Statistics

Problem Statement for "FilmSort"

Problem Statement

You have N reels, numbered 0 through N-1. One of the reels is empty. Each of the others contains a film with some movie. The films are numbered 1 through N-1.

The collection is messed up: the reel numbers don't necessarily match the film numbers, and some films are wound backwards on their reels.

You would like to sort your collection. More precisely, you would like to have it in the state in which reel 0 is empty and each other reel x contains the film x, wound in the correct direction (so that the movie plays forwards, not backwards, when played from the reel).

The only operation you can do is to take a reel with a film and to rewind the film from that reel onto the reel that is currently empty. Note that each such operation reverses the film.

You are given a description of the collection in the int[] reels with N elements. For each i, reel i contains the film abs(reels[i]), and if reels[i] is negative, that film is currently reversed. As a special case, 0 denotes the empty reel.

Find any sequence of at most 5*N operations that sorts the collection. Return the sequence as a int[] containing, for each operation in chronological order, the number of the reel from which you move a film. If there is no such sequence, return {-1} instead.

Definition

Class:
FilmSort
Method:
sort
Parameters:
int[]
Returns:
int[]
Method signature:
int[] sort(int[] reels)
(be sure your method is public)

Notes

  • Any valid solution with at most 5*N operations will be accepted. You are not required to minimize the number of operations.

Constraints

  • N will be between 1 and 50, inclusive.
  • reels will contain exactly N elements.
  • Absolute values of the elements of reels will form a permutation of 0, 1, ..., N-1.

Examples

  1. {0, 1, 2, 3}

    Returns: { }

    This collection is already sorted correctly, no moves are needed.

  2. {-2, 1, 0, 3}

    Returns: {0, 3, 0 }

    The shortest solution has just one operation: rewind the film from reel 0 onto reel 2. Note that this reverses the film. Our solution's output does two more operations after that - to illustrate that you do not have to return the shortest possible solution.

  3. {2, 0, 1, 3}

    Returns: {0, 2, 1, 0 }

    Note that this input cannot be solved in two operations. The sequence of operations {2, 0} produces the collection {0, -1, -2, 3} that is not correct yet: films 1 and 2 are wound incorrectly.

  4. {0, 1, -2}

    Returns: {-1 }

    We are sorry, but there is no way to fix this collection.

  5. {0}

    Returns: { }

  6. {0, 1}

    Returns: { }

  7. {0, -1}

    Returns: {-1 }

  8. {1, 0}

    Returns: {-1 }

  9. {-1, 0}

    Returns: {0 }

  10. {0, 1, 2}

    Returns: { }

  11. {0, 1, -2}

    Returns: {-1 }

  12. {0, -1, 2}

    Returns: {-1 }

  13. {0, -1, -2}

    Returns: {2, 1, 0, 2, 1, 0 }

  14. {0, -2, -1}

    Returns: {-1 }

  15. {0, -2, 1}

    Returns: {2, 1, 0 }

  16. {1, 0, -2}

    Returns: {2, 0, 1, 2, 0 }

  17. {-1, 0, -2}

    Returns: {-1 }

  18. {-1, 0, 2}

    Returns: {0 }

  19. {-1, 2, 0}

    Returns: {-1 }

  20. {-1, -2, 0}

    Returns: {1, 0 }

  21. {0, 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}

    Returns: { }

  22. {0, -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}

    Returns: {-1 }

  23. {0, -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}

    Returns: {-1 }

  24. {0, 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}

    Returns: {49, 1, 0, 49, 1, 48, 0, 1, 48, 0, 47, 1, 0, 47, 1, 45, 0, 1, 45, 0, 43, 1, 0, 43, 1, 41, 0, 1, 41, 0, 40, 1, 0, 40, 1, 37, 0, 1, 37, 0, 34, 1, 0, 34, 1, 33, 0, 1, 33, 0, 32, 1, 0, 32, 1, 31, 0, 1, 31, 0, 29, 1, 0, 29, 1, 28, 0, 1, 28, 0, 25, 1, 0, 25, 1, 24, 0, 1, 24, 0, 23, 1, 0, 23, 1, 19, 0, 1, 19, 0, 14, 1, 0, 14, 1, 13, 0, 1, 13, 0, 12, 1, 0, 12, 1, 11, 0, 1, 11, 0, 9, 1, 0, 9, 1, 5, 0, 1, 5, 0, 4, 1, 0, 4, 1, 3, 0, 1, 3, 0 }

