Statistics

Problem Statement for "RandomAppleEasy"

Problem Statement

Taro likes apples very much. He has N boxes numbered from 0 to N-1. Box i contains red[i] red apples and green[i] green apples. He decided to choose one apple from his boxes, and he does so in the following way:
  • First Step: He chooses a non-empty subset of his N boxes randomly and transfers all apples from those boxes to another box (this is a box other than the original N boxes and it is initially empty). Each non-empty subset of boxes has the same probability of being chosen.
  • Second Step: He chooses one apple from the new box randomly. Each apple in the box has the same probability of being chosen.

Return the probability that Taro chooses a red apple.

Definition

Class:
RandomAppleEasy
Method:
theRed
Parameters:
int[], int[]
Returns:
double
Method signature:
double theRed(int[] red, int[] green)
(be sure your method is public)

Notes

  • Your return value must have an absolute or relative error less than 1e-9.

Constraints

  • red will contain between 1 and 50 elements, inclusive.
  • red and green will contain the same number of elements.
  • Each element of red and green will be between 1 and 10, inclusive.

Examples

  1. {5}

    {8}

    Returns: 0.38461538461538464

    There is only one box which contains 5 red apples and 8 green apples. The probability of choosing a red apple is 5 / 13.

  2. {1, 2}

    {1, 1}

    Returns: 0.5888888888888888

    If he chooses only box 0 in the first step, the probability of choosing a red apple is 1 / 2. If he chooses only box 1 in the first step, the probability of choosing a red apple is 2 / 3. If he chooses both boxes in the first step, the probability of choosing a red apple is 3 / 5. So the probability of choosing a red apple is (1 / 2 + 2 / 3 + 3 / 5) / 3 = 53 / 90.

  3. {2, 5, 6, 4, 9, 10, 6, 2}

    {2, 5, 6, 4, 9, 10, 6, 2}

    Returns: 0.4999999999999999

  4. {2, 5, 6, 4, 9, 10, 6, 2}

    {6, 7, 4, 5, 3, 2, 9, 1}

    Returns: 0.5429014970733334

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

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

    Returns: 0.46460213827476854

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

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

    Returns: 0.5072370758536262

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

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

    Returns: 0.48605724542918993

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

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

    Returns: 0.5178352708850019

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

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

    Returns: 0.5129452414945551

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

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

    Returns: 0.5144483442732466

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

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

    Returns: 0.5225818608097335

  12. {9, 9, 5, 9, 9, 5, 9, 8, 5, 1, 6, 4, 5, 4, 2, 6, 9, 10, 5, 9, 10, 1, 8, 8, 3, 7, 10, 3, 1, 4, 2, 4, 3, 3, 2, 7, 3, 2, 8, 4, 3, 9, 7, 7, 4, 1, 1, 10, 10, 5}

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

    Returns: 0.47769043789224547

  13. {8, 9, 3, 1, 2, 7, 4, 4, 4, 6, 1, 6, 9, 1, 3, 6, 2, 2, 8, 3, 9, 7, 1, 7, 7, 4, 10, 4, 8, 4, 7, 5, 5, 8, 1, 7, 5, 2, 9, 7, 10, 7, 7, 1, 7, 1, 4, 4, 7, 3}

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

    Returns: 0.48032358025892197

  14. {1, 5, 1, 7, 6, 2, 8, 1, 6, 10, 5, 3, 10, 2, 6, 8, 10, 10, 6, 7, 5, 3, 3, 10, 3, 6, 10, 8, 9, 7, 8, 2, 4, 6, 9, 10, 3, 2, 2, 5, 6, 4, 1, 8, 8, 1, 8, 7, 8, 4}

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

    Returns: 0.4723755998839298

  15. {6, 8, 6, 9, 5, 10, 9, 1, 1, 10, 4, 6, 1, 6, 9, 3, 6, 9, 7, 10, 6, 5, 8, 8, 4, 7, 9, 5, 3, 10, 5, 8, 10, 2, 1, 5, 4, 2, 6, 6, 9, 10, 4, 5, 6, 6, 3, 5, 4, 2}

