Statistics

Problem Statement for "MagicBlizzard"

Problem Statement

Today is the Christmas Eve. People around the world celebrate this holiday. The following story takes place in the land of reindeer, where Santa Claus resides.


For Christmas, the land should be covered by snow, but there was no snowfall yet. Luckily, the reindeer know a spell called Magic Blizzard that can make it snow.


The land can be imagined as an infinite grid of unit squares with integer coordinates. When a reindeer casts Magic Blizzard, the effect depends on two parameters: the range of the spell R and the amount A. The spell will generate A snowballs. Each snowball will fall on some square with coordinates (x,y) such that -R <= x, y <= R. For each snowball, the target square is chosen uniformly at random. Targets for snowballs are chosen independently of each other. (Hence it is possible that multiple snowballs will hit the same square.)


N reindeer are going to cast Magic Blizzard, one after another. You are given two int[]s range and amount of length N. The spell by reindeer i will have range equal to range[i] and the amount of snowballs it produces will be amount[i].


The beauty of the landscape can be computed as the total beauty of all squares. The beauty of a square that was hit by x snowballs is x^2.


Your method must compute and return the expected value of the beauty of the landscape.

Definition

Class:
MagicBlizzard
Method:
expectation
Parameters:
int[], int[]
Returns:
double
Method signature:
double expectation(int[] range, int[] amount)
(be sure your method is public)

Notes

  • The returned value must be accurate to within a relative or absolute error of 1e-9.

Constraints

  • range will contain between 1 and 50 elements, inclusive.
  • amount will contain between 1 and 50 elements, inclusive.
  • range and amount will contain the same number of elements.
  • Each element in range will be between 0 and 10,000, inclusive.
  • Each element in amount will be between 1 and 10,000, inclusive.

Examples

  1. {1,0}

    {1,1}

    Returns: 2.2222222222222223

    The second snowball will surely fall on the square (0,0). The first snowball will fall on the same square with probability 1/9. If that happens, the beauty of the landscape will be 2^2 = 4. Otherwise, we will have two squares containing one snowball each, for a total beauty of 1^2 + 1^2 = 2. So the expected beauty is (1/9) * 4 + (8/9) * 2 = 20/9.

  2. {1,0}

    {2,1}

    Returns: 3.666666666666667

  3. {5,2,6,5}

    {1,2,2,3}

    Returns: 8.46525111252384

  4. {7,11,2,13,3,19,5,17}

    {16,8,4,15,12,9,10,6}

    Returns: 98.55659436211914

  5. {0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.0E10

    Note that the answer can be very large.

  6. {89,46,30,55,97,87,31,99,37,69,84,0,15,96,28,42,37,91,5,71,16,74,97,13,4,40,57,69,1,5,86,38,21,27,98,63,22}

    {20,67,63,46,31,78,58,33,47,70,18,86,16,14,48,100,60,91,52,34,83,20,70,51,61,45,30,97,43,92,69,71,31,96,58,5,5}

    Returns: 11612.580357888419

  7. {53,2,90,17,84,5,20,73,27,64,82,56}

    {69,12,86,31,86,32,36,87,11,21,53,38}

    Returns: 602.4470436954125

  8. {29,25,45,46,35,29,16,94,85,55,98,24,48,69,54,95,85,51,48,27,23,0,52,95,86,64,19,95,41,72,66,74,67,16,91,36,84}

    {28,77,9,93,31,92,80,15,33,20,93,41,54,84,73,78,22,37,35,26,56,61,35,92,13,19,7,42,56,78,5,62,96,93,8,36,31}

    Returns: 5776.178151797337

  9. {83,44,53,38,98,25,74,80,36,49,82,34,2,31,62}

    {96,24,91,87,69,42,42,4,11,35,43,32,26,9,45}

    Returns: 709.6811808592843

  10. {51,56,77,100,23,50,38,86,78,9,90,33,99,86,82,72,12,6,10,37,91,47,50,91,94,35,46,83,5,92,95,60,17,100,27,27,92,80}

    {92,78,67,76,96,83,68,85,72,14,92,85,51,19,50,96,90,82,93,15,50,21,16,33,98,94,58,89,9,95,67,52,10,63,78,38,16,98}

