Statistics

Problem Statement for "RandomPancakeStack"

Problem Statement

Charlie has N pancakes. He wants to serve some of them for breakfast. We will number the pancakes 0 through N-1. For each i, pancake i has width i+1 and deliciousness d[i].

Charlie chooses the pancakes he is going to serve using the following randomized process: He starts by choosing the first pancake uniformly at random from all the pancakes he has. He places the chosen pancake onto a plate. This pancake now forms the bottom of a future stack of pancakes. Then, Charlie repeats the following procedure:

  1. If there are no more pancakes remaining, terminate.
  2. Choose a pancake uniformly at random from the pancakes that have not been chosen yet.
  3. If the width of this pancake is greater than the width of the pancake on top of the stack, terminate without taking it.
  4. Place the chosen pancake on top of the stack and go back to step 1.

You are given the int[] d with N elements. The total deliciousness of a serving of pancakes is the sum of the deliciousness of all pancakes used in the serving. Compute and return the expected value of the total deliciousness of the pancakes chosen by Charlie.

Definition

Class:
RandomPancakeStack
Method:
expectedDeliciousness
Parameters:
int[]
Returns:
double
Method signature:
double expectedDeliciousness(int[] d)
(be sure your method is public)

Notes

  • Your return value must have an absolute or relative error smaller than or equal to 1e-6

Constraints

  • The number of elements in d will be between 1 and 250, inclusive.
  • Each element of d will be between 1 and 1,000, inclusive.

Examples

  1. {1,1,1}

    Returns: 1.6666666666666667

    The following scenarios may occur: With probability 1/3, Charlie chooses pancake 0 first. In this case he won't be able to add any more pancakes and the total deliciousness of his serving of pancakes will be 1. With probability 1/3, Charlie chooses pancake 1 first. What happens in the second round? With probability 1/2 he will choose pancake 0 and with probability 1/2 it will be pancake 2. In the first case the total deliciousness of Charlie's pancakes will be 2, in the second case it will be 1. With probability 1/3, Charlie chooses pancake 2 first. If he chooses pancake 0 next, the total deliciousness of his pancakes will be 2. If he happens to choose pancake 1 next (followed by pancake 0 in the third round), the total deliciousness will be 3. Summing this up, we get the expected deliciousness to be 1/3 * (1) + 1/3 * (1/2 * 1 + 1/2 * 2) + 1/3 * (1/2 * 2 + 1/2 * 3) = 5/3 = 1.666...

  2. {3,6,10,9,2}

    Returns: 9.891666666666667

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

    Returns: 10.999999724426809

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

    Returns: 7.901100088183421

  5. {2,7,1,8,2,8,1,8,2,8,4,5,90,4,5,2,3,5,60,2,8,74,7,1}

    Returns: 19.368705050402465

  6. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: 1.718281828459045

  7. {1000}

    Returns: 1000.0

  8. {417,1,507,752,109,952,41,87,2,285,366,2,163,9,1,140,77,81,7,1,1,1,95,4,206,669,52,113,30,2,987,2,4,622,33,188,6,961,4,976,6,4,4,146,14,34,5,34,295,341,97,1,2,22,50,423,819,222,151,179,30,234,98,81,579,74,33}

    Returns: 341.4971589996257

  9. {11,34,60,576}

    Returns: 186.91666666666666

  10. {836,688,195,1,700,2,3,534,109,204,190,406,18,493,401,20,1,165,12,401,783,77,807,1,165,18,7,406,9,12,285,311,39,1,302,11,31,274,487,72,317,8,15,488,36,246,136,1,8,160,30,19,7,8,48,189,71,71,4,130,57,898,1,25,289,5,2,1,114,9,102,1,36,188,1,6,1,247,33,204,511,7,109,4,1,167,11,98,4,1,12,22,384,179,36,167,19,7,193,724,1,287,976,1,888,184,500,416,77,48,1,3,898,73,282,129,1,3,3,40,6,2,5,22,18,3,5,525,1,464,658,70,59,75,889,7,6,88,18,1,8,395,3,224,32,477,3,7,4,588,29,450,83,2,160,1,236,81,44,226,6,78,260,23,956,112,91,323,4,10,434,136,58,350,21,1,40,716,185,1,54,4,6,48,855,14,84,12,42,2,3,3,6,9,6,2,11,4,32,135,225,14,222,1,370,29,692,11,413,3,86,35,17,153,5,74,66,3,41,52,10,55,321,79,13,23,2,1,147,134,8,8}

    Returns: 280.71729820790284

  11. {8,7,35,2,12,23,7,311,83,826,6,906,1,6,26,100,136,384,24,4,745,813,5,4,1,48,12,117,923,3,2,1,2,711,893,294,65,265,10,10,29,344,1,491,10,1,5,29,2,5,21,3,1,134,1,45,31,122,861,4,167,539,349,532,15,79,944,3,3,31,56,6,66,89,215,35,132,1,15,5,3,2,3,402,25,2,2,6,2,45,440,210,2,23,25,187,843,210,185,14,10,54,270,884,31,54,3,151,4,114,88,303,402,36}

    Returns: 280.8058755839003

  12. {227,8,265,264,20,31,3,234,92,280,318,559,67,69,313,69,25,15,195,349,3,20,16,10,529,34,308,1,897,7,5,21,20,908,21,2,519,3,1,879,74,752,2,192,10,20,995,112,2,108,269,2,1,374,36,1,3,153,13,28,144,1,3,142,739,68,850,9}

    Returns: 315.1525918327499

  13. {311,424,14,173,290,206,4,169,225,3,212,253,243,2,18,7,1,3,24,252,17,5,1,582,23,185,846,366,538,224,1,1,40,2,792,33,11,4,17,203,7,3,45,11,2,121,1,3,412,2,4,1,487,40,5,5,49,1,190,1,9,3,12,26,3,51,5,3,2,85,438,1,6,3,680,25,31,1,3,981,4,4,34,2,283,1,364,7,327,40,8,14,15,2,8,16,10,37,6,12,66,1,8,168,3,43,257,148,8,810,3,4,2,45,105,10,672,210,24,457,29,298,259,124,11,15,14,169,4,29,52,866,12,34,55,10,55,61,290,125,75,67,158,619,50,232,343,69,4,1,1,420,602,558,909,1,966,33,518,1,894,1,75,4,844,479,873,2,3,973,113,18,177,300,124,5,5,49,762,6,1,178,363,437,21,3,380,135,282,42,100,194,4,3,15,892,324,27,157,126,1,2,30,1,656,1,39,5,289,10,860,970,234,11,35,31,3,33,208,3,10,125,531,83,226,11}

    Returns: 263.85790111432055

  14. {34,12,2,172,31,44,532,17,107,15,273,276,1,9,19,11,1,254,1,24,111,15,27,118,802,192,12,31,23,167,24,258,3,18,60,71,1,78,55,62,154,35,3,1,2,143,5,166,68,3}

