,633,643}

    {15,6,11,6,12,7,14,6,7,11}

    {205,28,35,145,222,152,185,272,230,261}

    Returns: {4.531733053951937, 4.647220616404372, 4.737602187019322, 4.79283536906179, 4.9535137168217, 5.782011447458734, 6.580381987890785, 6.866590294838124, 7.192968188725441, 7.243180172400413 }

  92. {20,23}

    {9,9}

    {316,214}

    Returns: {0.16666555277857859, 0.16666423666445584 }

  93. {373,580}

    {210,208}

    {590,540}

    Returns: {0.49285712915455626, 0.49759613732844143 }

  94. {390,503}

    {138,131}

    {25,39}

    Returns: {0.4094083063750541, 0.4312925782558489 }

  95. {71,86,289,350,406,600}

    {630,539,571,492,594,513}

    {121,113,130,126,127,122}

    Returns: {0.11347245078848717, 0.116514510233992, 0.15768371472982406, 0.17005475647487706, 0.18141177840476178, 0.22075574723329094 }

  96. {8,54,79,115,190,245,266,550,660,691,696,730,761,771,814,820,833,839}

    {128,148,127,138,117,150,144,106,153,159,94,146,113,131,84,107,105,118}

    {75,71,78,75,71,76,79,77,77,82,83,81,75,81,72,79,82,82}

    Returns: {0.4825439012291989, 0.4713740054019704, 0.46530340984369406, 0.4565617522397761, 0.43834996556494704, 0.4249946553367391, 0.4198953550677869, 0.3509333895257676, 0.32422276906935166, 0.3166952305770889, 0.3154811114654337, 0.3072251015061779, 0.29969756301391515, 0.29726932479060464, 0.2868279004303693, 0.28537095749638297, 0.2822142478060793, 0.28075730487209294 }

  97. {663,786,799,822}

    {206,226,191,147}

    {156,26,30,130}

    Returns: {0.3186528909226862, 0.18095537351215754, 0.16640197736307727, 0.14065366109931987 }

  98. {68,115,228,247,303,322,329,448,462,466,519,527,530,557,578,596,639,706,719,728,747,752,755,792,857,858}

    {147,119,131,268,86,100,127,138,235,109,214,97,274,32,76,74,255,80,85,139,218,244,40,161,158,48}

    {152,99,155,82,109,114,124,99,99,123,177,126,155,147,146,121,148,168,79,107,178,158,135,96,178,95}

    Returns: {0.34369985016028326, 0.3305633167100955, 0.2989797362873035, 0.29366922276488716, 0.27801718290934424, 0.2727066693869279, 0.270750164404985, 0.23748957971195633, 0.23357656974807062, 0.2324585669012461, 0.21764502918082157, 0.21540902348717256, 0.2145705213520542, 0.20702400213598887, 0.20115448719016027, 0.19612347437945005, 0.18410494377608674, 0.1653783960917765, 0.16174488683959687, 0.15922938043424176, 0.1539188669118254, 0.1525213633532948, 0.15168286121817642, 0.14134133488504985, 0.12317378862415182, 0.12289428791244567 }

  99. {68,134}

    {44,88}

    {121,117}

    Returns: {0.749998428272898, 0.37499916452394355 }

  100. {117,170,172,199,363,366,379,402,413,547}

    {421,422,350,389,413,386,384,406,411,384}

    {22,7,44,32,3,30,49,36,6,24}

    Returns: {0.0843356527702232, 0.09086189399783982, 0.09110816725171214, 0.09443285617898853, 0.1146272629965192, 0.11499667287732769, 0.1165974490274978, 0.11942959144702954, 0.12078409434332733, 0.13728440235277312 }

  101. {0,1000}

    {1,1}

    {1000,1000}

    Returns: {499.9999960000001, 499.9999960000001 }

  102. {7,133,571,664}

    {64,86,24,134}

    {856,855,855,844}

    Returns: {2.471852183662387, 2.3549084932375615, 1.948389950332217, 1.86207436930437 }

  103. {4,57,68,71,113,136,137,140,147,159,191,212,236,286,298,300,341,384,393,408}

    {92,117,112,111,116,94,92,109,121,100,97,103,102,97,94,106,110,97,110,103}

    {996,996,996,996,996,996,996,996,996,996,996,996,996,996,996,996,996,996,996,996}