    Returns: 2922.6311519132673

  11. {11,91,94,99,53,16,24,13,79,87,100,82,95,97,30,19,70,84,3,65,99,36,36,56,45,86,39,86,28,93,7,67,80,53,16,39,99,65,94,88}

    {68,94,30,39,33,47,15,18,28,74,75,79,47,65,19,62,34,60,10,35,47,4,86,58,58,1,7,63,41,35,93,99,10,40,13,74,64,40,63,34}

    Returns: 2162.479942874084

  12. {86,37,55,93,14,30,78,54,37,59,75,81,94,9,46,78,31,38,34}

    {42,11,59,38,52,75,11,82,27,22,87,24,27,76,6,48,79,59,33}

    Returns: 947.2434484427968

  13. {36,50,34,11,25,35}

    {46,40,84,43,8,65}

    Returns: 303.1941326538094

  14. {73,11,47,65,11,57,37,1,58,52,63,6,37,100,73,58,15,97,41,87,2,80,60,43}

    {95,66,50,72,49,35,85,18,6,11,76,91,39,45,68,84,47,20,71,44,57,90,14,48}

    Returns: 1882.3782978965476

  15. {7,4,49,44,67,41,24,33,0,96,50,90,100,49,35,39,94,77,60,79,28,53,50,40,43,67}

    {78,9,48,27,14,98,61,90,19,48,67,8,55,59,91,1,41,51,65,54,16,83,7,82,42,40}

    Returns: 1781.095000952899

  16. {43,95,8,36,15,5,46,77,73,26,81,80,87,19,42,15,30,49,95,49,10,27,44,43,75,66,9,56,98,2,46,23,87,8,61,86,94,12,23}

    {993,725,692,520,656,655,784,686,428,59,896,524,800,613,880,384,3,616,834,50,828,271,988,881,455,882,339,981,420,454,736,454,30,456,906,539,569,915,444}

    Returns: 134396.5709724625

  17. {68,24,56,74,64,48,95,42,12,28,78,87,83,89,13,87,39,96,79,13,40}

    {631,610,997,275,496,471,824,493,561,841,732,319,580,859,603,487,210,605,512,920,387}

    Returns: 28128.430152405588

  18. {88,22,3,74,38,24,50,14,52,85,49,41,65,38,11,20,28,98,28,100,89,77,26,76,8,98,32,90,93,9,44,91,8,52}

    {634,455,668,581,874,437,966,659,340,424,122,568,426,968,952,553,316,483,630,293,698,484,403,901,873,836,460,136,532,656,890,677,549,420}

    Returns: 105057.61993403498

  19. {49,15,73,100,18,91,48,45,59,89,97,29}

    {82,634,329,306,452,981,522,445,410,580,307,284}

    Returns: 7731.318039733446

  20. {16,16,23,4,47,61,2,71,87,12,7,20,21,80,56,40,78,76,90,54,66,81,34,79,59,56,94,81,35}

    {220,981,539,924,318,471,437,504,577,643,528,411,590,879,735,623,185,84,618,222,703,800,402,317,613,151,971,617,50}

    Returns: 80240.40342388401

  21. {95,1,11,70,51,93,3,15,60,93,53,81,22,8,14,35,98,51,13,98,32,66,17,15,63,44,58,38,65,14,86,63,92}

    {799,94,602,633,49,891,915,147,44,264,975,729,568,620,901,785,322,31,188,904,391,760,637,696,130,178,759,69,60,544,997,866,875}

    Returns: 90963.85949788928

  22. {43,52,53,64,19,29,48,14,4,2,39,57,97,61,20,45,88,90,54,63,64,41,19,11}

    {895,883,284,653,515,42,757,873,75,539,13,828,696,89,259,289,55,478,547,184,483,659,647,14}

    Returns: 37661.8834471185

  23. {80,28,65,18,100,16,12,99,62,92,88,2,3,76,81,64,96,44,89,31,77,43,7,36,68,9,92,69}

    {347,438,127,202,557,23,581,220,132,761,313,274,438,356,98,740,53,101,356,464,528,303,666,206,695,84,74,612}

    Returns: 37482.32386064459

  24. {9,6,87,37,26,82,83,83,60,43,82,100,3,30,33,11,75,47,64,23,23,81,23,79,47,91,30,56,40,70,16,41,86,61,5,25,18,61,19,26,88,49,42,55,30,33,72,85,43,51}