    Returns: 162.77847084443314

  15. {39,11,217,2,162,17,225,11,15,711,118,59,206,79,909,1,480,5,15,2,10,2,11,169,331,171,361,327,1,488,5,9,338,10,7,112,836,58,193,12,7,1,6,4,1,2,1,190,48,74,3,38,25,4,14,258,1,1,57,133,19,144,1,69,702,23,2,122,21,84,1,241,91,4,525,74,430,4,1,42,293,9,5,155,1,11,33,64,10,449,3,233,3,690,2,166,3,596,153,12,22,13,64,105,222,12,439,25,201,23,83,85,1,1,42,14,7,18,4,1,10,9,1,179,883,578,101,110,11,1,49,2,2,1,450,723,12,55,46,247,821,75,4,35,3,17,258,3,90,1,4,23,7,1,8,36,5,4,174,9,37}

    Returns: 215.6914859715568

  16. {311,312,9,56,871,965,12,197,837,15,1,5,70,336,1,46,853,71,85,67,915,808,330,225,230,3,9,314,694,793,50,725,30,105,547,255,566,69,527,207,112,747,332,79,474,89,13,205,250,987,562,325,768,122,59,133,152,159,1,30,431,428,651,321,366,441,66,330,843,198,5,540,360,963,307,583,82,225,584,48,461,745,680,942,199,178,710,351,3,828,189,20,56,707,4,705,49,839,100,92,198,327,397,939,30,788,198,19,150,652,60,975,56,568,561,187,544,47,220,253,274,698,634,43,37,688,19,196,84,132,669,490,807,338,38,379,529,362,861,262,608,509,105,12,844,144,357,321,23,196,8,605,1,4,538,534,78,342,362,68,852,108,857,41,579,2,658,123,799,22,511,3,799,143,1,364,1,1,901,286,165,627,15,263,124,33,315,862,42,117,789,470,85,271,129,58,2,33,915,593,92,48,425,826,51,4,296,19,30,187,633,50,599,311,53,295,293,501,985,125,462,293,797,58,6,375}

    Returns: 571.0980541095327

  17. {1,25,6,1,116,724,4,4,50,1,482,489,103,303,30,500,441,331,260,163,1,530,427,13,393,499,1,743,238,40,8,97,303,1,48,794,358,43,423,129,327,34,371,56,38,3,916,57,480,836,1,78,47,99,89,380,174,21,156,272,21,553,126,11,961,170,40,8,359,369,4,757,283,230,463,470,1,1,182,359,777,448,173,489,423,131,44,64,451,261,741,207,241,34,1,11,10,383,565,604,386,721,35,917,297,875,353,118,50,851,11,300,489,536,403,287,125,54,280,332,10,1,1,543,980,733,364,704,26,70,941,79,12,338,303,129,1,285,171,280,611,366,395,327,870,247,4,568,234,239,240,823,833,819,4,653,35,405,42,120,817,201,678,610,788,665,279,616,499,18,155,8,377,249,31,82,127,360,476,530,18,1,42,313,609,900,102,372,711,848,569,54,745,8,801,59,348,491,535,592,72,432,1,24,168,67,49,10,422,826,196,664,172,269,481,98,8,89,662,928,105,684,73,886,824,318,145,380,144,292,430,590}

    Returns: 509.6028645971584

  18. {240,149,21,385,334,234,17,323,579,706,27,600,936,24,18,169,270,69,38,56,423,222,87,1,298,113,74,790,4,348,256,618,35,399,1,533,78,19,125,129,206,725,635,336}

    Returns: 451.55247163567367

  19. {254,25,56,782,63,1,101,329,377,79,166,18,30,490,177,907,587,333,513,152,756,599,580,420,88,1,191,967,1,818,873,189,20,813,914,876,437,461,325,392,342,7,444,51,169,199,161,357,583,86,194,982,34,52,2,1,503,109,85,1,696,188,578,559,978,553,8,81,130,89,426,790,58,151,205,10,440,94,6,18,26,615,22,335,927,990,52,313,540,100,446,48,124,802,14,435,581,420,604,440,19,297,266,911,1,775,46,105,806,602,225,494,201,115,732,10,193,563,288,218,314,1,958,320,5,189,626,310,254,18,245,49,778,234,84,403,476,4,61,683,855,531,335,953,27,1,566,655,267,544,84,32,442,900,954,66,2,21,8,114,128,259,2,7,1,523,182,846,378,93,983,83,21,137}

    Returns: 568.3894399232556

  20. {853,100,230,666,163,677,272,442,1,283,381,449,393,85,413,924,643,362,106,653,26,45,620,5,34,859,5,320,563,310,182,487,699,1,12,446,244,1,992,493,2,386,342,245,148,114,763,75,88,849,14,28,29,67,562,548,417,38,267,332,223,967,344,743,353,169,119,457,66,125,399,333,4,334,303,536,14,30,36,181,382,883,147,94,956,100,11,21,5,69,60,21,3,346,37,33,37,636,78,98,134,242,978,11,1,495,608,31,1,107,439,23,21,997,605,21,13,96,852,151,561,102,122,50,634,378,35,72,253,3,263,582,30,302,217,268,374,449,585,3,871,65,425,368,66,33,381,357,365,396,34,105,441,66,488,12,98,146,91,23,91,95,65,608,18,175,97,203,985,236,18,43,208,912,385,472,893,359,346,1,1,3,209,40,985,65,222,73,162,288,249,55,291,611,441,621,228,104,758,53,1,505}

    Returns: 503.6906931546093

  21. {225,336,708,42,367,547,826,526,1,480,935,560,301,621,387,895,130,23,296,446,250,735,1,205,60,19,395,9,141,171,852,201,162,123,756,287,519,707,10,399,90,211,531,413,99,898,781,287,288,96,194,319,898,130,34,543,61,885,810,90,131,301,188,1,20,761,819,625,366,265,274,914,1,72,181,467,65,173,16,5,979,805,683,1,93,410,778,16,145,1,45,27,407,8,65,775,390,300,120,1,142,551,25,12,78,107,596,998,328,418,352,121,546,5,13,92,953,1,787,7,693,209,514,971,773,37,97,497,946,322,998,64,75,12,23,68,476,151,88,34,641,94,262,793,468,58,1,951,56,32,157,277,560,98,189,35,260,607,838,10,32,423,37,517,226,938,363,273,292,88,622,187,887,57,39,1,793,187,133,443,474,523,164,416,696,479,111,5,212,23,218,30,1,1,25,263,32,645,321,209,881,630,936,828,737}