  25. {0, -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}

    Returns: {-1 }

  26. {-17, 8, 46, 4, 39, -3, -43, -28, 18, 30, 38, 0, 49, -9, 37, -23, 14, 47, 42, 13, -41, -2, 33, 25, 48, -5, -34, -26, 12, -22, -44, 11, 29, 24, 1, 35, 20, -16, -40, 36, -32, -15, 45, 31, 21, 27, -10, 7, 19, 6}

    Returns: {12, 49, 11, 24, 48, 11, 17, 47, 11, 2, 46, 11, 42, 45, 11, 44, 30, 43, 6, 18, 42, 6, 41, 20, 40, 38, 4, 39, 38, 0, 10, 38, 0, 14, 37, 0, 36, 4, 34, 26, 22, 33, 26, 20, 32, 26, 31, 30, 0, 9, 30, 0, 29, 20, 28, 7, 18, 27, 7, 18, 26, 7, 23, 25, 7, 24, 22, 23, 15, 0, 22, 15, 21, 11, 20, 9, 7, 19, 9, 8, 18, 9, 17, 10, 14, 16, 10, 6, 15, 10, 14, 0, 10, 14, 0, 13, 7, 11, 12, 7, 11, 8, 2, 10, 8, 0, 9, 8, 0, 1, 8, 0, 7, 1, 0, 6, 1, 5, 2, 3, 4, 2, 1, 3, 2, 1, 0, 2, 1, 0 }

  27. {0, -29, 31, 19, -38, 16, -28, 12, -33, 27, 42, 23, -34, -18, -14, -24, 35, -43, -1, -30, -36, -26, -2, -41, -21, 7, 20, -17, 39, 13, 3, 22, 25, 8, 40, 46, 44, -45, 32, 9, -5, 11, 15, -6, 37, -10, 4}

    Returns: {35, 46, 0, 45, 37, 36, 44, 37, 43, 17, 10, 42, 17, 41, 23, 34, 40, 23, 28, 39, 23, 38, 4, 37, 36, 20, 16, 35, 20, 34, 12, 33, 8, 32, 23, 2, 31, 23, 30, 19, 29, 1, 28, 6, 9, 27, 6, 26, 21, 25, 8, 24, 15, 11, 23, 15, 22, 2, 8, 21, 2, 20, 6, 3, 19, 6, 18, 13, 9, 17, 13, 5, 16, 13, 15, 10, 14, 0, 10, 14, 0, 3, 13, 0, 7, 12, 0, 9, 11, 0, 1, 9, 0, 7, 8, 0, 7, 1, 0, 7, 1, 6, 4, 2, 5, 4, 0, 2, 4, 0, 2, 3, 0, 2, 1, 0, 2, 1, 0 }

  28. {47, -21, -28, -29, 18, -35, 41, 37, 11, -9, 38, 0, 4, -39, 45, 43, -13, -7, 6, -32, 30, 8, -15, 24, -46, -42, -10, -20, -19, 27, 34, -22, -5, 33, 23, -26, 12, -40, 1, -3, -25, 17, 14, 49, 44, -36, -2, 16, -31, 48}

    Returns: {43, 49, 11, 48, 43, 0, 47, 43, 46, 24, 14, 45, 24, 15, 43, 24, 42, 25, 6, 41, 25, 40, 37, 39, 13, 10, 38, 13, 7, 37, 13, 14, 36, 13, 35, 5, 30, 34, 5, 32, 19, 11, 31, 19, 20, 30, 19, 29, 3, 28, 2, 27, 19, 13, 26, 19, 23, 24, 19, 20, 23, 19, 11, 22, 19, 21, 1, 2, 20, 1, 3, 19, 1, 4, 18, 1, 17, 6, 16, 0, 11, 15, 0, 2, 14, 0, 6, 13, 0, 2, 12, 0, 8, 11, 0, 10, 6, 9, 0, 6, 9, 0, 3, 8, 0, 1, 7, 0, 6, 4, 2, 1, 3, 2, 1, 0 }

  29. {-40, -21, -12, -6, -11, -10, -22, 31, -7, -25, 20, 36, 32, -30, 14, 47, -5, 0, 28, 23, 35, -17, -13, 26, 18, 38, 19, 33, -43, -39, 3, -42, -1, 46, 48, 15, 2, 4, -44, -16, 29, -41, -34, 24, -9, 8, -37, 27, -45}

