Statistics

Problem Statement for "ExpectedSum"

Problem Statement

This problem has a non-standard time limit: 5 seconds.

Alice came to the blackboard and wrote a sequence of nonnegative integers. You are given this sequence in the int[] sequence.

Bob will soon go to the blackboard and edit the sequence in one specific way: For each i, the probability that he will write a minus sign in front of sequence[i] is probMinus[i] percent.

Once Bob finishes his editing, Cecilia will compute the largest sum of a contiguous subsequence of the sequence on the blackboard. (Cecilia's subsequence may be empty, and therefore her result is always nonnegative.)

Return the expected value of the number reported by Cecilia.

Definition

Class:
ExpectedSum
Method:
solve
Parameters:
int[], int[]
Returns:
double
Method signature:
double solve(int[] sequence, int[] probMinus)
(be sure your method is public)

Notes

  • Minus zero is zero.
  • Bob's random choices are mutually independent.
  • Your return value must have an absolute or a relative error at most 1e-9.

Constraints

  • sequence will contain between 1 and 50 elements, inclusive.
  • Each element of sequence will be between 0 and 50, inclusive.
  • probMinus will contain the same number of elements as sequence.
  • Each element of probMinus will be between 0 and 100, inclusive.

Examples

  1. {10, 20, 30}

    {0, 0, 0}

    Returns: 60.0

    Bob will leave the sequence as is, and Cecilia will compute the answer 10 + 20 + 30 = 60.

  2. {10, 40, 20}

    {0, 100, 0}

    Returns: 20.0

    Cecilia will certainly see the sequence {10, -40, 20}. The contiguous subsequence with the largest sum is {20}.

  3. {1, 1, 1}

    {50, 50, 50}

    Returns: 1.375

    If Bob writes three minuses, Cecilia's answer will be 0. If Bob writes two minuses, Cecilia's answer will be 1. If Bob produces {-1,1,1} or {1,1,-1} (probability 2/8), Cecilia's answer will be 2. For {1,-1,1} Cecilia's answer will be 1. Finally, if Bob doesn't write any minuses (probability 1/8), Cecilia will compute the answer 3. Thus, the expected value of Cecilia's answer is (0+1+1+1+2+2+1+3)/8 = 11/8.

  4. {1, 1, 1}

    {30, 27, 43}

    Returns: 1.89227

    Compared to the previous example, Bob is less likely to write the minuses, which increases Cecilia's expected answer slightly.

  5. {47}

    {100}

    Returns: 0.0

  6. {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50}

    {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50}

    Returns: 395.68965384306813

  7. {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50}

    {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}

    Returns: 2500.0

  8. {0}

    {0}

    Returns: 0.0

  9. {0}

    {100}

    Returns: 0.0

  10. {0}

    {47}

    Returns: 0.0

  11. {47}

    {0}

    Returns: 47.0

  12. {47}

    {47}

    Returns: 24.91

  13. {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}

    {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    Returns: 0.0

  14. {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    Returns: 1332.8852434870291

  15. {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    Returns: 510.85947618498255

  16. {45,34,29,27,22,49,12,42,35,32,10,23,48,6,11,16,19,37,31,1,7,44,25,14,40,13,50,5,46,28,18,43,20,21,8,38,39,2,26,15,17,9,41,4,30,36,33,47,3,24}

    {25,39,13,42,15,6,38,24,26,1,14,8,21,32,45,44,43,31,22,50,41,47,40,48,12,4,28,33,18,16,5,36,2,3,35,46,23,20,9,27,7,49,10,17,29,19,30,11,37,34}

    Returns: 703.8090597240888

  17. {25,39,13,42,15,6,38,24,26,1,14,8,21,32,45,44,43,31,22,50,41,47,40,48,12,4,28,33,18,16,5,36,2,3,35,46,23,20,9,27,7,49,10,17,29,19,30,11,37,34}

    {45,34,29,27,22,49,12,42,35,32,10,23,48,6,11,16,19,37,31,1,7,44,25,14,40,13,50,5,46,28,18,43,20,21,8,38,39,2,26,15,17,9,41,4,30,36,33,47,3,24}

    Returns: 708.7881352921845

  18. {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    {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}

    Returns: 2451.0204081632646

  19. {45,46,47,48,49,50,45,46,47,48,49,50,45,46,47,48,49,50,45,46,47,48,49,50,45,46,47,48,49,50,45,46,47,48,49,50,45,46,47,48,49,50,45,46,47,48,49,50,45,46}