    {957,671,104,498,450,952,24,558,379,547,840,893,60,673,804,95,25,412,495,432,709,123,280,836,885,951,199,842,780,927,697,224,352,346,320,168,404,260,294,721,399,914,819,833,909,801,805,106,837,243}

    Returns: 113602.04005642213

  25. {77,19,17,71,73,13,19,9,54,24,86,70,38,57,98,86,26,7,84,5,31,96,50,59,90,99,23,53,65,37,60,67,93,41,67,35}

    {882,643,587,461,660,902,511,916,371,345,971,526,723,76,985,552,361,321,762,334,838,480,245,586,904,796,298,805,281,366,135,436,588,625,364,92}

    Returns: 64512.13300445606

  26. {784,921}

    {341,665}

    Returns: 1006.3106178555539

  27. {441,529,587,846,442,611,932,64,167,8,982,42,932,752,875,79,423,26,160,956,373,352,489,695,164,220,513,211,183,893,331,958,286,993,673,899,71}

    {772,729,511,502,390,822,35,33,484,798,315,244,224,582,879,321,641,400,402,36,840,535,154,920,862,549,725,595,52,90,327,581,171,70,817,301,566}

    Returns: 20368.95071552742

  28. {163,777,53,722,653,946,165,928,524,24,669,249,244,619,583,206,859,819,188,458,594,454}

    {318,846,844,811,61,961,7,681,926,451,869,464,465,394,792,194,150,999,700,359,503,721}

    Returns: 12859.861595423969

  29. {149,57,785,106,211,766,289,28,431,870,903,851,500,496,574,853,964,732,213,637,589,376,949,772,644,323,333,950,373,738,585,465,260,52,396,237,654,971,461,649,951,529}

    {566,483,676,675,172,262,889,534,599,706,831,211,609,603,565,629,992,315,295,122,717,477,549,548,236,278,79,116,638,685,711,810,236,644,879,311,908,231,318,526,825,397}

    Returns: 22559.747675623104

  30. {826,969,663}

    {734,384,755}

    Returns: 1874.2690860792761

  31. {1000,873,874,157,682,703,394,621,866,703,215,502,968,641,644,681,706,249,480,408,356,113,539,419,332,787,505,469,961,670,70,361,335,926,663,74,387,217,96,350,839,725,357,156,507,741,488,875,869}

    {679,353,979,542,991,316,237,114,424,834,249,13,331,86,81,616,228,408,764,803,730,426,678,32,709,241,636,299,763,542,639,850,316,661,807,810,199,757,545,490,396,609,252,484,59,199,904,177,77}

    Returns: 23988.076666055196

  32. {730,639,755}

    {38,178,274}

    Returns: 490.11086410341585

  33. {942,438,863,755,106,989,642,516}

    {88,86,763,856,342,335,617,989}

    Returns: 4086.0257036783037

  34. {3,704,306,205,840,986,320,791,67,166,142,10,867,507,652,633,626,307,87,260,402,610,454,266,764,198,673,697,878,421,528,203,103,184,277,826,61,521,718,539,134}

    {276,141,570,456,990,128,936,306,365,532,588,237,148,684,899,895,414,449,616,483,681,518,68,621,404,106,123,125,374,603,604,59,17,185,433,178,944,456,681,511,140}

    Returns: 20613.086610812636

  35. {39,930,930,722,837,889,756,817,122,714,917,900,813,369,649,340,172,432,798,517,731}

    {701,392,736,549,32,979,314,511,142,975,56,22,962,226,81,257,366,382,18,1000,394}

    Returns: 9219.968105692831

  36. {7015,6842,4290,5154,5224,3146,9594,1097,7029,860,8813,3205,5727,1651,4843}

    {971,216,270,571,787,472,971,322,56,431,77,751,716,711,432}

    Returns: 7754.73797325447

  37. {3467,6804,1581,4613,3558,8165,7609,338,2123,3112,1487,788,9568,1364,216,324,979,4010,3168,1442,26,6783,7839,6061,7926,6373,2040,1995,8970,7763,3849,3796,3381,1656,7268,506,676,4226,3220,1647,8381,7196}

    {256,803,338,952,390,278,896,288,73,875,265,536,617,249,808,911,442,88,933,268,389,127,658,707,289,295,437,590,337,640,184,192,919,299,429,454,289,119,582,159,300,560}