    Returns: {0.1845272915802325, 0.1870424143370979, 0.18756442094701334, 0.18770678638608118, 0.18969990253303112, 0.19079137089921797, 0.19083882604557392, 0.19098119148464177, 0.19131337750913344, 0.19188283926540484, 0.19340140394879524, 0.19439796202227022, 0.19553688553481302, 0.19790964285261053, 0.19847910460888196, 0.19857401490159385, 0.20051967590218783, 0.2025602471954937, 0.20298734351269726, 0.2036991707080365 }

  104. {12,30,38,63,68,76,106,177,208,229,257,264,343,349,370,378,401,461,465,487,508,542,582,588,597,647,654,681,755,812}

    {30,11,32,32,37,9,6,37,14,18,21,12,25,31,14,14,18,30,26,34,6,8,17,27,28,27,8,5,33,21}

    {854,855,854,855,854,854,853,853,855,853,854,853,853,854,853,854,855,855,854,855,854,854,855,853,853,855,855,854,853,853}

    Returns: {0.8651019136954166, 0.8859088302186061, 0.8951563486733571, 0.9240548438444538, 0.9298345428786732, 0.9390820613334241, 0.9737602555387401, 1.0558319818246547, 1.0916661158368146, 1.1159408517805358, 1.148307166372164, 1.1563987450200712, 1.2477179897607367, 1.2546536286017997, 1.278928364545521, 1.288175883000272, 1.314762498557681, 1.384118886968313, 1.3887426461956884, 1.4141733219462536, 1.4384480578899748, 1.4777500113226663, 1.5239876035964208, 1.530923242437484, 1.541326700699079, 1.5991236910412723, 1.6072152696891795, 1.6384256444739638, 1.7239651901804098, 1.7898537591705104 }

  105. {222,347,485}

    {184,207,202}

    {999,999,999}

    Returns: {0.45254042076110146, 0.44406509684112805, 0.4347083392334774 }

  106. {75,235,320,439,483,504,516,718}

    {55,25,52,13,7,17,19,23}

    {781,783,781,781,781,782,783,782}

    Returns: {1.868191851261202, 2.594794654536094, 2.9808023937758805, 3.5212132287115816, 3.7210289996121766, 3.816395617542007, 3.8708908277876235, 4.788226866922175 }

  107. {21,69,94,138,157,159,161,193,197,204,295,309,318,346,368,370,380,396,446,487,494,532,558,675,712,729,746}

    {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7}

    {999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999}

    Returns: {2.9455237968446077, 3.073934784245427, 3.1408155068500205, 3.2585255786341047, 3.309354927813596, 3.3147053856219633, 3.320055843430331, 3.4056631683642102, 3.4163640839809455, 3.4350906863102315, 3.6785365165909516, 3.715989721249524, 3.7400667813871777, 3.814973190704322, 3.8738282265963644, 3.879178684404732, 3.9059309734465693, 3.948734635913509, 4.082496081122696, 4.192180466194229, 4.210907068523515, 4.312565766882497, 4.382121718391274, 4.695123500180771, 4.794106969635569, 4.839585861006693, 4.885064752377817 }

  108. {21,80,145,166,174,175,244,277,279,328,387,461,499,563,682,709,724,748,854}

    {62,295,469,292,346,502,218,415,459,97,104,40,342,465,419,339,113,121,256}

    {994,994,993,993,995,994,995,993,993,995,995,993,995,994,995,995,995,994,993}

    Returns: {0.09800593506381536, 0.10751259116280146, 0.11798602584812515, 0.12136975090030663, 0.1226587890154234, 0.12281991877981299, 0.13393787252269504, 0.13925515474755168, 0.13957741427633086, 0.14747277273142104, 0.15697942883040714, 0.16890303139523716, 0.17502596244204177, 0.18533826736297587, 0.20451270932533766, 0.20886321296385674, 0.21128015942970066, 0.21514727377505094, 0.232227028800348 }

  109. {46,56,77,102,119,158,166,188,238,365,392,474,648,810}

    {42,78,23,48,18,76,32,8,92,106,48,20,64,35}

    {959,958,960,957,960,955,956,956,957,959,956,960,956,957}

    Returns: {0.2667874406144617, 0.302830166748131, 0.3785198916288366, 0.46862670696300984, 0.5298993413902477, 0.670465973311558, 0.6993001542184936, 0.778594151712566, 0.9588077823809126, 1.4165504042785129, 1.51386576483942, 1.8094161191355083, 2.4365595538613545, 3.020451717226798 }

