Statistics

Problem Statement for "PermutationSignature"

Problem Statement

The signature of a permutation is a string that is computed as follows: for each pair of consecutive elements of the permutation, write down the letter 'I' (increasing) if the second element is greater than the first one, otherwise write down the letter 'D' (decreasing).

For example, the signature of the permutation {3,1,2,7,4,6,5} is "DIIDID".

Your task is to reverse this computation: You are given a String signature containing the signature of a permutation. Find and return the lexicographically smallest permutation with the given signature. If no such permutation exists, return an empty int[] instead.

Definition

Class:
PermutationSignature
Method:
reconstruct
Parameters:
String
Returns:
int[]
Method signature:
int[] reconstruct(String signature)
(be sure your method is public)

Notes

  • For any positive integer N, a permutation of N elements is a sequence of length N that contains each of the integers 1 through N exactly once.
  • To compare two permutations A and B, find the smallest index i such that A[i] and B[i] differ. If A[i] < B[i], we say that A is lexicographically smaller than B, and vice versa.

Constraints

  • signature will contain between 1 and 50 characters, inclusive.
  • Each character in signature will be either 'I' or 'D'.

Examples

  1. "IIIII"

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

  2. "DI"

    Returns: {2, 1, 3 }

    There are two permutations with this signature: {3,1,2} and {2,1,3}. You must return the lexicographically smaller one.

  3. "IIIID"

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

  4. "DIIDID"

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

    This is the signature from the problem statement. Note that the correct answer is not the permutation from the problem statement.

  5. "D"

    Returns: {2, 1 }

  6. "I"

    Returns: {1, 2 }

  7. "DD"

    Returns: {3, 2, 1 }

  8. "DI"

    Returns: {2, 1, 3 }

  9. "ID"

    Returns: {1, 3, 2 }

  10. "II"

    Returns: {1, 2, 3 }

  11. "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII"

    Returns: {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, 51 }

  12. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

    Returns: {51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

  13. "DIDIIIDIDIDIDIDIDIIDIDIDIDIDDDDD"

    Returns: {2, 1, 4, 3, 5, 6, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 19, 21, 20, 23, 22, 25, 24, 27, 26, 33, 32, 31, 30, 29, 28 }

  14. "IIIDIDIDIDIIDDIDDDIDDIDIIIIIII"

    Returns: {1, 2, 3, 5, 4, 7, 6, 9, 8, 11, 10, 12, 15, 14, 13, 19, 18, 17, 16, 22, 21, 20, 24, 23, 25, 26, 27, 28, 29, 30, 31 }

  15. "IDIIDIDIDIDIDIDDDDDDDDDDDIIIIIIIIDIDDDDDI"

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

  16. "IDIIDIDIDIDIDIDDDDDDDDDDDIIIIIIIIDIDDDDDIDDDDD"

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

  17. "IDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDID"

    Returns: {1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48, 51, 50 }

  18. "DIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDIDI"

    Returns: {2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 51 }

  19. "IDIDIDIDIDIDIDIDIDIDIIIDIDIDIDIDIDIDIDIDIDIDIDIDID"

    Returns: {1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 22, 23, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48, 51, 50 }

  20. "IDIDIDIDIDIDIDIDIDIDIIIDIDIDIDIDIDIDDDIDIDIDIDIDID"

    Returns: {1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 22, 23, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 35, 34, 39, 38, 37, 36, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48, 51, 50 }

  21. "IIIIIIIIIIIIIIDIDIDIIIIIIIIIIDIIIIIIIIIIIIIIIIII"

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

  22. "IIIIIIIIIIIIIIDIDIDIIIIIIIIIIDIIIIIIIIIIIIIIIIIID"

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

  23. "DIIIIIIIIIIIIIIDIDIDIIIIIIIIIIDIIIIIIIIIIIIIIIIII"

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

  24. "DDDDDDDDDDDDDDDIIDDDDDDIDDDDDDDDDDDDDDDDDDDID"

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

  25. "DIIDIDIDIIDIID"

    Returns: {2, 1, 3, 5, 4, 7, 6, 9, 8, 10, 12, 11, 13, 15, 14 }

  26. "IIIIDIDIDIIDIDIID"

    Returns: {1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 11, 13, 12, 15, 14, 16, 18, 17 }

  27. "DIIDIDIIDIDDIDID"

    Returns: {2, 1, 3, 5, 4, 7, 6, 8, 10, 9, 13, 12, 11, 15, 14, 17, 16 }

  28. "IIIIIIIIDIDIDIDIDII"