    Returns: 19302.719184330752

  38. {4604,3013,1555,2076,7780,2582,7688,5540,970,2675,3377,2916,7808,6426,1806,1581,8599,2624,5555,6746,2494,6934,868,9115,942,7516,7633,8880,2989,4097,1408,1124,3815,1124,5034,9393,2579,6003,8919,163,7571,8354,9219,4985,5380,9163,270,7048,8254,8773}

    {944,332,308,153,398,792,440,528,206,137,481,179,788,317,101,527,30,848,866,166,354,989,636,911,685,727,95,144,950,591,186,74,483,695,837,116,442,735,828,74,746,429,812,415,267,570,790,161,715,563}

    Returns: 24571.540217453028

  39. {923,1002,6851,9140,840,5401,3668,3412,4696,4262,5076,1197,6058,7612,4561,92,527,3241,1574,5170,691,7837,339,2189,4836,2637,2932,8627}

    {992,404,636,822,136,172,180,935,259,835,683,59,858,611,271,740,121,445,404,574,94,558,536,642,238,63,428,88}

    Returns: 12806.654357696745

  40. {9914,5876,9002,9289,4932,9434,9020,744,9770,2515,1574,745,6511,4306,3003,8815,2070,5047,5363,6179,1852,6180,4563,4834,9827,1015,7347,2630}

    {431,743,56,89,549,924,705,874,749,764,759,464,238,59,429,40,565,115,557,928,248,878,336,482,612,605,614,549}

    Returns: 14365.394673122497

  41. {2476,2038,7579,8182,1612,838,5687,4977,3247,5164,403,8654,7991,5477,9626,7212,4593,860,113,1948,4881,5735,4006,2413,9105,6019,5037,8025}

    {645,821,182,243,266,581,866,234,803,517,959,562,146,223,790,523,167,407,269,33,25,292,262,995,662,365,797,540}

    Returns: 13181.781818747048

  42. {6197,3713,1766,5479,9778,1078,4341,604,6763,3280,1787,7874}

    {641,872,933,498,360,546,291,595,269,579,2,375}

    Returns: 5961.9905953312855

  43. {9076,5787,1463,4044,7432,2094,5779,4816,9384,338,6557,7872,7052,4012,3319,7798,1234,655,6833}

    {104,27,111,608,695,971,262,861,342,983,883,790,86,710,93,348,644,286,482}

    Returns: 9289.67152643784

  44. {2701,7766,3078,9293,8509,5599,241,2877,5998,143,5476,8716}

    {744,26,863,60,757,904,571,750,394,528,653,532}

    Returns: 6789.862969039239

  45. {4146,190,7566,2277,7110,7065,9980,5318,2356,2152,2609,353,7855,3993,7335,9852,5503,721,5531,4495,4554,1939,7162,4479,9495,9185,1550,8521,723,6499,214,9216,9390,5977,1115,7630,2602,3445,4860,8305,2729,5328,6928,5862}

    {177,688,637,255,587,700,26,20,74,776,748,677,982,144,822,542,250,72,584,657,753,938,259,871,911,661,471,943,474,443,643,749,314,185,77,205,279,308,211,992,891,18,825,94}

    Returns: 21953.409837586765

  46. {4177}

    {6741}

    Returns: 6741.650865595054

  47. {308,5649,4615,161,8884,4936,9234,9297,7355,1130,6388,8955,53,2282,9639,7197,5282,7922,291,1945,8847,4,91,6373,8565,1567,672,7618,2869,4803,4,46,3404,7585,2444,1331,3001,2764,52,6632,246,84,9674}

    {5069,9025,2906,3663,4853,7635,1944,5515,6606,1038,1828,7074,5257,9488,6723,7269,1936,7756,1005,2844,9066,9933,864,6220,7086,587,5784,9171,1291,1116,3166,3670,8103,5645,9167,3917,1590,8337,6430,636,4462,7720,9004}

    Returns: 2426350.136519094

  48. {4519,3297,4500,4860,8936,3254,1664,6778,1344,6368,4882,2536,1348,808,1262,2963,8489,9082,1180,8599,17,8385,9377,6423,294,6291}

    {2862,481,9233,7623,6311,3378,140,6873,6950,3827,5065,6546,4521,5104,8611,1281,434,1680,3174,1954,1487,1719,1124,4304,1871,6684}