  110. {22,57,65,72,87,113,158,159,234,236,241,253,277,359}

    {157,333,6,275,5,95,28,269,164,179,269,180,259,21}

    {995,995,994,995,995,995,995,993,993,993,993,994,994,994}

    Returns: {0.08561907770429811, 0.10140405822190812, 0.10501205376879041, 0.10816904987231242, 0.11493404152271672, 0.12666002705008417, 0.14695500200129702, 0.14740600144465732, 0.1812309596966788, 0.18213295858339937, 0.1843879558002008, 0.18979994912052423, 0.2006239357611711, 0.23760589011671457 }

  111. {17,99,139,168,192,261,275,291,301,435,455,472}

    {182,48,141,138,166,133,97,179,46,137,136,71}

    {940,943,940,941,941,941,940,939,942,943,941,940}

    Returns: {0.3196787215113518, 0.31576726576607506, 0.3138592385732571, 0.3124759188584641, 0.31133110254277335, 0.3080397556351624, 0.30737194611767615, 0.306608735240549, 0.3061317284423445, 0.2997398373464044, 0.29878582374999546, 0.29797491219304784 }

  112. {124,271,320,343,439,460,619,641,706,721,752,840}

    {52,20,112,57,5,13,45,67,105,121,60,76}

    {990,993,990,992,992,991,991,990,993,993,991,993}

    Returns: {1.7615925932449037, 1.501943049028532, 1.415393200956408, 1.374767762065411, 1.20520071278125, 1.1681079207503398, 0.8872624953734479, 0.8484033799124944, 0.733592356959677, 0.7070975055090267, 0.6523414791776829, 0.4969050173338687 }

  113. {24,43}

    {13,50}

    {997,997}

    Returns: {0.7307691532689617, 0.18999997987178685 }

  114. {552,601,700,818,841}

    {145,161,62,156,266}

    {998,998,998,998,998}

    Returns: {0.47910943705842346, 0.44672987081113275, 0.3813099308421169, 0.3033346488588454, 0.28813607694685184 }

  115. {24,119,121,130,239,386,418,521,544,577}

    {26,81,149,33,156,99,144,167,141,55}

    {969,969,969,969,969,969,969,969,969,969}

    Returns: {0.7780539203042289, 0.7037548346906153, 0.7021906434145393, 0.6951517826721969, 0.6099033581260508, 0.4949352993344592, 0.469908238917242, 0.38935238819932405, 0.3713641885244492, 0.34555503246919395 }

  116. {55,82,123,232,339,352,355,421,660,768}

    {18,22,8,15,8,23,14,19,17,9}

    {990,989,992,989,992,992,989,992,992,992}

    Returns: {2.1952599804654316, 2.4451220913561236, 2.824542333819767, 3.833244929637746, 4.823439220945303, 4.943743200263043, 4.9715056570286755, 5.58227970587259, 7.794022094867975, 8.793470538430743 }

  117. {49,77,127}

    {59,87,85}

    {996,994,997}

    Returns: {0.3409531766574635, 0.33860536820707854, 0.33441285311710534 }

  118. {22,148,168,213,226,286,301,316,440,502,524,577,671,681}

    {155,128,87,180,36,168,304,154,61,201,86,116,148,256}

    {875,876,877,877,873,874,877,872,871,873,878,873,872,870}

    Returns: {0.38763199030194395, 0.3625312247928873, 0.35854697629938626, 0.34958241718900884, 0.3469926556682332, 0.33503991018773, 0.33205172381760417, 0.3290635374474784, 0.30436119678777185, 0.29201002645791857, 0.28762735311506743, 0.2770690946072896, 0.25834312668783466, 0.2563510024410841 }

  119. {11,100,166,258,404,520,621,717,755,764,836}

    {66,18,12,36,72,42,56,45,34,32,12}

    {987,988,985,986,988,985,987,987,988,988,986}

    Returns: {2.275612203999131, 2.2080552874408315, 2.157956899880744, 2.0881227838878953, 1.9772990780731565, 1.8892473666039122, 1.812581652307415, 1.7397112704018332, 1.710866744230874, 1.7040351459272256, 1.6493823594980395 }

  120. {124,322,389,392,402,429,540}

    {157,107,164,107,38,38,112}

    {958,958,958,958,959,959,959}

    Returns: {0.692004029166255, 0.5889908106290676, 0.5541328023361809, 0.5525719959947084, 0.5473693081897999, 0.5333220511165471, 0.47557221648206316 }

