Statistics

Problem Statement for "IOISureWinner"

Problem Statement

The International Olympiad in Informatics (IOI) is currently in progress. To honor this competition, our problems for this round have IOI-flavored stories.


Topher Coder is leading the IOI after day 1. On day 2, he needs at least scoreNeeded points to be guaranteed the first place.

Day 2 contains N subtasks Topher may possibly solve. Each subtask offers some number of points. Additionally, for each subtask we are given the probability that Topher will successfully solve the subtask (and thus get the points). The tasks are such that each subtask is solved independently, so we will assume that all the random events "Topher solves subtask i" are mutually independent.


You are given the information about subtasks in the int[]s subtasks and p. For each i, Topher will solve subtask i with probability p[i] percent, and if he does, he will get subtasks[i] points.

Calculate and return the probability that Topher's day 2 score will be greater than or equal to scoreNeeded points.

Definition

Class:
IOISureWinner
Method:
probability
Parameters:
int, int[], int[]
Returns:
double
Method signature:
double probability(int scoreNeeded, int[] subtasks, int[] p)
(be sure your method is public)

Notes

  • Your return value must have an absolute error of at most 1e-9 to be accepted. In languages where you have the choice, we recommend the use of double-precision floating point variables ("double"s) when calculating the result.

Constraints

  • scoreNeeded will be between 1 and 300, inclusive.
  • N (the length of subtasks) will be between 1 and 50, inclusive.
  • Each element of subtasks will be positive.
  • sum(subtasks) will not exceed 300.
  • p will contain exactly N elements.
  • Each element of p will be between 1 and 100, inclusive.

Examples

  1. 31

    {10, 10, 10, 10}

    {50, 50, 50, 50}

    Returns: 0.0625

    Topher needs at least 31 points. There are four subtasks. Each gives 10 points and Topher will solve it with probability 50 percent. He needs to solve all four, which will happen with probability (1/2)^4 = 1 / 16.

  2. 40

    {10, 10, 10, 10}

    {50, 50, 50, 50}

    Returns: 0.0625

    The same situation as in the previous example. Getting exactly 40 points is still enough.

  3. 101

    {10, 20, 30, 40}

    {99, 98, 97, 96}

    Returns: 0.0

    There is no way to get 101 or more points.

  4. 100

    {20, 30, 100, 50}

    {12, 34, 56, 78}

    Returns: 0.57400256

    One option for Topher is to solve the subtask worth 100 points (and any other subtasks along with it). If he doesn't solve that subtask, he must solve all three remaining subtasks. The first option has probability 0.56, the second option has probability 0.12 * 0.34 * (1 - 0.56) * 0.78.

  5. 20

    {10, 11, 12, 13, 14}

    {10, 10, 10, 10, 10}

    Returns: 0.08146000000000005

    Any two (or more) of these five subtasks are enough.