    Returns: {-1 }

  30. {-45, 26, 5, 30, 18, 0, 7, 28, 22, -16, 9, -42, 19, -39, 38, 4, 3, 8, 43, 41, -17, 32, -37, 1, -21, -35, -25, -12, 6, 27, -29, -10, 31, 11, -24, 23, 2, -15, 13, -44, 40, -20, 33, -46, -34, 14, -36}

    Returns: {-1 }

  31. {-28, -11, -31, 38, 23, 2, 1, 22, -35, 8, -27, 25, 0, 12, 45, -17, -5, 6, -18, -26, 40, -46, 39, 7, -33, 13, -10, -9, -15, -43, -48, -47, 32, 29, -37, -4, 41, 16, -24, 19, -20, 3, 14, 30, 44, -36, -21, -42, -34}

    Returns: {48, 30, 47, 31, 46, 21, 14, 45, 21, 43, 29, 30, 42, 29, 36, 41, 29, 20, 40, 29, 22, 39, 29, 3, 38, 29, 37, 34, 14, 36, 34, 35, 8, 12, 34, 8, 33, 24, 31, 2, 30, 21, 29, 8, 28, 0, 27, 10, 26, 19, 11, 25, 19, 3, 24, 19, 4, 23, 19, 7, 22, 19, 3, 21, 19, 0, 7, 19, 0, 18, 1, 0, 18, 1, 17, 15, 16, 3, 8, 15, 3, 2, 14, 3, 13, 11, 12, 3, 11, 0, 7, 9, 0, 8, 7, 4, 6, 1, 0, 5, 1, 4, 3, 2, 0 }

  32. {9, -4, -32, -47, 22, 19, 13, 11, -5, -41, 39, 18, -2, 37, 0, -30, -29, 7, 3, 26, -42, -24, 14, 8, -23, -48, 16, -38, -27, 21, 44, 12, 20, -17, -15, 36, -10, 31, 40, -46, 45, -1, 35, 6, 33, -34, 28, -43, -25}

    Returns: {-1 }

  33. {0, 27, 47, -36, 33, 25, 24, -7, 45, -17, 48, -3, 8, 10, -6, -20, -4, 13, 16, -31, -12, -22, -42, -44, -21, -28, -9, -26, -1, 23, -34, 32, 39, -38, -41, -43, 37, -11, -29, 18, -15, 46, 30, 35, -2, 14, -19, -5, -40}

    Returns: {10, 48, 0, 2, 47, 0, 41, 46, 0, 8, 45, 0, 44, 23, 43, 35, 42, 22, 41, 34, 10, 40, 34, 32, 39, 34, 38, 33, 36, 37, 33, 36, 3, 35, 23, 34, 30, 4, 33, 30, 31, 32, 30, 31, 19, 3, 30, 19, 29, 23, 28, 25, 1, 27, 25, 1, 26, 25, 0, 5, 25, 0, 6, 24, 0, 23, 19, 22, 21, 0, 6, 21, 0, 20, 15, 3, 18, 15, 17, 9, 16, 3, 10, 15, 3, 14, 8, 10, 13, 8, 0, 12, 8, 4, 11, 8, 10, 0, 8, 10, 0, 1, 9, 0, 8, 1, 0, 8, 1, 7, 0, 1, 7, 0, 3, 6, 0, 2, 5, 0, 4, 1, 3, 0, 2, 1, 0, 2, 1, 0 }

  34. {32, 4, -27, 40, 1, 23, -36, -17, -16, 28, 19, 35, 20, -21, -26, -7, 24, 45, 34, -30, -31, -41, 10, 0, 8, 22, 37, 12, -15, -38, -3, -13, 42, -6, -2, -39, 29, 46, -33, -18, -5, 11, -44, 14, 43, 25, -9}

    Returns: {37, 46, 23, 17, 45, 23, 44, 42, 43, 23, 32, 42, 23, 41, 21, 3, 40, 21, 39, 35, 38, 29, 26, 37, 29, 36, 6, 11, 35, 6, 18, 34, 6, 33, 11, 0, 32, 11, 31, 20, 30, 19, 29, 0, 19, 29, 0, 9, 28, 0, 27, 2, 26, 14, 25, 17, 16, 24, 17, 5, 23, 17, 22, 14, 21, 13, 12, 20, 13, 10, 19, 13, 18, 14, 17, 7, 16, 8, 9, 15, 8, 10, 14, 8, 11, 13, 8, 12, 0, 5, 11, 0, 10, 1, 0, 10, 1, 2, 9, 1, 7, 8, 1, 7, 2, 3, 5, 2, 0, 4, 2, 1, 3, 2, 1, 0 }