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

    Returns: 2324.52090086503

  20. {4,27,35,29,36,21,16,32,24,25,39,2,50,26,42,1,6,0,16,50,30,46,34,0,20,36,27,14,15,33,32,22,28,15,2,35,23,45,44,22,38,21,35,36,48,12,15,50,46}

    {4,16,42,12,46,74,49,65,69,32,12,83,29,89,42,27,60,95,14,98,53,77,45,86,36,98,30,71,33,45,68,72,5,61,39,72,99,50,33,93,66,28,77,14,80,26,48,62,32}

    Returns: 181.79192530144172

  21. {28,0,10,35,40,48,5,4,17,32,39,34,30,50,27,23,48,2,38,16,41,38,33,43,30,45,40,20,1,36,15,13,22,27,44,11,11,30,12,8,6,8,46,50,36,22,33,25}

    {13,34,56,0,83,15,53,8,47,2,33,5,17,23,94,65,62,25,100,98,63,67,58,72,72,1,88,9,22,19,69,43,81,5,79,30,91,7,48,15,2,11,38,6,70,39,30,78}

    Returns: 273.76910606790494

  22. {35,37,48,17,39,36,5,36,31,21,35,3,7,26,26,22,19,36,48,31,38,8,4,32,7,29,41,50,29,1,27,36,33,48,4,50,50,18,50,45,31,32,7,48,15,22,50,21}

    {21,59,2,75,12,85,58,58,35,81,69,87,88,88,3,71,24,86,36,5,98,33,69,61,49,8,92,100,13,66,90,75,76,61,68,95,46,74,39,52,98,87,26,93,80,11,13,65}

    Returns: 151.28965930011537

  23. {25,21,34,23,6,5,39,47,27,23,3,22,37,3,25,40,17,16,13,18,13,29,42,19,28,49,28,20,43,3,9,37,30,0,1,27,29,33,28,39,16,18,6,19,7,10,27,21,31}

    {54,30,64,72,65,33,40,71,2,77,86,48,76,75,89,76,88,79,59,78,71,22,87,89,48,5,23,78,23,79,9,62,52,7,28,59,22,76,50,0,79,17,95,9,71,49,0,49,63}

    Returns: 203.1333731896774

  24. {40,23,46,7,32,25,6,5,50,26,26,35,6,39,11,42,31,30,28,38,5,25,33,32,20,27,47,12,20,25,4,8,45,31,21,41,41,6,16,31,50,5,22,1,25,39,5,38,14,33}

    {82,26,64,32,91,97,39,64,77,14,71,7,36,92,22,62,89,30,51,78,60,0,75,51,77,30,80,70,47,100,13,43,8,20,75,13,30,23,10,18,65,21,92,21,9,11,16,75,50,44}

    Returns: 224.6119373424533

  25. {26,18,35,40,14,43,22,49,5,41,20,6,2,12,35,8,21,5,20,49,45,42,27,32,34,36,48,49,43,22,33,33,27,40,28,27,43,26,46,31,1,12,20,3,38,27,6}

    {56,98,74,15,12,42,55,94,7,42,100,96,23,85,52,60,94,66,60,88,66,15,29,25,80,3,69,63,41,18,86,20,99,37,9,6,95,77,38,5,82,79,85,0,32,44,24}

    Returns: 195.4483776230412

  26. {23,23,8,12,28,39,2,50,47,19,38,42,19,26,7,27,26,22,48,31,16,2,46,36,46,44,31,14,17,25,3,1,25,12,49,26,23,33,5,22,46,39,40,21,28,4,4,30}

    {34,8,20,26,29,54,60,25,37,0,14,77,72,1,32,68,27,68,47,60,27,42,51,4,86,82,75,53,41,68,44,0,13,2,39,6,77,27,67,78,0,4,70,75,6,49,97,59}

    Returns: 295.2148623159295

  27. {5,17,43,40,25,32,22,2,4,19,38,45,19,3,39,28,29,26,46,46,21,46,5,16,26,23,6,45,24,24,11,18,1,1,36,43,36,12,8,35,14,5,0,27,27,26,45,27}