  6. 181

    {33}

    {75}

    Returns: 0.0

  7. 197

    {127, 135}

    {12, 17}

    Returns: 0.0204

  8. 202

    {59, 63, 59}

    {7, 50, 98}

    Returns: 0.0

  9. 238

    {25, 21, 24, 31}

    {33, 43, 53, 85}

    Returns: 0.0

  10. 58

    {17, 27, 26, 15, 25}

    {16, 12, 89, 41, 59}

    Returns: 0.34352409600000006

  11. 109

    {7, 9, 12, 6, 18, 14}

    {44, 65, 23, 96, 100, 42}

    Returns: 0.0

  12. 191

    {13, 15, 14, 19, 12, 15, 13}

    {41, 25, 72, 87, 64, 66, 96}

    Returns: 0.0

  13. 141

    {25, 23, 32, 42, 42, 25, 28, 26}

    {7, 28, 7, 73, 34, 89, 34, 23}

    Returns: 0.0879234830794

  14. 192

    {23, 23, 31, 22, 15, 19, 18, 21, 28}

    {35, 25, 6, 40, 6, 23, 8, 68, 40}

    Returns: 6.306047999999999E-7

  15. 158

    {26, 19, 26, 27, 23, 28, 22, 18, 20, 24}

    {96, 19, 58, 93, 57, 21, 85, 21, 68, 55}

    Returns: 0.2697654833128617

  16. 7

    {9, 5, 8, 10, 6, 9, 5, 6, 3, 7, 8}

    {66, 80, 54, 42, 47, 58, 63, 60, 64, 76, 22}

    Returns: 0.999562265745681

  17. 19

    {15, 17, 14, 23, 17, 17, 17, 20, 28, 24, 16, 17}

    {39, 74, 80, 23, 93, 75, 21, 40, 4, 6, 98, 69}

    Returns: 0.9999135541689411

  18. 277

    {6, 7, 7, 10, 10, 11, 8, 9, 9, 10, 8, 7, 8}

    {15, 16, 54, 93, 1, 4, 26, 50, 22, 87, 91, 87, 87}

    Returns: 0.0

  19. 248

    {3, 6, 7, 7, 5, 4, 6, 5, 6, 5, 8, 3, 4, 7}

    {13, 21, 91, 96, 71, 6, 19, 61, 77, 40, 79, 88, 53, 60}

    Returns: 0.0

  20. 260

    {17, 16, 10, 14, 12, 13, 16, 16, 16, 15, 8, 15, 22, 18, 16}

    {24, 36, 100, 37, 5, 76, 75, 88, 37, 32, 5, 38, 44, 4, 63}

    Returns: 0.0

  21. 292

    {11, 13, 7, 13, 6, 14, 11, 13, 18, 12, 11, 15, 24, 18, 13, 13}

    {8, 97, 1, 74, 52, 8, 83, 86, 66, 4, 86, 65, 13, 98, 18, 78}

    Returns: 0.0

  22. 19

    {14, 12, 15, 19, 14, 16, 12, 15, 13, 12, 21, 16, 13, 12, 18, 15, 17}

    {47, 83, 66, 28, 8, 3, 1, 30, 65, 40, 75, 88, 35, 87, 95, 98, 14}

    Returns: 0.9999994097482132

  23. 11

    {5, 7, 7, 5, 3, 5, 4, 8, 10, 8, 8, 6, 7, 7, 8, 5, 10, 8}

    {33, 49, 58, 46, 85, 71, 71, 10, 81, 48, 52, 35, 13, 72, 97, 70, 80, 58}

    Returns: 0.9999991301808897

  24. 70

    {14, 17, 13, 16, 7, 23, 6, 10, 19, 14, 16, 10, 9, 11, 16, 16, 12, 15, 15}

    {53, 64, 28, 66, 56, 96, 5, 82, 55, 82, 28, 1, 50, 58, 87, 38, 36, 46, 22}

    Returns: 0.9958918154197667

  25. 38

    {8, 10, 5, 11, 8, 15, 13, 6, 5, 6, 6, 6, 4, 12, 8, 7, 14, 7, 5, 11}

    {29, 49, 77, 87, 20, 95, 81, 8, 59, 25, 37, 86, 94, 67, 35, 17, 50, 10, 35, 16}

    Returns: 0.9986304478872496

  26. 127

    {6, 8, 11, 6, 3, 5, 14, 8, 12, 5, 8, 10, 8, 8, 8, 10, 7, 10, 9, 5, 8}

    {97, 96, 85, 78, 34, 62, 92, 67, 91, 53, 85, 75, 37, 75, 7, 60, 45, 49, 82, 73, 85}

    Returns: 0.32599012504597785

  27. 7

    {7, 10, 10, 14, 8, 9, 15, 14, 11, 15, 9, 8, 12, 7, 9, 7, 12, 8, 12, 14, 7, 14}

    {45, 15, 17, 75, 92, 55, 85, 44, 34, 65, 62, 97, 57, 80, 55, 57, 59, 66, 34, 73, 22, 96}

    Returns: 0.9999999999900367

  28. 115

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

    {45, 19, 37, 96, 98, 61, 92, 97, 7, 77, 29, 79, 28, 73, 81, 56, 23, 27, 42, 60, 3, 65, 24}