  121. {88,123,172,218,261}

    {48,98,43,68,96}

    {811,815,809,811,810}

    Returns: {0.5506887720574418, 0.5276429104065137, 0.49537870409521434, 0.46508985735399455, 0.4367763701828543 }

  122. {54,374,456}

    {22,271,358}

    {925,925,925}

    Returns: {6.222154501266294, 1.1598085239180378, -0.13741763277745278 }

  123. {12,16,21,24,26,36,39,41,42,43,51}

    {86,94,35,110,46,95,31,60,45,44,68}

    {994,994,994,994,994,994,994,994,994,994,994}

    Returns: {0.04533965123700079, 0.047398193831297605, 0.04997137207416862, 0.05151527901989124, 0.05254455031703965, 0.05769090680278169, 0.0592348137485043, 0.060264085045652706, 0.060778720694226906, 0.061293356342801114, 0.06541044153139475 }

  124. {0,4,6,7,9,11,12,16,19,22,25}

    {266,272,131,185,253,229,246,274,129,158,224}

    {998,998,998,998,998,998,998,998,998,998,998}

    Returns: {0.00803771114177191, 0.008928530685987944, 0.009373940458095961, 0.00959664534414997, 0.010042055116257987, 0.010487464888366004, 0.010710169774420013, 0.011600989318636047, 0.012269103976798073, 0.012937218634960099, 0.013605333293122124 }

  125. {124,131}

    {102,101}

    {884,885}

    Returns: {0.034313712943510516, 0.03465345270423452 }

  126. {7,8,19,43,44,73,85,94,99,102,110,111,117,148,153,193,237,242}

    {207,200,184,212,211,183,195,208,209,207,200,210,189,191,181,186,198,187}

    {943,949,950,951,951,946,943,947,945,951,943,946,943,943,947,945,948,945}

    Returns: {0.036718336237267155, 0.03702276615269599, 0.040371495222413234, 0.04767781319270539, 0.04798224310813423, 0.056810710655570584, 0.06046386964071667, 0.06320373887957623, 0.06472588845672042, 0.06563917820300694, 0.06807461752643768, 0.06837904744186651, 0.07020562693443955, 0.07964295431273358, 0.08116510388987778, 0.09334230050703138, 0.10673721678590033, 0.10825936636304453 }

  127. {12,146,155,188,386,502,514}

    {18,15,16,19,13,9,8}

    {999,999,999,999,999,999,999}

    Returns: {3.6418867002894855, 4.570828071602837, 4.633219656243286, 4.861988799924932, 6.23460366201481, 7.038761864047263, 7.121950643567862 }

  128. {31,63,92,116,125,210,226,227,242,305,356,361,392,405,436}

    {43,41,46,46,46,34,36,36,42,49,43,44,34,43,42}

    {981,981,981,981,981,981,981,981,981,981,981,981,981,981,981}

    Returns: {0.6746268751401581, 0.6704878607985387, 0.6667368790514461, 0.6636326182952316, 0.6624685205116512, 0.6514742636667247, 0.649404756495915, 0.6492754122977393, 0.6473352493251053, 0.6391865648400421, 0.6325900107330863, 0.6319432897422083, 0.6279336195987645, 0.6262521450224816, 0.6222424748790378 }

  129. {4,58,72,82,105,108,125,161,203,318,320,372,389,433,461,529,543,560,569,573,578,805}

    {336,175,363,313,321,266,284,200,33,293,236,138,138,181,333,57,295,69,72,149,393,35}

    {996,988,984,984,988,984,992,993,996,992,993,987,997,998,988,990,988,995,991,990,987,993}

    Returns: {0.03512763574260268, 0.06161885506542818, 0.0684869489639385, 0.0733927303200173, 0.08467602743899852, 0.08614776184582217, 0.09448759015115613, 0.11214840303303979, 0.13275268472857074, 0.1891691703234769, 0.19015032659469266, 0.2156603896463024, 0.22400021795163638, 0.24558565591838305, 0.25932184371540373, 0.2926811569367395, 0.29954925083524986, 0.3078890791405838, 0.31230428236105473, 0.31426659490348624, 0.31671948558152563, 0.42808072236451433 }

  130. {78,102,378,380,383}

    {47,33,63,50,56}

    {997,997,997,997,997}

    Returns: {1.9872255971455668, 1.8994005607177806, 0.8894126417982402, 0.8820938887625913, 0.8711157592091181 }