    {74,93,16,19,98,92,94,94,48,68,82,58,33,81,82,18,9,5,75,30,93,75,16,9,2,17,15,66,99,16,78,37,72,77,53,70,95,62,78,74,3,21,100,76,69,74,81,92}

    Returns: 161.2318759657737

  28. {14,7,9,18,39,30,41,31,29,38,19,26,48,28,38,11,0,27,50,31,31,46,26,21,23,35,19,19,25,24,2,39,48,33,17,9,29,25,6,49,42,6,37,2,23,40,21,42}

    {86,73,96,18,0,33,44,20,79,5,52,61,91,41,18,34,32,42,52,84,14,26,85,22,79,29,36,85,31,58,89,98,67,43,19,67,46,14,18,22,72,29,69,73,100,67,99,41}

    Returns: 228.37484252197717

  29. {50,40,15,2,23,24,48,11,31,38,46,46,10,12,25,46,42,3,30,20,35,34,4,16,6,8,42,32,47,37,42,13,17,38,24,7,16,35,22,7,24,23,41,34,14,18,16,38}

    {86,89,83,41,72,4,97,79,26,37,57,98,41,96,14,18,75,23,33,43,35,12,37,26,4,97,34,78,83,27,25,87,63,63,9,48,83,2,83,98,75,19,13,53,38,28,52,96}

    Returns: 219.93449449571588

  30. {5,13,41,40,42,14,35,5,35,26,19,20,23,7,5,44,20,29,13,49,7,41,5,34,42,21,48,36,44,30,50,14,3,20,19,50,46,47,42,50,24,16,49,37,3,4,16,29}

    {64,28,65,65,62,36,40,55,66,31,78,87,89,82,42,73,81,26,73,22,24,30,96,5,3,88,77,65,77,33,94,77,37,25,43,75,77,80,71,43,64,22,95,99,41,47,23,20}

    Returns: 185.02915743793804

  31. {4,2,25,29,44,28,18,39,6,50,40,44,31,40,17,21,18,44,13,44,27,4,16,39,24,20,29,18,10,15,11,23,14,19,2,13,44,36,30,1,22,0,40,18,17,35,26,48,33,15}

    {58,58,6,10,92,16,93,51,56,23,31,5,51,86,57,68,67,12,71,3,69,57,69,62,75,20,20,100,96,30,35,85,40,24,71,86,63,65,95,35,58,32,43,67,14,28,97,32,100,28}

    Returns: 207.8184525899021

  32. {50,8,15,44,47,45,28,47,45,49,5,20,46,35,47,41,41,13,20,40,6,50,16,33,10,17,23,8,47,10,5,11,3,49,32,11,38,41,35,39,39,6,18,2,20,11,5}

    {57,35,12,38,25,75,96,96,63,79,92,18,98,17,31,91,68,30,77,39,32,86,94,58,3,39,24,95,3,55,22,34,89,62,24,57,1,47,81,31,51,64,22,100,22,22,77}

    Returns: 207.9797949071979

  33. {13,20,39,25,41,19,46,17,40,5,19,14,2,35,30,19,15,18,29,11,11,35,19,50,29,18,18,39,47,3,19,2,42,4,39,38,25,36,32,27,9,24,24,42,34,14,33}

    {71,52,88,56,69,23,32,51,41,42,15,48,55,17,11,94,55,31,30,0,32,69,3,43,50,68,38,91,25,32,8,86,6,31,22,78,45,44,10,87,63,33,35,98,76,47,26}

    Returns: 285.44313353666246

  34. {16,31,14,42,6,33,19,11,25,17,47,37,45,12,33,17,48,10,10,20,9,17,30,6,18,44,16,9,25,43,14,14,48,50,11,5,18,33,9,29,49,18,2,6,43,35,14}

    {26,13,25,63,49,38,91,32,1,42,46,53,12,11,42,33,68,29,74,92,88,17,31,86,63,70,89,80,25,98,4,94,21,3,72,40,29,87,46,29,31,62,47,25,54,23,59}

    Returns: 231.88963892466052

  35. {2,49,26,29,14,27,49,1,27,39,32,4,31,12,25,12,46,0,15,31,33,0,35,18,30,20,19,39,44,42,33,45,44,47,40,32,24,39,14,43,3,13,13,48,31,37,28,31}

    {51,69,51,17,53,45,1,89,67,43,69,95,13,97,78,46,65,49,33,19,6,27,6,72,33,88,33,22,47,78,47,29,73,74,70,17,30,13,17,46,6,18,93,22,49,98,98,88}