    Returns: 584.9978710772903

  22. {149,7,18,804,882,125,921,164,131,2,47,51,393,702,34,680,190,205,51,483,421,133,865,818,127,621,94,326,184,153,824,423,690,8,503,964,803,622,424,86,5,4,301,546,112,648,836,345,323,3,814,776,656,514,35,63,4,139,13,324,682,19,690,643,19,154,199,60,29,33,294,97,739,150,132,31,10,903,33,732,126,10,36,649,91,1,26,433,111,187,753,281,90,1,790,55,742,596,1,662,58,23,1,1,901,786,471,604,57,418,335,61,559,135,38,437,455,155,764,30,158,1,102,638,29,856,63,607,707,527,277,1,18,844,742,367,20,522,780,256,3,453,582,173,14,40,24,726,973,70,248,518,121,535,954,141,755,113,407,188,632,994,37,31,437,546,1}

    Returns: 579.4486339626117

  23. {504,480,599,527,163,218,532,18,248,463,725,234,458,373,855,989,451,515,660,48,14,68,38,6,25,127,263,761,845,365,1,133,297,694,976,16,237,398,103,401,1,1,80,11,478,36,347,375,1,754,67}

    Returns: 607.1551956608901

  24. {375,340,652,432,183,648,483,145,43,184,223,865,571,263,567,902,931,685,988,167,586,286,591,692,851,131,548,504,249,303,437,885,506,226,686,255,259,63,168,201,194,12,700,699,387,283,822,175,82,74,803,866,988,184,214,892,472,737,803,555,683,92,627,621,729,219,576,813,525,686,494,251,814,936,54,369,182,727,446,676,574,422,724,810,953,347,320,512,243,567,877,509,656,232,15,809,796,144,88,584,700,278,287,632,119,805,673,397,878,561,862,668,136,37,106,364,697,686,469,255,345,748,639,110,285,869,667,468,426,480,609,216,178,313,570,163,847,414,175,95,541,728,834,127,647,666,464,759,624,57,533,714,823,542,378,496,495,768,761,634,991,742,536,732,362,261,106,768,256,695,104,591,29,249,325,163,455,498,488,927,289,180,865,606,207,161,130,848,303,45,68,413,449,109,913,992,262,128,193,332}

    Returns: 822.3837790662083

  25. {159,882,92,897,572,597,702,926,423,300,584,616,795,717,266,387,840,255,283,343,129,684,282,530,306,322,400,335,241,706,822,468,593,9,411,552,170,576,409,262,533,972,560,363,72,914,382,733,151,255,1,643,997,12,640,171,731,17,860,569,282,394,648,855,996,512,733,655,389,450,869,557,877,289,385,839,279,763,990,466,569,857,678,660,642,993,610,200,837,312,987,833}

    Returns: 887.8571584527683

  26. {421,277,830,774,648,639,773,548,532,8,105,469,756,124,868,685,233,705,285,292,336,115,550,795,587,94,269,762,222,563,462,635,162,99,953,185,852,373,285,287,363,776,964,540,867,453,7,727,365,218,231,309,86,133,700,903,505,69,42,206,348,246,100,922,244,539,533,25,937,367,532,165,69,67,761,45,613,999,8,419,948,32,817,713,452,714,509,349,192,144,626,567,12,526,789,911,844,424,377,580,545,5,226,509,970,903,754,415,248,920,540,12,433,451,397,275,799,403,412,930,53,359,257,312,653,935,312,361,231,595,788,807,848,652,95,513,431,856,142,565,302,737,149,906,104}

    Returns: 796.9463705107761

  27. {785,254,842,948,159,576,942,235,235,617,455,507,784,856,559,773,814,785,496,915,794,587,974,725,622,148,838,421,475,814,496,9,134,471,217,199,346,324,887,82,109,237,243,481,489,588,912,670,740,405,819,172,54,955,631,464,203,58,973,720,722,169,65,168,49,622,311,253,191,546,77,544,110,643,613,262,976,395,597,359,839,312,277,338,88,502,552,360,260,187,633,748,369,784,107,697,969,846,332,848,563,419,87,406,837,401,326,629,397,47,690,882,366,94,160,886,240,877,861,457,848,428,573,814,137,771,926,495,780,545,638,10,261,648,366,640,191,797,944,192,96,784,829,118,809,731,538,118,894,837,763,233,259,934,632,506,205,693,254,450,695,449,311,947,540,443,963,713,557,723,715,101,455,97,256,898,384,284,459,685,624,849,898,530,835,617,253,26,679,980,917,174,368,934,981,196,892,739,512,134,246,802,714,5,980}

    Returns: 888.3079554367057

  28. {114,365,781,836,405,359,596,936,952,727,22,908,240,770,301,590,759,997,275,589,903,19,73,672,464,260,169,772,230,256,644,165,988,592,163,685,986,51,225,778,508,169,684,757,773,162,423,920,807,202,328,34,282,44,383,302,564,343,783,113,400,372,477,750,702,445,410,790,895,85,76,58,158,841,661,893,673,739,214,963,693,517,752,987,847,169,189,587,587,835,265,926,104,740,408,899,360,699,622,459,103,714,17,63,855,300,581,327,909,481,134,727,317,852,204,581,677,697,712,606,316,939,954,69,94,579,355,918,643,398,859,293,316,895,625,533,522,847,914,104,368,397,645,889,774,290,149,934,276,742,47,31,777,411,32,529,392,146,566,333,349,473,143,377,668,305,836,756,906,954,287,311,860,353,179,710,517,327,478,962,898,866,446,855,718,611,460,55,915,190,209,429,192}

    Returns: 878.3406949806488

  29. {703,727,677,618,849,921,688,945,42,331,387,163,350,194,779,359,383,449,123,979,846,363,340,805,162,42,375,668,215,33,842,343,474,976,441,17,282,714,836,916,42,351,653,914,427,501,240,422,475,365,682,484,645,354,280,716,460,654,409,697,365,553,218,457,840,321,91,972,572,166,215,920,739,109,824,553,42,606,948,182,163,432,531,672,734,617,842,330,757,208,969,762,636,262,37,568,635,713,491,256,630,756,438,385,473,908,548,721,161,214,485,175,269,942,177,366,769,654,480,941,473,804,961,178,787,833,604,998,390,302,186,218,745,754,979,798,39,863,209,833,298,917,390,292,904,824,255,820,708,655,524,458}

    Returns: 891.8595552376322

  30. {201,128,796,202,129,856,894,827,126,603,302,735,822,525,627,496,412,448,413,980,605,823,525,589,960,348,861,583,718,169,954,290,953,195,957,982,237,659,588,608,55,504,818,352,865,582,502,223,69,919,676,466,132,489,950,628,758,68}

    Returns: 947.8094605338607

  31. {529,327,699,469,226,784,251,709,283,752,348,212,333,984,683,962,936,126,337,637,231,426,303,362,708,222,804,970,727,961,380,512,65,73,977,63,874,219,388,255,910,318,524,561,785,275,915,89,315,536,757,510,721,412,577,818,572,632,313,802,871,721,174,458,619,626,167,113,507,467,590,668}