    Returns: {1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 19, 20 }

  29. "IDDDIDI"

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

  30. "IIIIIIIIIDIDIDIIIIDIDIDIDDID"

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

  31. "DIIIIIIIDIIIIIIIDIDIDIIIIIIIIDDDDDDD"

    Returns: {2, 1, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 13, 14, 15, 16, 18, 17, 20, 19, 22, 21, 23, 24, 25, 26, 27, 28, 29, 37, 36, 35, 34, 33, 32, 31, 30 }

  32. "DIIDDIIIDIDIDDDDIIIIIIIIIIIDDDIDDDIIIIIIIDIDIDIDI"

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

  33. "IDDDIIDDDIDDDIDDDIDDDDIIDIDIDDDDDDIIDDDDDIDIDDIDDI"

    Returns: {1, 5, 4, 3, 2, 6, 10, 9, 8, 7, 14, 13, 12, 11, 18, 17, 16, 15, 23, 22, 21, 20, 19, 24, 26, 25, 28, 27, 35, 34, 33, 32, 31, 30, 29, 36, 42, 41, 40, 39, 38, 37, 44, 43, 47, 46, 45, 50, 49, 48, 51 }

  34. "DDDDDDDDDDDIIDDDDDDDDDDIIIDDDDDDDDDIDDDDDDDDDDDDD"

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

  35. "DDDDDDDDDIDDDDDDDDIDDDDDDDDDDDDDIIIIIIIDDDDDDDID"

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

  36. "DDDDDIDIDDDDDDDDDDDDIDDDDDDDIIIIDDDDDDIIDDDDDDDDID"

    Returns: {6, 5, 4, 3, 2, 1, 8, 7, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 29, 28, 27, 26, 25, 24, 23, 22, 30, 31, 32, 39, 38, 37, 36, 35, 34, 33, 40, 49, 48, 47, 46, 45, 44, 43, 42, 41, 51, 50 }

  37. "DDD"

    Returns: {4, 3, 2, 1 }

  38. "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII"

    Returns: {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 }

  39. "IDDDDDDDDDDDDDDDDII"

    Returns: {1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 19, 20 }

  40. "DDI"

    Returns: {3, 2, 1, 4 }

  41. "DDDIIIIDDD"

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

  42. "DDDDI"

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

  43. "DDIIIIDIIDDIIDDDDIDIDDD"

    Returns: {3, 2, 1, 4, 5, 6, 8, 7, 9, 12, 11, 10, 13, 18, 17, 16, 15, 14, 20, 19, 24, 23, 22, 21 }

  44. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDIIIIIIIIIIDDDDDDDDDDD"

    Returns: {30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 32, 33, 34, 35, 36, 37, 38, 39, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40 }

  45. "DIDDID"

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

  46. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

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

  47. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

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

  48. "DDDDDDDDDDDDD"

    Returns: {14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

  49. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

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

  50. "DDDDDDDDD"

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

  51. "DDDIDDD"

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

  52. "DDDDDIIIIIDDDDDIIIIIDDDDDIIIIIDDDDDIIIIIDDDDDIIIII"

    Returns: {6, 5, 4, 3, 2, 1, 7, 8, 9, 10, 16, 15, 14, 13, 12, 11, 17, 18, 19, 20, 26, 25, 24, 23, 22, 21, 27, 28, 29, 30, 36, 35, 34, 33, 32, 31, 37, 38, 39, 40, 46, 45, 44, 43, 42, 41, 47, 48, 49, 50, 51 }

  53. "DDDIIIIDDDIIIIIDDDDDDDIIIIIIIIIIIIIDDDDDDDDDDDD"

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

  54. "IDDDDDDDDDDDDDDDDIIDDDDDDDDDDDD"

    Returns: {1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 19, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20 }

  55. "IDDDDDIIDDDDIIDDDDIIDDDIIDDDDDDIIDDDDDDDIIDDDDIIDD"

    Returns: {1, 7, 6, 5, 4, 3, 2, 8, 13, 12, 11, 10, 9, 14, 19, 18, 17, 16, 15, 20, 24, 23, 22, 21, 25, 32, 31, 30, 29, 28, 27, 26, 33, 41, 40, 39, 38, 37, 36, 35, 34, 42, 47, 46, 45, 44, 43, 48, 51, 50, 49 }

  56. "DDIDIIDIIDDDDDDIIIIIIDDDDIIIDDIDIIDIDD"