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

    Returns: 0.4900258811893775

  16. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.5000000000000001

  17. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

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

    Returns: 0.6600647147059199

  18. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

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

    Returns: 0.6334003246104043

  19. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

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

    Returns: 0.6489879942885978

  20. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

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

    Returns: 0.6515827362758583

  21. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

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

    Returns: 0.6147075184473111

  22. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

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

    Returns: 0.9090909090909088

  23. {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}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.09090909090909087

  24. {2,8,5,1,10,5,9,9,3,5,6,6,2,8,2,2,6,3,8,7,2,5,3,4,3,3,2,7,9,6,8,7,2,9,10,3,8,10,6,5,4,2,3,4,4,5,2,2,4,9}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.3399352852940808

  25. {8,5,3,8,8,10,4,2,10,9,7,6,1,3,9,7,1,3,5,9,7,6,1,10,1,1,7,2,4,9,10,4,5,5,7,1,7,7,2,9,5,10,7,4,8,9,9,3,10,2}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.36659967538959487

  26. {4,6,10,9,5,1,8,7,4,7,2,6,5,3,1,10,8,4,8,3,7,1,2,7,6,8,6,5,2,3,1,1,2,5,7,1,8,2,8,8,8,8,4,4,6,10,10,9,2,9}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.35101200571140295

  27. {3,7,7,1,4,9,1,2,3,6,1,10,5,8,9,4,6,2,3,1,2,7,5,1,7,2,9,10,9,5,2,5,4,10,9,9,1,9,8,8,9,4,9,4,8,2,1,8,4,5}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.3484172637241423

  28. {10,7,6,2,1,10,10,7,9,4,5,9,5,10,10,3,6,6,4,4,4,8,5,4,9,1,9,9,1,7,9,2,10,9,10,8,3,3,9,3,9,10,1,8,9,2,6,9,7,2}

    {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: 0.3852924815526904

  29. {1}

    {10}

    Returns: 0.09090909090909091

  30. {10}

    {1}

    Returns: 0.9090909090909091

  31. {1}

    {1}

    Returns: 0.5

  32. {4, 4}

    {8, 2}

    Returns: 0.48148148148148145

  33. {8, 4, 4}

    {9, 7, 5}

    Returns: 0.4287444808453212

  34. {5, 10, 4, 1}

    {1, 10, 9, 5}

    Returns: 0.44566774356248046

  35. {4, 10, 6, 4, 4}

    {5, 10, 2, 3, 5}

    Returns: 0.5335477129559417

  36. {2, 8, 3, 7, 1, 3}

    {2, 1, 10, 4, 5, 6}

    Returns: 0.46248262975750154

  37. {3, 3, 7, 3, 9, 7, 2}

    {7, 8, 10, 2, 3, 5, 2}

    Returns: 0.48062182146563864

  38. {8, 2, 2, 10, 9, 2, 2, 10}

    {2, 8, 10, 9, 5, 2, 2, 5}

    Returns: 0.5085180573898116

  39. {7, 5, 8, 7, 10, 1, 4, 2, 5}

    {6, 1, 8, 6, 7, 2, 1, 8, 2}

    Returns: 0.5471841651621961

  40. {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: 0.5

  41. {7, 7, 7, 10, 10, 7, 7, 8, 10, 9, 7, 10, 8, 9, 7, 7, 6, 9, 9, 10, 6, 6, 6, 6, 10, 10, 6, 8, 7, 7, 9, 9, 9, 9, 8, 10, 9, 9, 7, 8, 10, 7, 9, 9, 6, 9, 8, 10, 7, 7}