    Returns: 890.2143839233344

  32. {409,95,211,430,448,163,229,964,313,951,788,897,795,516,332,299,564,362,219,443,913,91,708,310,963,721,872,272,544,869,848,886,369,574,877,159,127,20,861}

    Returns: 873.5353181597488

  33. {17,56,5,5,5,2,5,83,9,36,4,17,7,1,1,27,2,2,2}

    Returns: 28.73527103077818

  34. {39,80,1}

    Returns: 72.83333333333333

  35. {2,36,1,3,8,5,77,28,1,4,1,43,2,3}

    Returns: 26.22777212047487

  36. {1,2,30,29,70,14,18,86,17,7,2,3}

    Returns: 39.589277188218155

  37. {6,27,46,1,96,17,3,68,24}

    Returns: 51.38941523368607

  38. {45,40}

    Returns: 65.0

  39. {95,45,58,11,73,1,1,3}

    Returns: 76.72879464285714

  40. {24,59,97,53,41,98,55,76,55,17,1}

    Returns: 93.698600914903

  41. {38}

    Returns: 38.0

  42. {67,1,15,34,44,20,75,78,33,28,24,25,5,67}

    Returns: 63.05807381348397

  43. {86}

    Returns: 86.0

  44. {34,53}

    Returns: 60.5

  45. {65,37,19}

    Returns: 79.0

  46. {11,53,24,33,27,63,100,81}

    Returns: 72.14933035714286

  47. {47,41,34}

    Returns: 71.0

  48. {13,133,249,5,430,713,284,345,8,14,5,3,2,3,65,15,17,16,2,133,42,2,95,23,96,337,20,734,7,2,30,17,342,15,9,1,2,6,11,813,1,19,11,19,8,4,10,34,606,2,1,11,393,373,54,676,15,9,2,379,375,52,95,8,8,828,176,270,1,7,10,371,896,109,3,2,775,170,3,39,4,31,17,19,39,7,483,688,286,573,27,52,578,33,2,10,630,459,2,3,1,8,46,2,2,3,19,9,260,2,207,1,1,71,400,17,1,113,981,121,88,48,309,2,2,9,28,78,2,3,21,27,13,174,43,244,42,8,89,36,6,189,19,256,222,7,12,78,6,34,606,1,6,1,27,554,193,1,62,188,24,235,562,1,68,23,929,90,1,484,1,96,119,22,5,20,410,10,13,36,1,358,513,928,5,21,44,1,382,528,844,67,53,270,3,70,149,2,10,12,81,363,33,74,273,478,3,11,34,3,12,1,27,891,1,2,3,116,1,520,776,180,724,18,147,13,715,53,1,2,126,27,131,494,15,351,15,24,48,678,541,61,44,27,233,5,55,10,69,35}

    Returns: 254.1187248076587

  49. {718,123,316,4,8,1,6,32,596,3,229,9,1,285,547,44,15,4,4,7,341,904,1,479,365,5,2,2,163,164,25,46,4,167,41,187,1,117,36,9,329,21,24,14,17,1,150,15,683,6,4,34,22,11,72,2,3,6,6,98,79,2,23,154,2,66,209,1,117,12,508,36,373,33,818,8,381,177,1,69,4,30,908,353,1,571,8,279,348,9,31,723,365,3,502,468,23,100,16,448,3,8,4,1,3,5,67,1,1,2,3,123,9,1,13,12,1,203,4,40,14,300,627,1,34,28,228,124,848,404,7,69,357,1,6,687,418,2,27,80,69,408,309,31,101,144,35,36,1,63,54,4,28,183,1,5,34,5,1,185,157,191,14,231,2,3,170,276,1,2,2,4,11,11,143,26,123,456,825,25,10,18,190,9,4,394,19,856,1,487,820,973,957,197,766,10,64,374,5,843,2,16,9,83,1,235,1,3,195,2,3,53,15,26,23,41,41,3,112,545,20,2,5,8,5,132,6,6,8,2,97,8,52,44,15,5,5,3,99,1,9,119,2,5,524,18,3,21,1,67}

    Returns: 242.43010961640243

  50. {248,37,1,2,172,19,45,56,7,72,12,3,249,4,65,61,14,152,23,253,288,24,14,55,7,464,3,193,721,144,860,1,56,6,37,2,501,1,958,59,308,50,292,218,3,105,20,1,237,14,35,123,741,264,2,41,444,9,6,40,8,14,9,63,21,808,52,980,5,9,49,15,274,457,111,3,2,489,47,10,17,89,5,92,3,4,278,36,4,4,851,5,27,19,23,189,11,9,15,19,3,6,3,102,376,64,6,2,2,360,15,3,27,200,7,6,4,3,1,10,15,614,29,1,519,48,293,25,3,366,512,1,1,296,818,344,1,517,211,8,33,7,2,72,1,243,13,11,37,96,5,55,9,34,1,1,540,12,459,530,1,822,529,775,10,903,355,2,3,8,2,69,2,556,353,1,61,301,53,25,201,5,863,120,276,1,120,6,130,40,17,151,4,9,106,25,5,2,7,532,167,1,1,5,51,351,376,23,547,24,1,530,18,144,8,22,1,2,495,13,59,39,641,36,1,15,108,1,26,63,14,1,177,407,14,65,26,8,10,4,4,45,194,151,123,277,169,56,15,167}

    Returns: 241.90922995295466

  51. {64,305,19,10,27,39,6,14,65,193,8,195,2,126,29,123,102,80,2,50,3,168,53,2,725,2,129,4,102,92,1,3,2,18,13,43,54,76,14,6,81,16,246,770,1,103,47,1,904,15,6,2,1,73,21,204,3,3,350,234,1,5,36,30,1,602,321,136,26,29,46,4,794,61,11,931,231,5,3,6,1,323,5,5,816,958,73,317,3,31,30,3,23,8,599,306,44,1,108,438,74,1,32,1,45,58,40,131,20,651,239,14,17,460,13,24,39,2,10,18,103,30,418,18,822,430,131,16,67,17,151,20,20,16,263,18,2,47,1,588,79,5,297,236,8,163,17,172,2,2,102,5,27,155,5,2,434,563,49,21,757,17,24,3,5,13,15,17,44,1,990,40,3,89,240,62,4,16,39,45,416,10,1,348,1,35,6,64,4,29,94,34,559,27,1,51,43,2,8,10,2,641,47,512,247,489,64,756,1,38,11,9,1,8,16,2,262,212,143,16,132,2,1,1,64,3,8,24,31,11,98,2,92,861,63,30,6,36,2,196,30,22,8,3,51,71,483,1,36,3}