  131. {80,87,266,297,330,349,369}

    {122,119,121,124,122,118,118}

    {994,994,994,994,994,994,994}

    Returns: {0.48076486318253164, 0.4751890852609001, 0.33260847840774993, 0.30791574761195295, 0.28162993740997555, 0.2664956830512613, 0.25056488898945684 }

  132. {12,15,19,36,54,56,57,82,153,156,161,172,177,192,200,217,253,272,313,342,393,459,491,494,533,555,568,569,580}

    {147,160,202,73,152,236,123,36,161,93,65,78,47,198,180,155,86,61,28,17,89,94,181,49,102,176,236,34,42}

    {944,945,943,943,945,944,942,943,944,945,945,942,944,942,946,943,946,942,944,945,944,945,943,946,944,942,946,943,946}

    Returns: {0.11784576629214244, 0.11855668315408072, 0.11950457230333174, 0.1235331011876486, 0.12779860235927823, 0.12827254693390375, 0.1285095192212165, 0.13443382640403542, 0.15125885880324116, 0.15196977566517944, 0.1531546371017432, 0.15576133226218353, 0.15694619369874732, 0.16050077800843868, 0.16239655630694072, 0.1664250851912576, 0.17495608753451683, 0.1794585609934592, 0.18917442477328222, 0.1960466211053522, 0.20813220775830277, 0.22377237872094474, 0.23135549191495297, 0.23206640877689122, 0.24130832798208873, 0.2465217183029694, 0.24960235803803524, 0.249839330325348, 0.2524460254857883 }

  133. {46,57,68,74,89,100,119,122,132}

    {22,20,22,19,22,18,19,19,22}

    {980,982,980,982,981,980,980,982,981}

    Returns: {0.4709841029130729, 0.47071863355186555, 0.47045316419065825, 0.47030836272090876, 0.46994635904653514, 0.4696808896853278, 0.46922235169778787, 0.4691499509629131, 0.4689086151799974 }

  134. {71,114,123,439,469,490,515,557,586,611,647,661,689}

    {124,88,264,395,180,408,154,114,321,472,70,135,354}

    {974,974,974,974,974,974,974,974,974,974,974,974,974}

    Returns: {0.48059609178507645, 0.4518303505161257, 0.44580961397146157, 0.2344148641810326, 0.21434574236548554, 0.2002973570946026, 0.1835730889149801, 0.15547631837321418, 0.13607616728485206, 0.11935189910522948, 0.09526895292657306, 0.08590336274598442, 0.06717218238480716 }

  135. {252,262,431,691}

    {11,9,13,6}

    {985,985,985,985}

    Returns: {5.692708907476689, 6.1222958177494045, 13.382314601358292, 24.55157426844889 }

  136. {0,79,88,101,155,198,252,324,326,499}

    {18,19,12,19,19,18,19,17,17,15}

    {994,994,994,994,994,994,994,994,994,994}

    Returns: {1.347854993302842, 1.9599531920393334, 2.0296858982245034, 2.1304109182697486, 2.548807155380768, 2.8819745293765795, 3.3003707664875988, 3.858232415968958, 3.8737285728989956, 5.214146147347261 }

  137. {338,343}

    {111,184}

    {991,991}

    Returns: {0.022522513348718624, 0.013586950987642003 }

  138. {2,132,160,200,344,389,429,510,782}

    {49,49,49,49,49,49,49,49,49}

    {998,998,998,998,998,998,998,998,998}

    Returns: {1.014338725478054, 1.3155712927934637, 1.3804521534460135, 1.4731390972353702, 1.8068120948770547, 1.9110849066400812, 2.003771850429438, 2.191462911602885, 2.821734129370512 }

  139. {44,161,165,219}

    {223,103,189,59}

    {996,996,996,995}

    Returns: {0.2553751896021479, 0.3288531992030192, 0.3313652679073225, 0.36527819541541695 }

  140. {67,87,297}

    {3,2,2}

    {997,997,997}

    Returns: {22.758967744440056, 25.58645664636115, 55.27509011653265 }

  141. {96,140,202,434,478,525}

    {329,207,5,71,254,335}

    {913,912,912,911,914,911}

    Returns: {0.38787520664512376, 0.3819677657057831, 0.37364364438216674, 0.34249531942927963, 0.336587878489939, 0.33027765748655236 }