    Returns: 0.0

  29. 206

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

    {96, 24, 70, 74, 74, 44, 51, 41, 52, 75, 66, 49, 19, 83, 59, 16, 71, 30, 97, 81, 22, 98, 61, 45}

    Returns: 0.0

  30. 36

    {6, 5, 6, 4, 9, 8, 2, 6, 7, 4, 13, 6, 4, 5, 5, 3, 9, 5, 7, 6, 6, 7, 3, 11, 6}

    {61, 91, 81, 93, 75, 64, 98, 75, 36, 71, 6, 45, 43, 53, 22, 47, 23, 74, 52, 85, 31, 36, 80, 58, 84}

    Returns: 0.9998018176769037

  31. 204

    {4, 4, 4, 2, 5, 6, 2, 6, 2, 4, 5, 2, 3, 6, 2, 3, 4, 3, 3, 4, 2, 3, 4, 2, 2, 5}

    {2, 90, 47, 86, 3, 92, 45, 58, 36, 85, 42, 59, 27, 44, 71, 18, 54, 94, 19, 85, 92, 98, 77, 90, 55, 79}

    Returns: 0.0

  32. 229

    {13, 12, 7, 9, 7, 9, 12, 10, 11, 13, 13, 11, 11, 7, 4, 5, 13, 11, 13, 12, 18, 12, 5, 13, 9, 11, 11}

    {26, 66, 77, 76, 29, 15, 55, 61, 98, 40, 31, 11, 74, 50, 52, 22, 23, 35, 46, 25, 51, 61, 7, 73, 90, 27, 87}

    Returns: 1.1061936484443157E-4

  33. 223

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

    {95, 72, 76, 81, 65, 20, 83, 40, 80, 73, 65, 70, 68, 5, 57, 59, 68, 33, 39, 40, 7, 31, 35, 57, 68, 86, 99, 68}

    Returns: 0.0

  34. 128

    {8, 15, 12, 6, 12, 8, 13, 14, 12, 10, 9, 7, 11, 13, 12, 8, 13, 11, 11, 7, 12, 5, 7, 12, 9, 12, 4, 11, 14}

    {16, 68, 19, 70, 40, 53, 6, 10, 98, 26, 54, 58, 12, 58, 26, 88, 18, 37, 86, 78, 83, 79, 60, 55, 72, 72, 40, 43, 81}

    Returns: 0.8306505640148372

  35. 175

    {3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 3, 2}

    {63, 69, 38, 18, 50, 48, 30, 68, 68, 15, 22, 59, 25, 64, 23, 66, 71, 12, 1, 71, 95, 26, 9, 88, 15, 93, 62, 91, 35, 73}

    Returns: 0.0

  36. 6

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

    {70, 3, 54, 52, 29, 55, 1, 95, 51, 6, 49, 90, 31, 11, 22, 87, 76, 47, 48, 74, 94, 24, 50, 45, 39, 46, 15, 50, 99, 87, 2}

    Returns: 0.9999999999908428

  37. 165

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

    {49, 80, 78, 48, 52, 88, 50, 94, 38, 74, 18, 84, 59, 66, 97, 20, 78, 82, 41, 86, 44, 1, 52, 40, 23, 9, 98, 74, 69, 44, 52, 60}

    Returns: 3.5079370175979355E-9

  38. 137

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

    {53, 56, 97, 85, 73, 98, 20, 30, 34, 7, 10, 37, 1, 89, 62, 96, 47, 70, 35, 51, 25, 79, 5, 80, 38, 56, 51, 14, 1, 31, 87, 47, 4}

    Returns: 8.729050215372681E-6

  39. 100

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

    {45, 48, 27, 41, 30, 92, 50, 41, 53, 98, 72, 9, 67, 4, 98, 66, 59, 97, 13, 43, 6, 32, 79, 20, 96, 70, 76, 67, 64, 50, 48, 7, 90, 40}

    Returns: 0.22943847411212911

  40. 167

    {12, 9, 8, 4, 11, 11, 4, 6, 10, 10, 8, 6, 7, 11, 8, 9, 8, 8, 6, 5, 2, 15, 7, 4, 10, 8, 9, 4, 10, 9, 5, 7, 7, 8, 11}