    Returns: 212.26544908380336

  52. {12,2,713,74,7,1,17,25,116,184,83,3,697,6,2,32,244,184,72,77,646,43,60,28,4,416,1,69,74,74,850,31,2,12,310,87,62,20,134,621,22,47,456,1,29,329,9,110,489,5,182,530,39,85,38,33,3,659,511,45,2,1,70,4,21,1,3,3,219,387,214,80,709,29,182,287,4,398,1,8,5,1,3,553,28,76,156,170,61,4,11,486,4,14,2,26,1,130,212,169,296,85,1,935,186,5,369,19,129,935,842,240,70,16,3,58,2,718,4,290,47,21,28,591,5,1,6,1,100,123,12,2,43,14,24,616,2,16,80,27,8,6,362,19,2,30,600,1,4,437,2,1,23,11,467,46,8,975,3,195,24,179,5,8,40,1,12,11,273,47,10,4,263,6,33,348,118,143,3,46,3,85,70,2,228,121,255,21,837,244,73,6,3,23,312,21,10,5,5,234,337,48,7,257,1,29,30,236,12,997,1,459,10,379,474,149,6,288,25,8,2,3,66,140,730,152,81,28,489,193,1,11,627,2,8,100,982,394,355,1,7,19,510,213,21,3,43,68,4,8}

    Returns: 258.8789687348581

  53. {560,284,23,692,167,816,18,313,173,458,56,135,550,838,734,511,270,103,977,472,7,854,365,27,1,517,269,78,19,5,1,828,992,958,41,31,393,526,258,1,356,267,169,725,475,259,36,204,74,75,43,476,234,81,680,291,479,997,872,773,1,137,39,639,21,9,839,645,349,542,446,366,907,794,473,92,904,2,79,366,183,63,204,158,341,559,91,219,133,912,504,89,227,299,59,921,8,65,67,708,1,1,465,307,276,227,959,442,97,57,209,5,662,428,17,536,946,207,1,5,251,264,6,3,821,257,25,828,84,103,423,510,700,121,996,640,643,152,293,258,603,575,264,55,947,77,273,738,84,126,519,314,897,914,95,630,310,100,948,416,371,254,118,12,216,224,361,782,16,7,825,7,68,483,177,1,20,71,68,89,248,493,968,137,221,896,555,198,76,566,352,692,213,194,2,47,4,673,177,54,152,256,6,380,318,48,87,24,244,111,10,74,156,632,930,298,308,648,21,421,367,13,813,66,22,281,663,37,63,100,982,447,873,229,914,680,306,274,393,827,376,46,828,95,149,942,4,140,204,1}

    Returns: 588.111783039167

  54. {55,170,12,77,11,271,229,275,20,806,946,272,123,26,545,138,1,535,398,990,544,544,57,148,856,8,249,721,1,71,224,7,271,1,909,1,107,967,383,133,140,753,421,981,44,723,698,977,128,483,190,423,259,193,63,1,62,327,417,684,9,805,294,162,122,62,542,234,203,933,46,69,100,300,322,799,123,83,979,513,438,491,634,666,122,216,810,43,370,92,21,670,563,338,982,451,55,459,319,25,45,36,554,2,12,583,272,789,80,927,376,861,738,810,869,3,173,235,86,167,117,4,239,62,87,834,371,131,163,207,151,595,307,229,17,546,131,206,493,53,25,2,896,400,498,160,833,132,6,44,19,28,445,495,126,90,998,420,883,245,389,28,328,434,44,491,371,161,269,415,706,22,859,166,224,138,554,94,128,327,418,217,513,7,28,52,765,161,115,698,685,450,66,1,535,107,306,937,672,46,243,457,359,211,535,765,359,136,239,1,158,2,111,262,15,1,306,32,23,944,302,41,48,115,342,47,649,61,480,6,34,682,292,471,46,188,340,542,328,872,758,545,750,409,230,376,579,278,430,50}

    Returns: 567.2670318429684

  55. {1,174,152,636,43,107,127,474,154,830,668,50,264,845,147,108,151,851,66,258,432,11,841,99,586,655,1,745,3,407,467,1,10,137,36,724,112,376,377,894,104,18,623,839,743,4,347,581,183,509,205,872,309,308,487,57,932,12,42,63,226,563,517,57,973,33,15,873,17,122,566,77,243,389,980,40,409,659,38,748,406,25,41,63,6,540,261,904,25,726,325,976,514,770,224,8,699,455,554,108,853,18,690,27,889,590,170,9,956,1,342,521,923,1,278,483,6,77,103,140,3,1,24,5,56,10,81,571,12,13,584,444,764,305,19,861,33,494,1,85,111,146,376,121,766,473,116,68,373,419,199,514,767,228,949,15,929,81,136,96,344,237,8,650,81,847,1,437,604,376,85,8,125,180,969,450,280,117,377,508,126,1,250,247,969,139,541,190,83,1,103,688,401,903,12,952,20,113,791,150,28,85,24,385,965,178,764,561,18,611,603,699,92,257,333,714,827,702,660,95,89,833,761,535,516,375,44,23,841,892,395,226,575,886,1,61,676,671,658,65,376,35,140,908,443,173,479,1,267,831}

    Returns: 598.5127907651482

  56. {210,384,71,802,771,145,34,258,329,479,370,212,5,93,58,53,3,97,558,649,636,44,230,66,964,464,3,1,221,79,220,521,81,418,146,8,337,880,66,713,40,50,2,892,748,33,30,364,991,2,577,21,475,892,978,338,123,881,820,223,6,598,867,838,945,17,544,487,11,219,103,244,40,596,186,686,252,254,666,689,564,608,10,77,670,116,279,63,686,42,20,641,190,938,271,114,59,368,318,46,45,83,181,547,101,21,22,35,436,30,39,667,409,155,379,395,761,92,66,548,1,1,12,227,377,17,267,940,8,938,517,827,87,329,3,71,513,336,641,72,565,70,209,432,474,1,127,51,1,239,995,1,379,629,559,958,315,15,97,9,51,86,175,272,409,42,27,163,1,358,256,68,545,880,174,890,56,848,201,269,76,80,143,761,527,503,991,507,1,202,13,565,682,837,50,53,830,776,167,389,292,28,207,101,38,366,171,100,612,680,39,222,23,1,50,411,11,8,238,24,543,282,818,150,231,542,76,756,845,209,468,75,864,6,497,710,400,118,138,74,4,55,203,801,260,250,40,924,813,731}