    Returns: {3, 2, 1, 5, 4, 6, 8, 7, 9, 16, 15, 14, 13, 12, 11, 10, 17, 18, 19, 20, 21, 26, 25, 24, 23, 22, 27, 28, 31, 30, 29, 33, 32, 34, 36, 35, 39, 38, 37 }

  57. "DDDDDD"

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

  58. "DDDDDDIIIIIIIDDDDDDIIIIIIIIIDDDDDDDIIIIIIDIDIDIDDD"

    Returns: {7, 6, 5, 4, 3, 2, 1, 8, 9, 10, 11, 12, 13, 20, 19, 18, 17, 16, 15, 14, 21, 22, 23, 24, 25, 26, 27, 28, 36, 35, 34, 33, 32, 31, 30, 29, 37, 38, 39, 40, 41, 43, 42, 45, 44, 47, 46, 51, 50, 49, 48 }

  59. "DDDDDDDDDDDDDDIIIIIIIIIIIIIIIIIIIIIIDDDDDIIIIIIIII"

    Returns: {15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 42, 41, 40, 39, 38, 37, 43, 44, 45, 46, 47, 48, 49, 50, 51 }

  60. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

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

  61. "IDDDDD"

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

  62. "DDIDIDIDIDDDIDIDIDDDIDDIDIIIDIIDIDIDIDIDIIDIIIDIID"

    Returns: {3, 2, 1, 5, 4, 7, 6, 9, 8, 13, 12, 11, 10, 15, 14, 17, 16, 21, 20, 19, 18, 24, 23, 22, 26, 25, 27, 28, 30, 29, 31, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 42, 44, 43, 45, 46, 48, 47, 49, 51, 50 }

  63. "DDDDIIIIDDIIDDDDIDIDIDDDDD"

    Returns: {5, 4, 3, 2, 1, 6, 7, 8, 11, 10, 9, 12, 17, 16, 15, 14, 13, 19, 18, 21, 20, 27, 26, 25, 24, 23, 22 }

  64. "DIDDDIIDIIDDDDDIIIDDDDDDIIDDIDDDIDIDDDIDIIDIDDD"

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

  65. "DDDDDDDDDDIIIIIIIIIIDDDDDDDDDDIIIIIIIIIIDDDDDIIIII"

    Returns: {11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 32, 33, 34, 35, 36, 37, 38, 39, 40, 46, 45, 44, 43, 42, 41, 47, 48, 49, 50, 51 }

  66. "DDDDDDDDDIDDDDDDDDIDDDDDDDDDIDDDIIDDIIIDIDIIDI"

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

  67. "DDDDIIIIDDDD"

    Returns: {5, 4, 3, 2, 1, 6, 7, 8, 13, 12, 11, 10, 9 }

  68. "DDDDDDDDDDDDDDD"

    Returns: {16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

  69. "DIIIDDDDDDDIDIDIDDDID"

    Returns: {2, 1, 3, 4, 12, 11, 10, 9, 8, 7, 6, 5, 14, 13, 16, 15, 20, 19, 18, 17, 22, 21 }

  70. "DDDDDDDDDDDDDDDDDDDDDDDDIDDDDDDDDDDDDDDDDIDDDDDDDD"

    Returns: {25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43 }

  71. "IIDDDI"

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

  72. "DIDIDI"

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

  73. "DDDIIIIDDDIDIDIDDDD"

    Returns: {4, 3, 2, 1, 5, 6, 7, 11, 10, 9, 8, 13, 12, 15, 14, 20, 19, 18, 17, 16 }

  74. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDI"

    Returns: {50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 51 }

  75. "IIDDI"

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

  76. "DIIDDD"

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

  77. "DIIDIDDIIDIDDIIDIDDIIDIDDIIDIDDIIDIDDIIDIDDIID"

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

  78. "DDDDDDDDIIIIIIIIIIIIIIIIIIIDDDDDDDIIIIIIIIIIIIIIII"

    Returns: {9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 35, 34, 33, 32, 31, 30, 29, 28, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 }

  79. "IDDIIDDDIIIDDDDIIIIDDDDDIIIIIDDDDDDDDDDDDDDDDDDDDI"

    Returns: {1, 4, 3, 2, 5, 9, 8, 7, 6, 10, 11, 16, 15, 14, 13, 12, 17, 18, 19, 25, 24, 23, 22, 21, 20, 26, 27, 28, 29, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 51 }

  80. "DDDDDDDDDDDDDDDDDDD"