    {69, 82, 54, 25, 21, 65, 61, 16, 55, 21, 97, 99, 80, 62, 85, 16, 15, 60, 39, 8, 94, 35, 82, 95, 99, 5, 2, 64, 15, 18, 15, 11, 18, 92, 38}

    Returns: 0.0407808148565734

  41. 8

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

    {12, 56, 31, 99, 92, 7, 79, 81, 50, 72, 86, 95, 51, 79, 71, 54, 45, 72, 2, 33, 85, 60, 85, 97, 45, 14, 65, 15, 38, 12, 13, 50, 91, 30, 28, 10}

    Returns: 0.9999999999999948

  42. 203

    {5, 6, 2, 11, 4, 8, 7, 5, 5, 6, 5, 5, 5, 8, 11, 4, 4, 5, 7, 13, 6, 4, 5, 6, 6, 8, 3, 6, 4, 8, 3, 4, 8, 4, 5, 6, 9}

    {42, 98, 15, 23, 55, 40, 43, 22, 89, 94, 96, 65, 15, 99, 58, 80, 74, 53, 45, 55, 72, 36, 67, 38, 17, 29, 59, 52, 70, 21, 70, 31, 90, 43, 71, 81, 74}

    Returns: 2.1107364953180376E-7

  43. 79

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

    {22, 73, 15, 84, 72, 70, 29, 46, 22, 68, 62, 54, 81, 18, 23, 94, 70, 93, 100, 25, 97, 70, 3, 49, 53, 75, 85, 26, 74, 51, 5, 12, 27, 28, 58, 75, 90, 43}

    Returns: 0.9510534564045761

  44. 183

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

    {27, 64, 18, 46, 56, 49, 64, 10, 21, 39, 58, 66, 77, 97, 43, 54, 29, 76, 78, 35, 93, 92, 43, 74, 1, 9, 18, 35, 8, 73, 66, 57, 69, 15, 57, 12, 7, 93, 87}

    Returns: 0.0

  45. 287

    {3, 1, 3, 3, 2, 3, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 2, 4, 1, 2, 2, 1, 2, 1, 1, 2, 3, 3}

    {1, 66, 67, 57, 88, 11, 78, 51, 88, 31, 19, 42, 96, 23, 41, 17, 49, 75, 68, 36, 52, 3, 15, 81, 6, 34, 72, 99, 90, 78, 4, 99, 46, 51, 29, 92, 69, 88, 90, 39}

    Returns: 0.0

  46. 18

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

    {53, 52, 85, 38, 73, 29, 29, 21, 21, 59, 93, 76, 81, 11, 11, 19, 12, 25, 53, 37, 99, 95, 80, 14, 80, 83, 100, 45, 93, 41, 51, 17, 67, 24, 38, 72, 71, 90, 99, 88, 18}

    Returns: 0.9999999934795829

  47. 287

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

    {34, 38, 49, 50, 4, 63, 27, 81, 95, 46, 23, 42, 20, 73, 10, 45, 98, 26, 75, 50, 6, 54, 74, 72, 15, 70, 40, 19, 39, 66, 34, 28, 65, 38, 96, 87, 97, 6, 6, 39, 33, 98}

    Returns: 0.0

  48. 228

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

    {72, 13, 93, 44, 13, 90, 25, 88, 63, 75, 33, 67, 25, 15, 65, 45, 28, 1, 7, 48, 33, 10, 52, 1, 25, 87, 76, 19, 78, 57, 92, 59, 33, 56, 52, 73, 93, 25, 89, 100, 80, 79, 59}

    Returns: 1.1172112450861683E-6

  49. 168

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

    {49, 91, 42, 80, 1, 73, 12, 36, 40, 20, 89, 61, 8, 88, 31, 6, 60, 84, 32, 72, 98, 47, 55, 92, 61, 62, 57, 96, 53, 12, 35, 70, 52, 2, 7, 59, 39, 34, 99, 82, 38, 12, 76, 42}