  35. {-32, 46, -43, -19, 42, 24, 0, -33, -25, 28, 18, 30, 26, 44, 20, -10, -7, 29, -17, -2, -40, -31, -21, -22, 12, -5, 37, 4, -1, 27, 39, -34, 6, -15, 8, 35, 14, 38, -23, 11, 41, 47, 36, -45, -13, 3, -9, 16}

    Returns: {-1 }

  36. {12, -26, -44, 36, -5, -10, -43, -4, -23, 33, 24, -3, -19, 9, -49, -31, 18, -27, -40, 48, 20, -13, 25, 38, -15, -45, -14, -32, 8, -47, 37, -39, -11, -28, -29, 41, 0, 42, 22, -46, -6, 17, 30, 16, -21, -1, -7, -34, 2, 35}

    Returns: {-1 }

  37. {-20, -21, -23, -31, 37, 34, -24, 6, -39, 14, 7, -18, 0, -25, 3, -35, -46, 30, -8, -42, 11, -28, 10, -36, -13, -26, -9, -16, 1, -29, -5, -33, -19, -2, 12, 17, 41, -15, -22, 4, -38, -40, -45, 27, -32, -44, 43}

    Returns: {-1 }

  38. {21, 29, -20, 0, -5, 11, 12, -30, -25, 9, 33, 17, 3, -14, -32, 13, 4, 45, 34, -31, 46, -40, -23, -43, 8, -22, 1, -6, -41, 42, 36, 26, -19, -35, 44, -2, 39, 15, -16, 37, -27, 28, 7, 18, -10, -24, 38}

    Returns: {20, 46, 3, 17, 45, 3, 34, 44, 3, 43, 23, 29, 42, 23, 41, 28, 40, 21, 36, 39, 21, 38, 20, 37, 36, 0, 30, 36, 0, 35, 33, 18, 34, 33, 0, 10, 33, 0, 32, 14, 31, 19, 30, 7, 1, 29, 7, 28, 23, 27, 7, 26, 14, 25, 8, 17, 24, 8, 23, 22, 0, 14, 22, 0, 21, 19, 20, 2, 14, 19, 2, 18, 3, 11, 17, 3, 16, 0, 15, 14, 13, 0, 6, 12, 0, 5, 11, 0, 2, 10, 0, 8, 5, 1, 7, 5, 0, 6, 5, 4, 3, 1, 0, 3, 1, 2, 0, 1, 2, 0 }

  39. {-43, -47, -8, 33, 31, -13, -32, 7, -38, 19, 35, -17, 14, 23, 41, 18, -28, 44, -21, -6, 11, 0, 39, 45, 5, -42, 4, 1, -40, -20, 27, 3, -36, -34, -22, -46, 9, 10, 2, 30, -26, -25, -29, -37, 16, -24, -12, -15}

    Returns: {-1 }

  40. {-40, -18, -47, -4, 14, -35, 0, 19, -21, 6, 36, -27, -34, 3, -12, -24, 22, 41, 9, -30, -1, 33, 15, 48, -25, 17, 37, -16, 5, 13, 11, -49, -38, -45, -43, -2, -10, -44, 29, 31, -28, 23, -20, 26, 46, -32, 39, -8, -7, -42}

    Returns: {49, 31, 23, 48, 31, 47, 2, 44, 46, 2, 45, 33, 44, 37, 43, 34, 6, 42, 34, 17, 41, 34, 40, 0, 33, 39, 0, 38, 32, 26, 37, 32, 10, 36, 32, 35, 5, 34, 12, 21, 33, 12, 2, 32, 12, 21, 31, 12, 30, 19, 29, 0, 28, 5, 27, 11, 25, 24, 15, 23, 17, 16, 22, 17, 21, 8, 6, 20, 8, 7, 19, 8, 18, 1, 17, 11, 5, 16, 11, 5, 15, 11, 4, 14, 11, 7, 13, 11, 4, 12, 11, 0, 4, 11, 0, 9, 8, 1, 5, 7, 1, 6, 0, 5, 4, 3, 0, 2, 1, 0, 2, 1, 0 }

  41. {22, -27, 11, 37, -24, 12, -43, -32, 41, -14, -7, 0, 28, 16, 13, -21, -1, 42, -38, 31, 45, 25, 34, 3, -10, 30, -9, 18, 44, 29, -6, -39, 26, 20, 17, -8, 2, 4, 36, 5, -15, 35, -46, -23, 19, 40, 33}