    Returns: 105315.70180705865

  49. {361,9631,45,8758,4200,9644,6320,2525,4111,1833,2190,2988,867,263,2687,1876,3905,2314}

    {2239,1314,4261,2471,8678,3958,6939,348,236,4654,7955,8198,1051,4383,9326,2095,4769,7338}

    Returns: 82836.21188338264

  50. {1049,8647,1073,5199,4210,4692,9281,4213,3109,7479,7753,7329,8342,2671}

    {1416,7619,8409,9476,5758,8860,9520,9999,2209,9467,6221,6811,9120,435}

    Returns: 95390.99645223154

  51. {2346,6821,4705,4867,7160,6721,6299,913,7708,5665,2382,5543,2392,4490,7909,7499,9260,6842,227,2588,2001,7445,8220,8448,8708,3955,9294,2762,1059,1153,3490,6105,8434,7810,5043,1993,778,6433,7469,1670,3663,7530,3579,82,9126}

    {6241,1388,9702,2157,7033,1988,3525,6169,1317,7400,8201,747,8801,1691,6040,4578,815,8470,7483,3220,8575,5287,1313,9344,6771,6172,7814,579,4527,5329,645,302,6742,6438,8172,7111,147,3813,9407,5567,9253,6178,2080,7781,4383}

    Returns: 234479.26432692754

  52. {8428,7351,8013,1681,6249,8016,7177,3249,333,2963,2164,7276,2918,2074,7813,646,831,8814,380,847,9445,5475,8626,4881,8131,3003,5481,1747,2234,7082,9843,6289,4768,1358,8852,7920,8368,1446,4897,5003,6272,2675}

    {7715,7533,4945,3546,8990,3576,6719,185,1144,2576,604,8670,8116,931,6227,508,2131,3178,1367,8759,300,9342,6828,9493,3488,5549,7577,7727,4510,7645,8796,8732,2564,1088,4094,7040,9448,1945,3001,208,6422,4222}

    Returns: 207833.963242905

  53. {3703,8520,7646,5436,6545,1965,9699}

    {5480,5744,2363,3887,7766,2153,2724}

    Returns: 30122.10274087293

  54. {5384,6666}

    {3059,9294}

    Returns: 12353.886369584467

  55. {586,9279,6735,3877,1909,1022,4609,4069,8363,431,3025,222,429,5725,5581,4441,1577,9053,2433,1125,6571,1386,2060,3205,3431,9721,5888,7686,917,792,9093,2009,4162,7249,6210,6654,3108,8120,5918,6782,3350,2513,870,6632,1527,7116,5241,552,5270}

    {870,5433,5405,9849,6997,1490,5706,6633,2761,5131,9858,3193,9470,7214,1155,117,9281,7589,2563,5654,52,6775,9386,3081,9891,2577,6066,2512,4344,6457,1835,983,12,9087,8722,9770,4783,820,1970,1508,8011,7119,6107,4571,2340,4846,8242,2795,4994}

    Returns: 248007.3836731786

  56. {8,6,3,10,9,0,6,2,10,8,7,0,0,0,4,4,8,0,1,1,4,2,2,10,4,5,5,10,0,0,3,5,0,1,10,0,1,1,9,1,5,2,8}

    {3083,2499,2225,8548,2880,1404,7224,1974,474,70,1720,2337,6937,2414,6966,4311,3174,3478,1210,8785,2169,8219,595,2561,986,6020,5914,3705,5206,7190,6539,6362,6644,8832,994,6784,1305,1219,9522,972,6905,7633,5980}

    Returns: 2.3428220536582484E9

  57. {0,0,0,5,7,4,10,5,0,4,3,4,10,9,4,3,7,3,0,4,10,8}

    {8098,282,7140,5362,8086,6199,5740,5794,5474,2460,3323,1497,2401,6032,1230,1151,9229,9167,5842,1698,2379,4928}

    Returns: 7.86950303613898E8

  58. {0}

    {6713}

    Returns: 4.5064369E7

  59. {10,8,0,6,3,7,4,1,7,2,6,7,8,1,3,9,5}

    {2017,7687,9906,9595,2385,9822,5115,504,4671,4051,6492,2993,1704,593,5178,6160,4185}