    Returns: 0.0

  50. 263

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

    {79, 69, 9, 94, 82, 40, 28, 34, 65, 1, 33, 61, 17, 77, 57, 23, 13, 97, 35, 61, 5, 14, 82, 5, 45, 13, 28, 21, 26, 49, 100, 69, 86, 25, 28, 20, 21, 85, 6, 6, 89, 47, 100, 95, 96}

    Returns: 0.0

  51. 68

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

    {86, 57, 20, 38, 52, 9, 31, 73, 51, 82, 48, 95, 100, 23, 83, 57, 62, 15, 18, 43, 78, 90, 74, 69, 39, 4, 20, 3, 40, 89, 53, 21, 14, 36, 78, 92, 13, 1, 71, 47, 86, 69, 19, 44, 78, 50}

    Returns: 0.31955408065419116

  52. 26

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

    {83, 8, 33, 43, 37, 54, 98, 14, 65, 62, 44, 46, 5, 69, 69, 90, 11, 5, 60, 96, 43, 97, 50, 83, 85, 89, 81, 22, 48, 31, 50, 81, 98, 96, 2, 49, 59, 88, 47, 28, 92, 99, 8, 3, 61, 64, 99}

    Returns: 0.9999999999901601

  53. 133

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

    {93, 3, 5, 87, 81, 57, 70, 84, 79, 8, 4, 80, 23, 10, 78, 10, 84, 98, 74, 33, 36, 46, 11, 5, 54, 25, 95, 17, 39, 26, 26, 44, 78, 28, 89, 93, 68, 68, 49, 91, 41, 63, 41, 84, 83, 33, 10, 64}

    Returns: 0.8079023294381145

  54. 36

    {1, 2, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 2, 1, 4, 1}

    {62, 36, 40, 77, 77, 19, 23, 87, 40, 57, 32, 61, 59, 10, 26, 91, 29, 44, 16, 60, 60, 3, 27, 15, 64, 90, 74, 64, 21, 43, 49, 91, 21, 28, 89, 17, 78, 35, 42, 50, 84, 26, 13, 64, 13, 40, 40, 5, 55}

    Returns: 0.09782118524936874

  55. 168

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

    {32, 83, 80, 22, 6, 89, 94, 80, 26, 92, 13, 34, 13, 57, 42, 12, 21, 98, 53, 9, 96, 56, 69, 43, 82, 71, 99, 52, 94, 65, 61, 1, 56, 98, 49, 19, 61, 34, 70, 61, 10, 30, 88, 33, 31, 24, 4, 22, 84, 91}

    Returns: 0.0

  56. 20

    {10, 11, 12, 13, 14 }

    {10, 10, 10, 10, 10 }

    Returns: 0.08146000000000005

  57. 100

    {20, 30, 100, 50 }

    {12, 34, 56, 78 }

    Returns: 0.57400256

  58. 227

    {7, 4, 2, 8, 2, 5, 7, 1, 1, 2, 6, 13, 5, 7, 16, 9, 8, 12, 2, 1, 9, 4, 5, 1, 14, 3, 5, 16, 8, 2, 7, 1, 3, 2, 2, 20, 1, 1, 5, 2, 7, 2, 1, 9, 8, 9, 16, 4, 5, 6 }

    {42, 30, 97, 73, 83, 22, 39, 10, 11, 86, 82, 84, 85, 91, 76, 78, 25, 29, 82, 53, 30, 39, 56, 13, 53, 67, 25, 61, 97, 100, 56, 79, 45, 41, 21, 99, 70, 86, 6, 28, 95, 68, 93, 38, 46, 20, 84, 32, 84, 96 }

    Returns: 0.01407102566260013

  59. 60

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

    {10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30 }

    Returns: 2.8670835503923185E-13

  60. 50

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

    {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 1.0000000000000005E-100

  61. 150

    {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 }

    {90, 97, 89, 21, 23, 52, 35, 69, 39, 37, 34, 51, 48, 60, 27, 15, 27, 99, 19, 73, 78, 22, 23, 46, 43, 59, 92, 87, 77, 40, 88, 24, 94, 36, 75, 41, 65, 36, 76, 92, 42, 20, 93, 79, 100, 34, 54, 32, 46, 5 }

    Returns: 1.7362726020673768E-17

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