  142. {31,43,45,68,72,88,136,158,169,206}

    {244,199,233,70,149,181,149,156,284,248}

    {869,868,869,869,868,869,868,869,869,868}

    Returns: {0.06910059829172416, 0.07270026550630607, 0.07330021004206971, 0.08019957220335171, 0.08139946127487901, 0.08619901756098822, 0.10059768641931585, 0.10719707631271602, 0.11049677125941611, 0.12159574517104366 }

  143. {100,152,212,250,348}

    {72,15,46,127,21}

    {998,998,998,998,998}

    Returns: {0.5928322316685066, 0.7330619491029977, 0.8948654692197182, 0.9973410319603078, 1.2616201148176178 }

  144. {10,33,43,48,101,120,121,158,181,188,189}

    {82,46,69,84,125,132,152,37,76,83,49}

    {999,999,999,999,999,999,999,999,999,999,999}

    Returns: {0.23834247253527557, 0.22729719731679282, 0.22249490374353945, 0.22009375695691274, 0.19464160101866987, 0.18551724322948845, 0.18503701387216312, 0.16726852765112563, 0.15622325243264287, 0.1528616469313655, 0.15238141757404017 }

  145. {193,264,270,395,492,509,521,613,684,689}

    {239,369,374,284,178,189,153,268,259,181}

    {999,999,999,999,999,999,999,999,999,999}

    Returns: {0.19011487770673963, 0.19267950156335104, 0.19289623033996608, 0.19741141318611294, 0.2009151950747229, 0.20152925994179888, 0.20196271749502898, 0.20528589206979306, 0.2078505159264045, 0.20803112324025036 }

  146. {90,93}

    {21,19}

    {982,982}

    Returns: {0.07142852204063152, 0.0789473138335462 }

  147. {48,199,204}

    {48,48,40}

    {999,999,999}

    Returns: {1.595749966552003, 0.9126003692766048, 0.8899795216847042 }

  148. {5,20,33,42,54,57,67,86,140,150,182,213,220,225,271,275,299,322,332,388,394,422}

    {27,52,41,52,29,15,56,51,47,5,30,47,20,7,39,23,35,43,10,38,9,55}

    {989,989,989,988,989,989,989,988,988,988,989,989,989,989,988,988,988,989,988,988,989,988}

    Returns: {0.37995685934064405, 0.396479737586749, 0.4107995654000399, 0.4207132923477029, 0.43393159494458683, 0.4372361705938078, 0.44825142275787777, 0.46918040186961074, 0.5286627635555885, 0.5396780157196585, 0.5749268226446823, 0.6090741043532992, 0.6167847808681481, 0.6222924069501832, 0.672962566904905, 0.677368667770533, 0.703805272964301, 0.7291403529416618, 0.7401556051057316, 0.8018410172245235, 0.8084501685229655, 0.8392928745823613 }

  149. {13,18,70,96,103,109,124,143,153}

    {50,39,7,2,29,30,23,46,6}

    {971,971,971,971,971,971,972,971,973}

    Returns: {0.5663143554353434, 0.5690715275495112, 0.597746117536856, 0.6120834125305284, 0.6159434534903634, 0.6192520600273647, 0.627523576369868, 0.6380008304037056, 0.6435151746320411 }

  150. {1,12,21,41,42,44}

    {4,34,49,29,25,29}

    {999,999,999,999,999,999}

    Returns: {0.5125764584846297, 0.41113098344601784, 0.3281301402326082, 0.14368382198058666, 0.13446150606798557, 0.11601687424278345 }

  151. {28,60,93,108,114,130,146,156,169,175,186,188,215,241,263,265,266}

    {34,35,34,36,36,34,35,37,34,38,38,37,37,36,37,34,38}

    {999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999}

    Returns: {0.6091355698546985, 0.5584486465423735, 0.5061777568765382, 0.4824182615738859, 0.47291446345282495, 0.4475710017966624, 0.4222275401404999, 0.4063878766053983, 0.3857963140097662, 0.37629251588870527, 0.35886888600009353, 0.3557009532930732, 0.31293386174829896, 0.27175073655703486, 0.23690347677981138, 0.23373554407279107, 0.2321515777192809 }