    Returns: 1.4042934552031243E8

  60. {1,8,4,7,0,10,7,2,9,9,3,8,2,10,7,6,3,2,9,3,7,4,9,3,5,5,10,8,5,7,4,7,8,4,5,4,6,6,9,4,9,7}

    {9885,258,9778,5945,2494,4685,8008,1902,8201,6259,8309,8786,1363,612,6819,1423,9054,8253,2144,5718,6506,409,662,2558,110,1592,6330,2302,1895,2784,4138,1485,5200,8305,7440,4696,9747,2589,4508,9876,8767,536}

    Returns: 2.6816899138882643E8

  61. {1,1,7,7,2,0,3,1,0,8,2,3,9,0,0,1,9,4,6,6,3,1,1,6,7,1,5,9}

    {2696,2619,8713,7978,7895,9270,3066,9787,4365,6197,3778,9929,1262,1057,7218,7076,1160,5664,1869,981,500,2583,3981,3004,3117,5426,7751,1193}

    Returns: 9.325367903767642E8

  62. {6,2,6,10,1,2,0,2,6,7,9,1,8,3,2,3,7,2,2,5,7,10,4,0,9,7,0,0,3,3,10,2,6,5,10,2,8,0,9,1,3,3}

    {2067,106,5504,65,7079,1626,7501,2233,1851,9145,4589,4707,5019,6101,9445,879,1470,1995,9159,3078,8102,7282,4054,1055,505,3367,2392,6648,5045,6213,2588,1634,2943,104,5390,1053,7021,9602,9336,8375,9829,9021}

    Returns: 1.2847994053176103E9

  63. {6,1,2,10,3,3,9,6,9,7,2,7,7,1,5,6,2,2,10,5}

    {5909,1179,550,2956,9160,1288,7562,2961,1772,5402,1426,7685,3243,4574,1793,578,5351,9456,7737,6478}

    Returns: 6.102290907161842E7

  64. {8,7,10,10,4,4,0,10,1,9,7,5,2,6,7,0,0,6,5,2,8,10,0,9,10,1,5,2}

    {7559,5222,6400,1277,9973,8629,2352,1643,2483,9923,2607,661,2724,9545,3714,1002,1028,2289,6459,1193,8335,7900,9866,1933,2833,994,9366,9763}

    Returns: 3.2540694524777764E8

  65. {3,1,8,4}

    {9111,3847,5727,1100}

    Returns: 5825755.569038072

  66. {1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,1,0,1,1}

    {2851,428,6660,1442,7032,5112,2574,8684,2145,7541,9260,9504,9903,786,1863,545,8196,694,5299,5604,2999,6859,3364,6860,234,2383,8401,9350,8202,1113,8825,4806,1175,5609,323,9825}

    Returns: 1.253191073611111E10

  67. {0,1,0,0,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0}

    {6684,1423,4693,2820,8120,4632,502,5138,1643,6886,1245,6721,6890,1745,328,427,8620,7935,2772,3977,2323,2795,8751,1738,1502,6215,5475,5515,2573,2179,447,7588,2199,3182,4056,8319,1737,4187,8352,4334,9792,5864,1669,4493,3705,5276,3630}

    Returns: 1.2235090822333334E10

  68. {1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,1,0}

    {8310,1233,2107,2221,3371,1042,855,1820,1295,6308,5880,1093,4901,587,66,5589,4072,1659,348,8651,8090,2891,2127,6892,2458,1963,6794,2617,5515,1735,4073,3214}

    Returns: 1.9202968561111112E9

  69. {0,0,1,1,0,1,0,1,1,1,1,0}

    {8597,8445,4689,7822,1514,1485,3404,217,4711,882,8142,2463}

    Returns: 8.349787396666667E8

  70. {1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,1,1}

    {4572,6143,6350,63,4593,7125,9214,9351,7599,6252,9427,2149,220,1989,605,3578,7266,3888,9770,396,2900,3617}

    Returns: 4.140306697E9

  71. {0,1,0,0,1,1,0,0,0,1,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,1,1,1,1,1}

    {975,8523,3043,5699,5273,1730,8089,7635,3156,403,2612,3492,25,7420,3084,7968,2265,95,1342,9712,2476,6018,9281,2012,2389,2027,2843,3636,8474,3402}

    Returns: 4.0292194792222223E9

  72. {0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,1}

    {3087,900,8204,7600,2331,132,2561,2574,5560,2073,9501,3192,1005,7295,4154,1873,532}