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

    Returns: 0.4951046340219333

  42. {6, 10, 9, 7, 6, 6, 9, 6, 7, 10, 9, 10, 9, 6, 7, 8, 9, 9, 6, 8, 9, 9, 7, 8, 7, 7, 9, 10, 10, 7, 10, 9, 7, 8, 9, 8, 9, 10, 7, 10, 6, 6, 8, 6, 6, 6, 9, 6, 9, 8}

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

    Returns: 0.4974815816662419

  43. {6, 10, 10, 10, 10, 8, 10, 9, 7, 6, 9, 6, 10, 6, 10, 9, 6, 8, 7, 8, 6, 6, 8, 6, 10, 9, 9, 7, 6, 7, 7, 8, 10, 7, 6, 7, 8, 9, 8, 7, 10, 8, 7, 9, 6, 6, 10, 10, 8, 9}

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

    Returns: 0.4999916360212732

  44. {10, 10, 8, 8, 10, 6, 6, 8, 8, 8, 7, 10, 9, 9, 9, 7, 8, 10, 8, 10, 9, 8, 6, 8, 7, 6, 6, 10, 10, 10, 9, 8, 6, 8, 10, 7, 7, 8, 9, 8, 6, 6, 10, 10, 9, 9, 7, 8, 10, 7}

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

    Returns: 0.5111980890585633

  45. {9, 9, 10, 8, 8, 8, 10, 6, 6, 7, 9, 6, 10, 10, 10, 9, 10, 9, 9, 7, 10, 9, 10, 10, 9, 7, 7, 7, 6, 7, 6, 7, 8, 9, 10, 6, 7, 9, 7, 8, 8, 9, 6, 7, 9, 9, 7, 6, 8, 8}

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

    Returns: 0.5037241813708578

  46. {9, 8, 8, 9, 9, 8, 9, 10, 8, 9, 9, 8, 10, 10, 8, 10, 8, 8, 9, 9, 9, 9, 9, 10, 9, 9, 10, 8, 9, 8, 9, 8, 8, 10, 8, 10, 9, 10, 9, 8, 10, 10, 8, 8, 9, 8, 9, 9, 9, 8}

    {2, 2, 3, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 2, 2, 3, 3, 3, 2, 2, 1, 3, 3, 2, 3, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 3, 2, 3, 3, 1, 3, 2}

    Returns: 0.8158975952122257

  47. {9, 8, 8, 9, 10, 9, 8, 9, 8, 8, 8, 10, 9, 10, 10, 10, 10, 10, 8, 8, 8, 8, 10, 10, 8, 9, 9, 8, 9, 10, 10, 9, 9, 9, 9, 8, 10, 9, 8, 10, 9, 8, 8, 8, 8, 8, 9, 8, 10, 10}

    {3, 1, 3, 2, 1, 3, 3, 1, 1, 3, 3, 1, 2, 3, 3, 2, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 3, 1, 1, 3, 3, 1, 2, 1, 3, 2}

    Returns: 0.8256922945449038

  48. {9, 10, 8, 9, 8, 9, 10, 9, 9, 8, 10, 8, 8, 9, 8, 9, 10, 9, 8, 9, 8, 10, 8, 8, 8, 10, 9, 10, 8, 10, 10, 10, 9, 9, 9, 10, 9, 9, 10, 10, 10, 9, 10, 10, 9, 9, 8, 8, 9, 10}

    {3, 1, 3, 1, 2, 2, 3, 1, 1, 3, 2, 1, 3, 3, 3, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 3, 1, 2, 3, 3, 3, 1, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 3, 1, 1, 2, 1, 1, 3, 3}

    Returns: 0.8207457602548267

  49. {2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 2, 1, 3, 3, 1, 3, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 1, 2, 1, 2, 1, 1, 3, 1, 3, 2, 3, 2, 1, 3, 3, 1, 1, 2, 1, 2, 2, 2, 1}

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

    Returns: 0.17122328982831436

  50. {2, 1, 1, 2, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 1, 2, 2, 1, 2, 3, 3, 2, 2, 2, 2, 1, 3, 2, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 3, 3}