  152. {0,1}

    {1000,1000}

    {1,1}

    Returns: {-4.990027410324371E-4, -4.990027410324371E-4 }

  153. {0,1}

    {1,1}

    {1,1}

    Returns: {-0.197429336933033, -0.19742933693303283 }

  154. {0,2}

    {1,1}

    {1,1}

    Returns: {5.551115123125783E-17, 5.551115123125783E-17 }

  155. {0,2}

    {1000,1000}

    {1,1}

    Returns: {3.3306690738754697E-19, -1.6653345369377353E-19 }

  156. {0, 23, 45, 56, 78, 123, 233, 331, 365, 389, 390, 401, 412, 560, 580, 600, 623, 684, 730, 890, 923 }

    {56, 78, 123, 233, 331, 365, 56, 78, 123, 233, 331, 365, 56, 78, 123, 233, 331, 365, 23, 322, 55 }

    {1, 10, 10, 10, 1, 10, 10, 10, 1, 10, 10, 10, 1, 10, 10, 10, 1, 10, 10, 10, 8 }

    Returns: {0.16297411171567316, 0.16678194626008996, 0.1704242227808365, 0.17224536104120974, 0.17588763756195627, 0.18333774862711957, 0.20154913123085216, 0.21777381755054118, 0.22340279035533123, 0.22737618292341835, 0.22754174094708865, 0.2293628792074619, 0.23118401746783518, 0.255686604971039, 0.2589977654444449, 0.2623089259178508, 0.2661167604622676, 0.2762157999061557, 0.28383146899498934, 0.3103207527822367, 0.3157841675633565 }

  157. {100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345 }

    {190, 107, 575, 237, 339, 221, 307, 897, 577, 500, 145, 719, 465, 472, 790, 804, 133, 119, 528, 461, 782, 604, 411, 773, 218, 249, 510, 666, 454, 630, 184, 246, 644, 337, 872, 644, 269, 35, 219, 579, 884, 659, 853, 140, 757, 495, 392, 554, 868, 245 }

    {880, 798, 743, 544, 644, 485, 595, 701, 28, 100, 610, 541, 452, 847, 325, 798, 84, 137, 500, 156, 545, 108, 799, 848, 476, 133, 650, 281, 25, 623, 756, 856, 697, 218, 649, 286, 403, 110, 592, 396, 59, 468, 16, 129, 869, 353, 217, 16, 715, 859 }

    Returns: {0.012100828685847085, 0.012031539488391954, 0.011962250290936822, 0.011892961093481692, 0.011823671896026561, 0.011754382698571429, 0.011685093501116298, 0.011615804303661168, 0.011546515106206037, 0.011477225908750905, 0.011407936711295774, 0.011338647513840644, 0.011269358316385512, 0.011200069118930381, 0.01113077992147525, 0.011061490724020118, 0.010992201526564988, 0.010922912329109857, 0.010853623131654725, 0.010784333934199595, 0.010715044736744464, 0.010645755539289332, 0.010576466341834201, 0.01050717714437907, 0.01043788794692394, 0.010368598749468808, 0.010299309552013677, 0.010230020354558547, 0.010160731157103416, 0.010091441959648284, 0.010022152762193154, 0.009952863564738023, 0.00988357436728289, 0.00981428516982776, 0.00974499597237263, 0.009675706774917497, 0.009606417577462367, 0.009537128380007236, 0.009467839182552104, 0.009398549985096974, 0.009329260787641843, 0.00925997159018671, 0.00919068239273158, 0.00912139319527645, 0.009052103997821317, 0.008982814800366187, 0.008913525602911056, 0.008844236405455924, 0.008774947208000794, 0.008705658010545663 }

  158. {0, 11, 39, 45, 85, 113, 120, 123, 145, 161, 165, 180, 189, 194, 198, 225, 235, 241, 249, 306, 313, 340, 372, 379, 423, 426, 448, 482, 500, 594, 611, 636, 661, 667, 679, 711, 716, 718, 743, 793, 847, 848, 891, 894, 911, 944, 956, 961, 975, 1000 }

    {291, 419, 185, 569, 747, 81, 650, 427, 799, 866, 414, 70, 827, 57, 10, 14, 767, 295, 56, 594, 567, 162, 977, 384, 152, 997, 778, 88, 687, 899, 904, 232, 97, 611, 264, 49, 862, 546, 476, 459, 291, 681, 671, 709, 333, 648, 4, 377, 963, 963 }

    {14, 810, 679, 220, 314, 372, 550, 807, 326, 642, 567, 600, 446, 573, 669, 943, 70, 167, 488, 823, 649, 336, 354, 767, 373, 807, 438, 259, 312, 379, 684, 902, 130, 679, 956, 834, 363, 314, 817, 270, 568, 850, 663, 407, 807, 875, 757, 661, 377, 16 }