    Returns: 1.7173503453333335E9

  73. {0,1,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0,1,0}

    {5349,3613,944,5624,7130,4581,7954,4290,6941,9463,4328,8954,8718,6485,3994,4559,1091,6222,7582,4075,2476,1213,2976,952,1435,3104,982,2372,6324,6443,2900,5544,8417,462,1646}

    Returns: 1.4445269919222221E10

  74. {0,0,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0}

    {6288,9345,5088,5642,8362,6239,9314,5927,2187,28,2752,489,3664,906,3033,7748,3197,6435,1391,770,1690,8478,7212,7312,473,3283,6793,826,1963,5070,4525,5672,1940,4601,7907,4712,5340}

    Returns: 8.727854528444445E9

  75. {0,0,0,0,1,1,0,0,1,1,0,1,1}

    {7471,3726,2701,800,3092,8466,6104,592,2299,6546,5300,8924,1226}

    Returns: 9.975578356666666E8

  76. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {9343,4870,5965,2079,3383,7858,2154,3405,3248,4032,6140,660,6580,3932,9504,8029,7654,5087,6684,6442,8418,6596}

    Returns: 1.4899375969E10

  77. {0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {7376,9192,5801,6538,3722,4781,6688,7380,1294,578,8606,5759,2030,9951}

    Returns: 6.351452416E9

  78. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {3911,8928,7578,1902,5274,1004,4803,796,6598,4680,3074,6282,6816,7907,7445,699,2332,4639,1070,412,6982,702}

    Returns: 8.804819556E9

  79. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {2306,1453,2137,891,9025,4431,1288,1009,3255,6728,1705,2712,1703,7919,5180,5645,3988,8831,5499,8610,1294,2882,8490,1819,1199,8481,5117,6796,4581,4699,1740,7378}

    Returns: 1.9262941681E10

  80. {0,0}

    {8834,5166}

    Returns: 1.96E8

  81. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {5314,3539,7814,2490,7588,4262,1596,729,8403,38,1770,4619,8477,1524,3672,3043,1613,2804,5598,1581,3289,8847,3106,7303,3164,4021,9439,8432,3382,3815,5991,4671,7410,7108,1897,2759,9609,7939,4982,5177,7046,7329,8225,3547,9113}

    Returns: 5.0209605625E10

  82. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {4779,6832,7090,1302,3981,8339,531,1488,4110,5873,2690,8077,8147,1628,869,1619}

    Returns: 4.536696025E9

  83. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {9209,1989,9193,9351,5995,1033,1649,9844,5976,5428,9463,2151,2960,3944,9194,2066,3823,2334,9290}

    Returns: 1.1002331664E10

  84. {0,0}

    {1717,1104}

    Returns: 7958041.0

  85. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {5668,2548,202,107,9403,5870,3470,774,5013,388,6111,1225,1327,5904,2400,1384,9645,789,9558,3252,1053,5206,3212,1388,4384,261,8086,1095,8935,9470,1333,8048,3723,9556,6763,7569}

    Returns: 2.40622144E10

  86. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.849E11

  87. {0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 8.1E9

  88. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 4.84E10

  89. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 4.41E10

  90. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.681E11

  91. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 6.76E10

  92. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.369E11

  93. {0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.96E10

  94. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.681E11

  95. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 2.209E11

  96. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 2.5E11

  97. {69,31,43,53,10,19,42,62,19,34,89,9,14,88,69,80,65,83,3,77,17,64,33,63,84,63,28,50,58,22,0,7,13,11,57,27,27,99,85,79,93,15,51,8,42,49,66,71,34,16}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.5172572627147523E8

  98. {9,88,20,11,73,66,52,3,19,82,20,63,56,22,61,36,13,15,46,88,8,86,93,68,13,95,37,80,93,83,95,58,41,91,31,8,49,80,98,90,26,18,86,67,12,68,9,37,8,93}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 4.704631659887769E7

  99. {65,79,51,52,35,70,27,72,11,72,42,58,3,97,99,12,0,58,68,47,14,43,57,92,34,83,10,14,40,87,45,67,85,59,80,64,19,80,58,45,15,35,68,25,4,56,96,42,50,63}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.4088891886903134E8