    Returns: 557.9650628424621

  57. {218,66,750,70,410,658,181,657,610,143,374,313,804,340,695,320,50,996,1,318,20,51,187,38,44,1,480,405,495,897,300,80,910,9,479,647,502,132,1,25,560,276,106,187,936,801,991,42,37,242,527,846,5,645,167,49,237,187,821,264,995,298,836,1,30,584,305,357,395,122,154,703,945,745,84,1,11,27,268,2,305,358,125,230,725,165,314,246,174,914,709,332,376,25,518,146,54,282,1,467,1,521,322,73,72,887,144,185,105,494,158,973,639,184,76,18,310,1,335,100,382,36,305,12,974,252,35,582,1,55,142,51,568,1,275,648,925,598,11,98,42,28,97,175,1,213,7,75,1,66,401,630,646,1,334,959,122,543,905,247,201,877,56,96,255,235,566,298,380,291,779,877,839,655,412,10,70,97,200,468,146,461,918,626,408,155,105,346,763,681,46,671,565,661,301,952,132,398,893,177,1,309,261,32,228,921,583,96,897,575,16,534,877,114,494,17,728,297,466,15,3,24,24,16,79,98,567,261,688,612,958,253,203,237,891,818,79,606,330,38,612,1,119,581,37,349,1,1,364,41}

    Returns: 587.5859209085822

  58. {914,29,378,408,590,496,372,556,226,994,14,77,130,583,92,800,281,562,853,248,279,441,775,274,309,780,228,153,434,808,78,247,769,722,165,675,868,435,515,973,967,77,89,631,539,986,841,485,17,40,873,411,418,134,516,437,45,351,238,398,387,818,362,516,864,586,762,825,41,894,793,218,541,33,995,971,940,652,256,11,549,769,439,868,153,906,746,185,451,776,390,926,134,659,547,912,313,190,904,127,265,529,549,311,264,42,393,715,624,447,799,543,923,75,587,521,799,312,141,230,620,499,891,356,811,612,88,727,596,767,367,113,457,204,307,37,640,733,868,501,658,740,324,400,838,782,55,563,605,464,365,845,394,780,319,390,786,340,420,235,691,942,855,699,206,751,946,597,53,972,384,171,360,225,810,767,893,61,297,724,785,918,370,634,183,602,202,116,254,833,812,524,445,710,143,551,925,984,125,508,706,903,990,198,12,988,344,660,91,537,758,764,804,808,939,562,25,843,846,562,81,605,481,589,205,663,469,708,262,950,954,751,803,238,771,367,837,832,362,134,589,638,381,214,907,224,489,227,904,685}

    Returns: 874.259740167179

  59. {416,507,897,140,950,664,688,468,176,444,756,443,916,171,996,799,52,711,212,847,131,749,700,202,380,372,905,854,114,384,310,284,263,528,446,589,663,810,113,594,604,390,744,764,41,126,67,305,857,683,142,231,482,278,142,324,255,545,200,861,887,718,54,683,506,316,174,715,840,754,575,290,227,901,518,723,331,387,870,411,606,596,978,360,802,672,540,463,56,540,76,21,402,874,328,976,858,222,78,90,588,972,668,812,52,675,736,907,427,288,518,4,74,294,388,114,261,270,178,792,903,411,227,104,582,724,26,723,707,69,802,541,265,32,364,901,254,620,71,178,539,124,821,737,595,91,574,442,307,260,998,802,753,451,536,509,715,898,298,619,444,206,975,848,89,173,139,511,73,972,127,444,612,799,978,823,513,948,745,190,390,396,854,153,412,433,113,150,761,552,373,405,43,813,815,686,994,150,348,784,952,665,590,656,755,732,510,71,890,903,835,165,959,953,8,778,806,105,576,585,894,401,614,32,891,456,966,828,747,315,850,282,928,948,641,76,909,998,452,180,455,752,474,462,688,944,886,235,497,932}

    Returns: 872.0744059641966

  60. {579,404,304,983,837,81,864,896,597,584,304,956,888,460,277,251,606,781,774,732,792,279,813,982,205,33,968,581,76,311,447,93,599,860,242,191,873,424,659,139,743,502,422,884,208,398,403,309,869,421,977,779,157,711,899,949,957,509,636,982,581,870,37,717,967,754,319,47,381,140,372,749,905,314,518,270,444,773,982,524,28,232,499,592,752,83,678,310,761,271,967,143,319,962,334,384,149,572,55,721,910,681,327,397,891,129,782,732,735,92,350,585,300,292,348,379,552,547,102,703,725,769,906,139,872,168,606,862,278,860,674,812,217,287,155,670,911,883,533,672,608,166,147,340,182,29,477,507,734,344,314,678,250,98,551,593,489,212,89,104,938,867,154,868,825,649,124,125,922,35,835,861,99,839,210,907,353,982,963,151,372,595,101,876,497,816,893,385,340,803,3,490,197,426,524,160,841,825,717,598,224,509,353,279,132,966,710,49,837,808,424,188,371,338,600,465,115,16,799,617,10,746,820,319,886,84,413,712,18,408,462,755,304,897,463,199,144,638,548,790,405,543,699,352,659,822,249,813,202,646}

    Returns: 897.3766315583092

  61. {248,818,256,291,781,553,131,490,846,570,65,936,10,902,928,899,617,527,961,664,997,278,238,108,763,633,621,43,995,426,531,84,815,415,5,735,660,812,141,27,294,326,217,561,466,37,492,22,948,386,924,293,587,913,828,70,906,922,792,536,745,121,16,956,407,438,606,276,783,613,233,698,970,898,43,961,966,159,609,530,135,954,266,196,255,707,140,649,150,916,792,415,71,466,435,207,249,486,330,114,294,869,121,257,377,548,513,509,507,820,961,631,508,552,734,693,732,904,15,978,930,263,518,663,165,452,394,425,121,934,123,806,671,625,440,593,108,161,308,684,26,934,389,934,415,978,470,226,184,852,833,612,7,965,578,673,42,428,554,410,839,401,603,866,492,57,537,366,890,766,387,738,730,831,237,136,826,99,136,94,107,117,414,287,651,24,985,35,996,282,96,995,993,460,318,618,455,714,498,888,886,315,799,611,674,563,953,976,197,682,287,425,465,851,179,925,55,343,89,579,299,868,441,122,933,595,239,300,640,8,430,259,241,700,746,95,589,459,926,425,580,485,999,403,85,414,558,901,13,878}