    Returns: 290.91885559020795

  36. {33,4,39,46,34,9,15,20,29,33,47,45,16,6,22,48,16,0,40,35,17,34,17,29,33,39,29,9,23,8,42,13,1,6,3,24,31,13,42,43,33,43,36,10,40,44,23,3,35}

    {95,23,70,30,61,99,61,54,7,89,63,88,89,88,99,29,65,73,41,65,28,49,94,58,17,81,21,21,25,42,0,75,66,94,25,70,57,20,37,66,82,55,83,60,70,55,87,2,21}

    Returns: 184.58464314676075

  37. {25,2,35,3,3,38,44,6,13,30,12,35,2,50,34,49,7,1,21,16,30,17,6,48,47,42,7,22,30,0,17,36,29,28,11,7,16,23,29,3,31,44,2,27,41,5,44,48,44,13}

    {47,25,29,92,74,18,26,63,65,95,13,37,98,77,81,94,87,69,97,12,62,24,4,19,94,64,96,33,18,35,47,18,42,85,68,47,16,18,54,52,73,40,86,23,77,99,48,2,13,54}

    Returns: 207.6870558142901

  38. {43,4,6,8,6,50,4,13,1,11,24,6,4,35,30,47,1,7,11,21,42,46,8,44,8,17,14,8,3,24,10,26,35,1,4,15,43,44,32,27,32,40,38,4,49,22,15,22}

    {34,24,5,39,5,22,7,67,39,39,55,91,43,6,47,95,100,83,76,32,81,23,66,100,80,20,24,79,3,68,96,59,29,100,33,53,61,0,96,83,6,43,79,52,11,9,79,43}

    Returns: 175.1677703147872

  39. {16,21,44,7,39,9,38,28,24,37,21,12,16,17,43,29,15,30,11,36,26,24,12,2,20,2,15,4,7,17,15,30,28,48,8,39,6,44,0,37,21,18,36,2,16,23,23,23}

    {20,11,95,32,11,61,68,64,59,85,43,77,49,20,37,15,57,54,74,86,33,31,92,30,97,5,20,4,97,39,82,53,63,31,27,7,88,34,74,74,27,65,4,41,35,17,53,15}

    Returns: 205.07489244201219

  40. {14,33,11,44,46,39,48,11,38,7,25,20,17,0,44,44,32,34,17,46,11,32,0,40,32,37,19,36,19,42,26,36,37,23,21,15,18,13,43,44,21,25,50,44,23,43,47}

    {27,17,97,45,65,3,59,18,69,45,50,11,11,9,71,53,100,64,19,85,23,21,57,8,27,46,86,49,24,63,89,9,80,71,63,25,7,2,41,71,24,48,1,17,71,85,50}

    Returns: 260.6211188479173

  41. {14,6,15,12,24,16,37,29,46,50,25,26,30,2,10,9,12,22,38,49,46,34,22,9,44,3,41,2,8,40,11,11,3,0,44,22,13,1,32,8,1,46,21,47,16,19,26,47,9}

    {57,92,56,20,84,20,67,54,1,16,23,62,16,53,47,3,1,74,58,26,38,21,35,66,92,98,39,84,78,53,23,41,12,74,47,70,84,98,28,92,26,78,58,56,23,28,83,35,3}

    Returns: 265.9324704058714

  42. {25,3,23,36,40,3,28,2,6,16,21,42,13,23,0,22,14,13,12,11,21,15,24,3,42,7,8,50,39,32,39,26,20,23,28,31,29,50,31,37,10,48,2,26,37,32,34}

    {59,41,47,55,21,66,83,70,68,29,63,52,99,95,5,44,38,79,31,60,31,26,11,63,84,48,74,27,63,3,41,31,24,42,93,75,66,28,2,50,90,5,65,74,42,71,69}

    Returns: 221.79904602265339

  43. {22,40,32,29,50,39,2,36,38,11,48,6,13,4,16,36,17,24,37,50,42,1,6,33,32,49,43,23,46,26,16,49,22,17,44,9,31,49,35,42,40,8,39,39,34,9,19,18,2}

    {77,55,46,69,96,78,49,90,79,97,72,80,100,86,56,70,79,92,0,33,36,61,32,98,71,93,84,49,20,25,50,52,91,81,59,7,37,63,12,66,80,38,91,46,66,70,31,10,73}