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

    Returns: 0.17617366630785636

  51. {2, 3, 1, 2, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 1, 1, 1, 3, 2, 3, 1, 3, 3, 3, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 2, 2, 1, 1, 2, 3}

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

    Returns: 0.1865240168559933

  52. {5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3 }

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

    Returns: 0.46460213827476854

  53. {2, 5, 6, 4, 9, 10, 6, 2 }

    {6, 7, 4, 5, 3, 2, 9, 1 }

    Returns: 0.5429014970733334

  54. {10, 7, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 10, 10, 8, 8, 9, 5, 8, 7, 9, 3, 10, 10, 8, 8, 9, 7, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2 }

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

    Returns: 0.4999999999999996

  55. {1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 }

    {5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 8, 9, 2, 5, 9 }

    Returns: 0.3321663358376393

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

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

    Returns: 0.4999999999999996

  57. {8, 5, 2, 2, 9, 7, 9, 4, 1, 9, 5, 8, 9, 1, 7, 3, 4, 1, 5, 8, 3, 7, 7, 1, 10, 1, 6, 6, 9, 9, 2, 7, 9, 9, 6, 1, 6, 3, 7, 5, 6, 10, 6, 6, 3, 8, 1, 3, 3, 4 }

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

    Returns: 0.4999999999999996

  58. {1, 1, 2, 10, 9, 8, 1, 7, 6, 5 }

    {3, 3, 4, 4, 5, 5, 7, 8, 9, 10 }

    Returns: 0.4578987403432567

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

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

    Returns: 0.49094618666565465

  60. {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: 0.49999999999999994

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

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

    Returns: 0.5

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

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

    Returns: 0.46728728828417426

  63. {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 }

    {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 }

    Returns: 0.25

  64. {5, 1, 2, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 }

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

    Returns: 0.4833259138875869

  65. {5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 10, 10, 6, 4, 5, 3, 10, 2, 10, 2, 5, 6, 3, 2, 5, 6, 7, 3, 4, 2 }

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

    Returns: 0.4795399528534544

  66. {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    Returns: 0.5000000000000001

  67. {1, 4, 5, 4, 3, 1, 2, 3, 6, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

    {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 }

    Returns: 0.37761897654088844

  68. {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: 0.5

  69. {5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 5, 1, 2, 8, 4, 1, 1, 2, 3, 4 }

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

    Returns: 0.49999999999999967

  70. {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    Returns: 0.5

  71. {6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

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

    Returns: 0.5930700755048613

  72. {5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 3, 4, 5, 6, 7, 4, 4, 3, 1, 2, 3, 4, 5, 6, 6, 7, 8, 7, 8, 5 }

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

    Returns: 0.3805430925238606

  73. {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 }

    {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

    Returns: 0.3333333333333333

  74. {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: 0.49999999999999994

  75. {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 }

    {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 }

    Returns: 0.5000000000000001

  76. {4, 7, 1, 1, 10, 3, 4, 1, 6, 2, 7, 6, 10, 5, 2, 9, 3, 8, 1, 8, 4, 7, 1, 1, 10, 3, 4, 1, 6, 2, 7, 6, 10, 5, 2, 9, 3, 8, 1, 8, 2, 3, 4, 5, 7, 1, 5, 3, 1, 3 }

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

    Returns: 0.5078036447352833

  77. {4, 3, 2, 1, 5, 6, 7, 8, 9, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 4, 5, 3, 2, 1, 2, 3, 6, 4, 2, 3, 1 }

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

    Returns: 0.487613236964089

  78. {2, 3, 4, 5, 6, 7, 3, 3, 4, 3, 4, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 7, 5, 4, 5, 6, 3, 3 }

    {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    Returns: 0.3393384683923623

  79. {1, 2, 3, 5, 6, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 6, 2, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 5, 6 }

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

    Returns: 0.4800472611558422

  80. {5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 }

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

    Returns: 0.49014616999401694

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