    Returns: 876.5817747431568

  62. {771,664,162,693,223,156,2,421,515,416,28,961,997,752,879,38,896,252,965,934,587,137,983,592,746,752,295,239,642,541,842,32,879,719,935,841,503,460,24,140,475,337,270,198,199,441,551,183,949,74,375,538,749,142,979,1,523,455,819,949,96,890,553,309,918,31,561,158,246,220,39,253,877,156,697,185,405,92,135,511,448,402,59,269,203,794,569,461,225,737,916,730,315,717,276,211,984,786,282,680,34,507,285,528,408,787,593,728,634,291,182,940,843,91,750,122,567,967,289,556,272,294,772,946,828,773,933,388,960,360,591,315,40,609,438,203,440,324,710,716,91,831,714,201,805,423,752,902,375,502,574,47,485,764,145,5,958,302,158,38,947,858,439,775,245,594,94,455,23,634,31,109,945,346,272,371,790,773,275,272,422,900,366,454,209,460,250,482,730,796,473,555,958,904,686,755,910,134,505,109,144,219,792,187,364,192,214,638,851,525,6,65,365,274,976,898,695,346,908,483,25,10,709,432,852,681,806,362,295,580,566,600,223,313,744,38,796,584,262,334,702,234,945,835,559,541,190,181,721,265}

    Returns: 841.6973994142286

  63. {735, 661, 211, 582, 129, 203, 550, 565, 460, 962, 586, 883, 278, 615, 982, 807, 577, 138, 887, 100, 912, 93, 386, 796, 279, 914, 358, 260, 947, 794, 639, 636, 923, 769, 193, 418, 562, 135, 154, 788, 858, 90, 633, 75, 271, 143, 929, 136, 725, 415, 540, 422, 158, 590, 230, 239, 508, 247, 431, 611, 527, 426, 76, 187, 572, 688, 996, 923, 851, 710, 266, 781, 947, 396, 931, 427, 404, 594, 621, 996, 200, 984, 345, 632, 327, 883, 199, 791, 693, 672, 181, 883, 610, 57, 780, 270, 815, 844, 128, 445, 400, 547, 897, 380, 194, 862, 802, 404, 474, 732, 494, 919, 447, 561, 90, 748, 549, 537, 778, 734, 887, 867, 324, 7, 856, 913, 347, 177, 350, 883, 329, 885, 900, 787, 989, 917, 139, 435, 925, 283, 748, 794, 479, 437, 940, 614, 802, 648, 780, 268, 980, 345, 356, 267, 15, 35, 76, 854, 221, 794, 463, 135, 412, 62, 796, 153, 25, 835, 994, 79, 69, 509, 767, 200, 86, 41, 309, 355, 709, 103, 866, 623, 23, 948, 922, 539, 650, 715, 971, 549, 702, 723, 341, 350, 101, 420, 580, 354, 760, 291, 235, 957, 56, 958, 775, 313, 38, 417, 77, 732, 815, 350, 641, 631, 912, 346, 84, 585, 378, 828, 185, 681, 665, 730, 172, 587, 439, 860, 151, 489, 336, 577, 603, 171, 865, 208, 847, 890, 578, 655, 152, 966, 494, 783, 293, 591, 787, 401, 526, 872 }

    Returns: 913.3230969088601

  64. {1 }

    Returns: 1.0

  65. {722, 406, 344, 97, 333, 763, 92, 472, 291, 894, 494, 108, 608, 725, 600, 555, 508, 309, 43, 578, 19, 188, 562, 247, 275, 795, 12, 20, 756, 577, 49, 114, 636, 577, 250, 614, 790, 541, 975, 382, 561, 576, 391, 888, 846, 483, 902, 59, 783, 332, 991, 812, 369, 63, 340, 68, 609, 613, 951, 720, 451, 751, 613, 226, 89, 289, 941, 595, 523, 488, 140, 311, 83, 93, 252, 339, 232, 308, 581, 797, 300, 523, 674, 202, 915, 543, 451, 635, 159, 987, 547, 495, 731, 896, 88, 541, 50, 433, 475, 176, 7, 215, 333, 20, 458, 468, 38, 962, 599, 323, 683, 483, 613, 536, 85, 791, 607, 140, 962, 101, 882, 906, 715, 256, 516, 878, 622, 863, 135, 466, 276, 856, 293, 479, 112, 119, 411, 739, 411, 458, 993, 201, 504, 550, 984, 382, 530, 511, 82, 780, 239, 348, 207, 935, 764, 959, 61, 488, 732, 326, 631, 323, 47, 451, 138, 218, 177, 765, 968, 162, 354, 957, 278, 284, 131, 758, 991, 860, 92, 739, 230, 83, 4, 58, 390, 278, 488, 630, 417, 119, 478, 928, 566, 314, 680, 609, 86, 400, 834, 406, 137, 932, 842, 616, 394, 554, 432, 311, 423, 12, 239, 399, 80, 299, 755, 46, 140, 116, 782, 960, 127, 994, 439, 589, 202, 35, 821, 284, 378, 470, 319, 400, 665, 87, 775, 814, 827, 915, 424, 916, 885, 110, 568, 942, 568, 977, 252, 230, 527, 528 }

    Returns: 805.1436138071878

  66. {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 24, 89, 156, 225, 296, 369, 444, 521, 600, 681, 764, 849, 936, 25, 116, 209, 304, 401, 500, 601, 704, 809, 916, 25, 136, 249, 364, 481, 600, 721, 844, 969, 96, 225, 356, 489, 624, 761, 900, 41, 184, 329, 476, 625, 776, 929, 84, 241, 400, 561, 724, 889, 56, 225, 396, 569, 744, 921, 100, 281, 464, 649, 836, 25, 216, 409, 604, 801, 1000, 201, 404, 609, 816, 25, 236, 449, 664, 881, 100, 321, 544, 769, 996, 225, 456, 689, 924, 161, 400, 641, 884, 129, 376, 625, 876, 129, 384, 641, 900, 161, 424, 689, 956, 225, 496, 769, 44, 321, 600, 881, 164, 449, 736, 25, 316, 609, 904, 201, 500, 801, 104, 409, 716, 25, 336, 649, 964, 281, 600, 921, 244, 569, 896, 225, 556, 889, 224, 561, 900, 241, 584, 929, 276, 625, 976, 329, 684, 41, 400, 761, 124, 489, 856, 225, 596, 969, 344, 721, 100, 481, 864, 249, 636, 25, 416, 809, 204, 601, 1000, 401, 804, 209, 616, 25, 436, 849, 264, 681, 100, 521, 944, 369, 796, 225, 656, 89, 524, 961, 400, 841, 284, 729, 176, 625, 76, 529, 984, 441, 900, 361, 824, 289, 756, 225, 696, 169, 644, 121, 600, 81, 564, 49, 536, 25, 516, 9, 504, 1, 500 }