    Returns: 159.2669100127144

  44. {2,8,17,44,20,26,5,13,39,36,18,12,21,6,34,13,49,30,49,11,4,31,3,12,4,23,2,28,4,49,46,44,35,4,30,49,46,13,10,4,10,4,12,13,11,36,50}

    {95,84,27,50,95,70,60,51,4,69,21,24,99,71,78,6,85,43,11,34,64,59,56,52,28,62,26,33,79,65,21,84,99,49,38,73,79,22,92,74,20,39,3,5,97,68,69}

    Returns: 150.1388264303645

  45. {12,37,5,41,27,35,14,35,0,32,9,15,45,29,27,5,32,48,49,49,33,3,39,38,50,10,42,46,24,18,21,19,25,31,5,19,18,19,31,38,36,7,47,20,33,21,21,28}

    {25,5,78,0,3,93,63,65,59,84,70,36,54,42,81,16,82,8,87,13,47,27,35,62,93,36,76,47,92,40,26,24,27,23,20,26,61,47,76,38,20,51,85,40,75,49,14,15}

    Returns: 202.5019530306774

  46. {46,0,1,12,24,10,43,45,43,43,42,30,7,2,15,42,1,13,4,27,26,44,12,14,37,8,30,35,28,49,4,10,50,19,5,42,27,43,37,50,25,18,33,11,9,43,13,22,33,23}

    {32,9,17,69,85,10,31,77,39,46,58,92,80,21,82,64,56,77,55,12,20,90,95,70,5,18,60,100,76,39,78,87,52,59,64,52,84,66,64,53,64,29,64,34,22,54,77,14,15,92}

    Returns: 158.93034824582074

  47. {24,12,14,25,44,50,2,9,4,49,38,11,23,22,41,27,18,45,38,3,28,27,45,1,45,46,49,35,2,1,44,3,38,7,2,6,34,7,34,15,0,34,9,19,32,30,0,5,32}

    {76,69,79,73,33,99,60,23,27,27,42,89,98,10,85,76,74,63,14,2,59,87,56,3,5,63,58,26,95,98,15,74,51,41,54,46,94,99,20,37,53,98,85,61,72,31,37,58,42}

    Returns: 174.06631074568787

  48. {33,19,27,39,48,21,28,0,9,46,15,39,22,14,7,19,50,5,48,44,30,20,6,20,0,25,12,49,33,17,34,15,8,47,50,40,2,3,19,8,38,31,50,33,19,6,31,27,12,46}

    {53,14,46,80,50,59,23,35,99,36,4,75,74,87,36,31,4,37,43,3,62,72,49,88,85,35,82,53,77,22,85,14,75,0,49,83,68,97,71,47,93,11,71,84,88,25,72,56,65,69}

    Returns: 219.06784713825587

  49. {15,38,22,34,30,40,49,25,23,27,18,25,10,11,13,31,22,34,39,16,26,48,22,24,16,10,25,3,38,48,2,24,34,28,20,2,17,45,42,49,24,24,14,24,14,23,1,7}

    {37,15,68,78,90,14,91,52,80,82,50,32,47,48,46,6,43,99,87,54,21,83,64,20,53,90,90,98,3,32,33,44,88,7,91,72,93,62,30,78,12,39,85,71,96,9,54,62}

    Returns: 142.194239100078

  50. {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50 }

    {72, 38, 4, 99, 39, 52, 12, 18, 40, 66, 27, 42, 95, 95, 10, 43, 57, 93, 21, 68, 46, 74, 78, 35, 100, 81, 36, 32, 94, 12, 74, 14, 47, 30, 77, 57, 78, 0, 95, 98, 46, 68, 42, 42, 47, 13, 76, 90, 78, 85 }

    Returns: 287.2041349848164

  51. {50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 49, 48, 50, 49, 48 }

    {50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 50, 49, 48, 49, 48, 50, 49, 48 }

    Returns: 409.6400243867617

  52. {41, 2, 3, 44, 5, 26, 7, 8, 39, 10, 31, 32, 33, 24, 25, 26, 47, 48, 49, 40, 41, 42, 43, 44, 25, 26, 27, 28, 29, 43, 43, 43, 41, 42, 42, 42, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50 }

    Returns: 294.586925963433

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