  100. {26,97,75,50,97,9,17,87,86,49,28,33,8,10,78,37,93,21,68,55,9,49,99,73,87,93,60,40,20,68,0,8,20,69,15,12,77,69,19,10,3,35,27,32,93,94,20,13,50,41}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.5795788726162633E8

  101. {56,34,36,51,85,79,43,20,56,20,5,48,79,39,36,23,16,69,70,40,63,73,53,89,14,76,9,60,54,10,1,91,9,23,35,85,98,5,9,48,60,13,97,1,51,92,29,98,51,64}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 9.542546903118032E7

  102. {62,55,78,24,88,80,52,0,71,74,98,44,64,51,8,6,47,50,66,58,19,31,64,74,55,15,48,94,40,52,76,86,19,80,93,98,24,19,59,17,43,41,34,20,78,84,21,9,95,10}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 1.3224760570835944E8

  103. {52,71,4,43,43,68,80,6,37,62,79,88,35,95,17,45,38,23,38,1,69,74,34,30,15,34,84,4,67,93,8,97,26,31,17,3,27,31,19,26,60,4,77,94,23,94,74,12,49,16}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 8.955809370159775E7

  104. {34,8,40,64,95,71,0,5,45,74,56,0,97,71,90,87,12,15,30,6,96,91,59,83,67,6,25,55,92,11,68,21,42,99,78,82,58,34,83,10,89,2,42,74,82,96,17,42,36,30}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 4.7314290544726866E8

  105. {89,14,83,17,43,91,40,76,46,31,46,37,1,69,60,50,48,37,32,14,26,84,36,17,42,35,95,65,19,25,30,50,91,46,93,21,63,73,12,4,4,10,25,81,94,85,7,21,97,73}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 5.914906803013157E7

  106. {4,11,31,52,39,57,88,42,17,4,7,20,29,26,14,35,53,45,5,1,99,7,43,23,96,5,61,80,68,52,95,77,38,84,0,98,41,83,99,31,99,70,35,2,97,54,84,20,99,70}

    {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 2.3718790825524017E8

  107. {9967, 9441, 9008, 9911, 9940, 9583, 9672, 9084, 9767, 9237, 9031, 9789, 9347, 9624, 9616, 9149, 9184, 9115, 9015, 9487, 9965, 9065, 9542, 9466, 9602, 9089, 9580, 9270, 9557, 9645, 9482, 9356, 9250, 9934, 9454, 9531, 9020, 9509, 9006, 9144, 9473, 9378, 9055, 9588, 9165, 9558, 9145, 9938, 9771, 9957 }

    {9142, 9306, 9040, 9277, 9807, 9178, 9155, 9955, 9155, 9834, 9042, 9387, 9350, 9342, 9817, 9476, 9783, 9471, 9818, 9882, 9440, 9782, 9815, 9296, 9124, 9186, 9437, 9120, 9530, 9830, 9486, 9818, 9657, 9642, 9346, 9703, 9810, 9158, 9908, 9270, 9155, 9841, 9721, 9794, 9447, 9071, 9396, 9048, 9287, 9038 }

    Returns: 473979.83440440515

  108. {6415, 9069, 2219, 6755, 9008, 2528, 6420, 7065, 8319, 8487, 6870, 9927, 2434, 5451, 9869, 404, 8346, 5199, 7901, 9035, 6026, 418, 7369, 6542, 9932, 1006, 9531, 4934, 7844, 6819, 7418, 1376, 3149, 2837, 4817, 7652, 9468, 9941, 8192, 8552, 5872, 795, 8786, 7100, 6833, 5694, 102, 3202, 3541, 7654 }

    {5458, 4955, 2239, 9526, 1370, 8671, 819, 8422, 5156, 4475, 7111, 4419, 9325, 9232, 969, 1106, 1089, 7511, 7584, 5338, 2625, 4328, 1282, 2320, 6627, 462, 7469, 24, 2079, 2310, 5363, 3861, 7230, 3433, 5691, 8511, 284, 4209, 5604, 8881, 3458, 9368, 7752, 6244, 2755, 533, 1656, 8807, 4030, 2392 }

    Returns: 234933.72299496393

  109. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000 }

    {10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000 }

    Returns: 1.2524782598982143E8

  110. {5, 10, 15 }

    {10000, 10000, 10000 }

    Returns: 2056894.0268063205

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