    Returns: {20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

  81. "IDD"

    Returns: {1, 4, 3, 2 }

  82. "DDDIIDDDDIIDDDI"

    Returns: {4, 3, 2, 1, 5, 10, 9, 8, 7, 6, 11, 15, 14, 13, 12, 16 }

  83. "DDDDDDDIIDDDIDDIDDDD"

    Returns: {8, 7, 6, 5, 4, 3, 2, 1, 9, 13, 12, 11, 10, 16, 15, 14, 21, 20, 19, 18, 17 }

  84. "DDDIIIDDDIIIDDDIIIDDDIIIDDD"

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

  85. "IDDDDDDDDDDDDIIIIIIIIIIIIIDIID"

    Returns: {1, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 27, 29, 31, 30 }

  86. "DDDDD"

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

  87. "IDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

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

  88. "IIDIDIDDDIDIDIDDDIDIDIDIDIDDDIDIIIDDDIIIIDDDIDIDID"

    Returns: {1, 2, 4, 3, 6, 5, 10, 9, 8, 7, 12, 11, 14, 13, 18, 17, 16, 15, 20, 19, 22, 21, 24, 23, 26, 25, 30, 29, 28, 27, 32, 31, 33, 34, 38, 37, 36, 35, 39, 40, 41, 45, 44, 43, 42, 47, 46, 49, 48, 51, 50 }

  89. "IDDI"

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

  90. "DIIDIDDIIDIDDIIDIDDIIDIDDDIIIDDDDDDDDDDIIIIIII"

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

  91. "IIIDIDIDDIDIDIDIIIDIDIDIIDDDDDIDIDIDDDDDDDIIIIIIID"

    Returns: {1, 2, 3, 5, 4, 7, 6, 10, 9, 8, 12, 11, 14, 13, 16, 15, 17, 18, 20, 19, 22, 21, 24, 23, 25, 31, 30, 29, 28, 27, 26, 33, 32, 35, 34, 43, 42, 41, 40, 39, 38, 37, 36, 44, 45, 46, 47, 48, 49, 51, 50 }

  92. "IDDIDDIDDDIIDIIDIIDIDIDD"

    Returns: {1, 4, 3, 2, 7, 6, 5, 11, 10, 9, 8, 12, 14, 13, 15, 17, 16, 18, 20, 19, 22, 21, 25, 24, 23 }

  93. "DDDDDDDDDDDDDI"

    Returns: {14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15 }

  94. "DDIIDDIIDDII"

    Returns: {3, 2, 1, 4, 7, 6, 5, 8, 11, 10, 9, 12, 13 }

  95. "IDDD"

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

  96. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDIII"

    Returns: {31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 33, 34 }

  97. "DIDIDIDIDIDIDDIIDIDIDIDIDIDIDIDIDIDIIDDIDIDIDIDDI"

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

  98. "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD"

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

  99. "DDIDDI"

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

  100. "DDDIDI"

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

  101. "DIDIDIIDIIDIDDIDIIIIIDDIIIIDDIDIDDIIIDIIDDDDIDIIDI"

    Returns: {2, 1, 4, 3, 6, 5, 7, 9, 8, 10, 12, 11, 15, 14, 13, 17, 16, 18, 19, 20, 21, 24, 23, 22, 25, 26, 27, 30, 29, 28, 32, 31, 35, 34, 33, 36, 37, 39, 38, 40, 45, 44, 43, 42, 41, 47, 46, 48, 50, 49, 51 }

  102. "DDDDDDDDDD"

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

  103. "DIIDIDD"

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

  104. "IIDDDIIDDDIIDDIDDDDDDDDDIIIIDIIDDDIDDIDDDDIIII"

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

  105. "DDDDDDDDDDDDDDDDDDDIDDDDIIDIIIDIIDDDIDIIDDIDIIDDDI"

    Returns: {20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 26, 28, 27, 29, 30, 32, 31, 33, 37, 36, 35, 34, 39, 38, 40, 43, 42, 41, 45, 44, 46, 50, 49, 48, 47, 51 }

  106. "DDDIDDDI"

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

  107. "DIDIIDIDDIIDDIIIDIDDDIIIIDDDDIDIDIDIDIDIDIDIDIDIDI"

    Returns: {2, 1, 4, 3, 5, 7, 6, 10, 9, 8, 11, 14, 13, 12, 15, 16, 18, 17, 22, 21, 20, 19, 23, 24, 25, 30, 29, 28, 27, 26, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 51 }

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