    Returns: 787.1527411014703

  67. {1, 1, 1 }

    Returns: 1.6666666666666667

  68. {42, 468, 335, 501, 170, 725, 479, 359, 963, 465, 706, 146, 282, 828, 962, 492, 996, 943, 828, 437, 392, 605, 903, 154, 293, 383, 422, 717, 719, 896, 448, 727, 772, 539, 870, 913, 668, 300, 36, 895, 704, 812, 323, 334, 674, 665, 142, 712, 254, 869, 548, 645, 663, 758, 38, 860, 724, 742, 530, 779, 317, 36, 191, 843, 289, 107, 41, 943, 265, 649, 447, 806, 891, 730, 371, 351, 7, 102, 394, 549, 630, 624, 85, 955, 757, 841, 967, 377, 932, 309, 945, 440, 627, 324, 538, 539, 119, 83, 930, 542, 834, 116, 640, 659, 705, 931, 978, 307, 674, 387, 22, 746, 925, 73, 271, 830, 778, 574, 98, 513, 987, 291, 162, 637, 356, 768, 656, 575, 32, 53, 351, 151, 942, 725, 967, 431, 108, 192, 8, 338, 458, 288, 754, 384, 946, 910, 210, 759, 222, 589, 423, 947, 507, 31, 414, 169, 901, 592, 763, 656, 411, 360, 625, 538, 549, 484, 596, 42, 603, 351, 292, 837, 375, 21, 597, 22, 349, 200, 669, 485, 282, 735, 54, 1000, 419, 939, 901, 789, 128, 468, 729, 894, 649, 484, 808, 422, 311, 618, 814, 515, 310, 617, 936, 452, 601, 250, 520, 557, 799, 304, 225, 9, 845, 610, 990, 703, 196, 486, 94, 344, 524, 588, 315, 504, 449, 201, 459, 619, 581, 797, 799, 282, 590, 799, 10, 158, 473, 623, 539, 293, 39, 180, 191, 658, 959, 192, 816, 889, 157, 512 }

    Returns: 902.2512931558906

  69. {958, 198, 26, 125, 802, 208, 784, 463, 506, 207, 133, 810, 973, 381, 992, 702, 347, 153, 72, 755, 948, 623, 195, 935, 260, 189, 812, 339, 270, 139, 360, 227, 336, 385, 704, 138, 944, 487, 952, 449, 45, 436, 259, 18, 816, 250, 719, 162, 755, 142, 916, 54, 764, 462, 989, 24, 650, 152, 714, 919, 291, 73, 498, 978, 809, 201, 115, 752, 39, 418, 552, 84, 853, 162, 453, 668, 412, 171, 181, 518, 665, 448, 571, 428, 909, 911, 803, 910, 63, 868, 181, 705, 940, 678, 34, 100, 230, 501, 851, 268, 918, 755, 703, 123, 916, 155, 142, 679, 678, 323, 196, 342, 122, 767, 121, 383, 677, 924, 644, 91, 791, 824, 147, 83, 853, 181, 182, 82, 681, 385, 702, 598, 139, 404, 72, 54, 911, 214, 733, 588, 888, 928, 929, 361, 694, 49, 743, 723, 324, 387, 813, 115, 562, 960, 549, 415, 140, 730, 848, 172, 114, 549, 121, 252, 305, 193, 658, 215, 406, 390 }

    Returns: 816.1813783103511

  70. {164, 366, 497, 917, 918, 828, 953, 773, 276, 758, 245, 302, 805, 729, 986, 468, 260, 267, 686, 883, 853, 579, 288, 572, 559, 765, 381, 354, 690, 434, 233, 693, 7, 250, 33, 18, 498, 481, 551, 605, 560, 463, 721, 337, 823, 815, 854, 782, 883, 283, 685, 404, 477, 192, 884, 838, 347, 363, 600, 790, 463, 877, 916, 1, 825, 588, 398, 222, 822, 258, 337, 358, 750, 247, 843, 627, 660, 896, 188, 562, 47, 743, 167, 38, 789, 625, 122, 444, 687, 518, 377, 732, 141, 446, 167, 817, 70, 805, 53, 984, 838, 953, 810, 56, 82, 834, 489, 752, 93, 991, 222, 960, 676, 8, 91, 63, 545, 488, 951, 65, 162, 106, 785, 105, 855, 932, 986, 478, 894, 699, 898, 88, 141, 72, 620, 308, 893, 408, 392, 903, 241, 230, 11, 142, 681, 540, 826, 455, 692, 139, 224, 742, 753, 322, 385, 842, 75, 58, 90, 371, 392, 253, 231, 657, 23, 221, 264, 162, 474, 813, 579, 434, 685, 458, 572, 451, 583, 565, 164, 897, 278, 60, 57, 945, 246, 880, 696, 406, 2, 483, 159, 820, 377, 701, 299, 18, 296, 647, 532, 952, 125, 543, 763, 558, 248, 860, 28, 885, 250, 585, 849, 357, 404, 52, 361, 822, 945, 587, 333, 903, 57, 255, 140, 894, 354, 137, 788, 491, 922, 296, 760, 272, 658, 950, 31, 308, 703, 7, 416, 388, 541, 60, 645, 402, 275, 358, 519, 413, 366, 158 }

    Returns: 857.3768146299927

  71. {1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000 }

    Returns: 1718.2818284590444

  72. {676, 573, 204, 611, 243, 112, 332, 2, 100, 350, 668, 502, 49, 37, 69, 107, 793, 688, 655, 725, 17, 599, 201, 572, 336, 890, 448, 711, 873, 616, 935, 220, 893, 152, 523, 528, 281, 625, 657, 99, 261, 849, 445, 735, 277, 619, 323, 978, 379, 734, 973, 297, 241, 463, 25, 643, 333, 391, 394, 287, 446, 961, 689, 489, 840, 468, 598, 594, 819, 694, 207, 796, 525, 723, 401, 917, 161, 651, 645, 236, 256, 158, 944, 510, 125, 813, 465, 946, 515, 589, 330, 495, 424, 684, 742, 367, 298, 532, 763, 467, 341, 499, 454, 320, 613, 973, 78, 27, 204, 218, 395, 698, 373, 158, 225, 354, 633, 131, 608, 77, 85, 319, 304, 238, 436, 157, 708, 485, 884, 198, 399, 23, 426, 783, 365, 879, 465, 699, 300, 830, 846, 998, 598, 127, 759, 80, 955, 599, 540, 202, 987, 131, 420, 193, 281, 687, 479, 912, 102, 375, 268, 99, 78, 206, 93, 146, 503, 379, 308, 79, 332, 430, 566, 657, 385, 896, 864, 28, 671, 535, 840, 451, 950, 317, 746, 56, 274, 319, 763, 74, 797, 594, 337, 323, 852, 469, 999, 673, 763, 457, 782, 857, 399, 2, 87, 504, 6, 140, 570, 919, 744, 725, 998, 727, 91, 314, 157, 892, 767, 668, 863, 552, 508, 148, 29, 693, 713, 420, 624, 959, 808, 221, 661, 931, 528, 593, 342, 220, 879, 646, 337, 32, 170, 805, 658, 479, 699, 863, 457, 406 }

    Returns: 824.9790201433141

  73. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    Returns: 3.0287594181612323

  74. {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 }

    Returns: 173.3102563139802

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
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