    Returns: {0.042272172827361565, 0.04226009112266384, 0.04222933769252417, 0.042222747671779956, 0.042178814200151855, 0.04214806077001219, 0.04214037241247727, 0.04213707740210516, 0.04211291399270971, 0.042095340604058465, 0.042090947256895654, 0.042074472205035116, 0.0420645871739188, 0.04205909548996528, 0.04205470214280247, 0.04202504704945351, 0.04201406368154648, 0.042007473660802264, 0.04199868696647665, 0.04193608176940661, 0.04192839341187169, 0.04189873831852272, 0.04186359154122024, 0.041855903183685324, 0.04180757636489441, 0.041804281354522306, 0.04178011794512685, 0.04174277449424297, 0.041723004432010324, 0.04161976077368429, 0.04160108904824235, 0.041573630628474786, 0.041546172208707224, 0.04153958218796301, 0.04152640214647458, 0.0414912553691721, 0.041485763685218585, 0.04148356701163718, 0.04145610859186962, 0.0414011917523345, 0.04134188156563656, 0.04134078322884586, 0.04129355474684565, 0.041290259736473545, 0.041271588011031604, 0.04123534289693842, 0.041222162855449995, 0.04121667117149648, 0.041201294456426646, 0.041173836036659084 }

  159. {0, 1, 3, 1000 }

    {1000, 1000, 1000, 1 }

    {1, 2, 3, 1000 }

    Returns: {-0.4959899670014234, 0.0015139420138527981, 0.9965217600444052, 497.00791904827474 }

  160. {16, 33, 320, 566, 649, 916, 973 }

    {347, 28, 445, 184, 264, 507, 418 }

    {637, 933, 361, 762, 269, 775, 535 }

    Returns: {0.6312201516923563, 0.6254572561054437, 0.5281660188440365, 0.44477352976283036, 0.4166370395443746, 0.32612567944404103, 0.30680302953498106 }

  161. {0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 560, 580, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 860, 880, 900, 920, 940, 960, 980 }

    {577, 137, 121, 947, 716, 47, 917, 925, 1, 733, 409, 715, 883, 737, 262, 610, 473, 873, 201, 251, 272, 842, 385, 764, 826, 273, 121, 529, 217, 446, 183, 380, 64, 261, 711, 365, 929, 516, 161, 751, 946, 333, 45, 297, 194, 47, 176, 396, 891, 33 }

    {257, 984, 707, 407, 281, 793, 761, 211, 481, 31, 114, 405, 137, 824, 167, 75, 445, 47, 343, 825, 169, 911, 43, 170, 655, 259, 61, 564, 851, 857, 816, 69, 825, 997, 989, 369, 151, 932, 905, 401, 772, 17, 199, 101, 701, 650, 461, 945, 841, 901 }

    Returns: {0.032625058760607575, 0.03307916549415742, 0.03353327222770725, 0.03398737896125709, 0.034441485694806935, 0.03489559242835678, 0.03534969916190661, 0.03580380589545645, 0.036257912629006295, 0.036712019362556136, 0.03716612609610597, 0.03762023282965581, 0.038074339563205654, 0.03852844629675549, 0.03898255303030533, 0.03943665976385517, 0.03989076649740501, 0.04034487323095485, 0.04079897996450469, 0.041253086698054525, 0.04170719343160437, 0.04216130016515421, 0.04261540689870405, 0.04306951363225389, 0.04352362036580373, 0.04397772709935357, 0.0444318338329034, 0.044885940566453245, 0.045340047300003086, 0.04579415403355293, 0.04624826076710277, 0.046702367500652604, 0.047156474234202446, 0.04761058096775229, 0.04806468770130212, 0.048518794434851964, 0.048972901168401806, 0.04942700790195165, 0.04988111463550148, 0.050335221369051324, 0.05078932810260116, 0.051243434836151, 0.05169754156970084, 0.05215164830325068, 0.05260575503680052, 0.05305986177035037, 0.0535139685039002, 0.053968075237450036, 0.05442218197099988, 0.05487628870454972 }

  162. {1, 3, 100, 1000 }

    {2, 4, 5, 7 }

    {1000, 1, 2, 3 }

    Returns: {0.9507370559832464, 0.9547480314948115, 1.149280343805716, 2.9542193240099843 }

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