    Returns: {46, 42, 20, 45, 42, 28, 44, 42, 43, 6, 17, 42, 6, 8, 41, 6, 40, 20, 39, 31, 38, 18, 3, 37, 18, 36, 31, 35, 8, 22, 34, 8, 33, 11, 32, 7, 19, 31, 7, 25, 30, 7, 12, 28, 7, 27, 1, 26, 11, 21, 25, 11, 24, 4, 23, 17, 0, 22, 17, 21, 15, 20, 8, 12, 19, 8, 18, 7, 0, 17, 7, 13, 16, 7, 6, 15, 7, 14, 9, 13, 7, 5, 12, 7, 2, 11, 7, 10, 2, 1, 9, 2, 8, 5, 6, 0, 4, 3, 1, 0, 3, 1, 2, 0, 1, 2, 0 }

  42. {-24, 22, -39, -30, 32, 6, -1, -8, 45, -27, 37, 26, -40, 43, -25, 11, -3, -41, 4, -10, 13, -9, -17, -34, 14, 16, 15, 23, -29, 0, 42, -2, -12, -28, -35, -21, -33, 20, -7, -36, 38, 46, 44, 18, -19, 5, -31}

    Returns: {-1 }

  43. {-23, -11, -17, 0, -25, -31, -28, -41, -20, 22, -37, -15, -42, -18, 34, -43, 4, 1, 21, -7, 47, 12, 46, -24, 3, 39, -13, 5, 8, -48, -16, 14, -44, -36, 33, 40, 32, -29, 26, -19, 49, 30, -9, -2, -35, 45, -10, -6, 27, 38}

    Returns: {-1 }

  44. {-13, 25, 34, -27, -2, -26, 11, 10, 35, 38, 29, -3, 44, -23, -36, -18, 41, -40, 42, 45, -1, -31, -4, 37, -17, -8, -16, 24, 32, -12, 43, 33, -6, -20, -30, -5, 19, -7, 14, -22, 46, 15, -9, 0, 28, 21, 39}

    Returns: {40, 46, 43, 19, 45, 43, 12, 44, 43, 0, 30, 43, 0, 18, 42, 0, 16, 41, 0, 40, 17, 0, 39, 17, 9, 38, 17, 23, 37, 17, 36, 14, 8, 35, 14, 2, 34, 14, 31, 33, 14, 28, 32, 14, 31, 21, 2, 30, 21, 10, 29, 21, 28, 12, 27, 3, 26, 5, 1, 25, 5, 24, 12, 23, 13, 0, 22, 13, 21, 19, 20, 14, 19, 17, 18, 15, 5, 17, 15, 3, 16, 15, 0, 3, 15, 0, 14, 9, 2, 13, 9, 10, 12, 9, 6, 11, 9, 7, 10, 9, 0, 5, 9, 0, 1, 8, 0, 7, 1, 0, 7, 1, 6, 2, 5, 0, 3, 4, 0, 3, 1, 2, 0 }

  45. {2, 28, 47, 29, 33, 43, 32, 6, 12, 19, -10, 4, -17, -9, 22, 40, 15, 45, 11, 30, -8, 0, -27, -38, 36, 20, 5, -13, 31, 41, -37, 21, -3, -35, 24, -46, -16, -25, -26, -42, 39, 34, 44, 18, 7, 1, 23, -14}

    Returns: {2, 47, 21, 46, 35, 17, 45, 35, 42, 44, 35, 5, 43, 35, 42, 39, 29, 41, 39, 15, 40, 39, 15, 38, 23, 37, 30, 24, 36, 30, 35, 33, 34, 29, 4, 33, 29, 6, 32, 29, 28, 31, 29, 19, 30, 29, 0, 3, 29, 0, 1, 28, 0, 27, 22, 15, 26, 22, 23, 25, 22, 4, 24, 22, 23, 21, 14, 22, 21, 0, 1, 21, 0, 20, 14, 9, 19, 14, 18, 5, 17, 12, 16, 4, 15, 12, 2, 14, 12, 1, 13, 12, 0, 8, 12, 0, 2, 11, 0, 10, 1, 0, 10, 1, 0, 9, 1, 0, 7, 1, 6, 0, 4, 5, 0, 4, 2, 3, 1, 2, 0, 1, 2, 0 }

  46. {34, 41, 3, 17, 28, -9, -39, 38, 0, 49, -11, -36, -48, 23, -47, -22, 44, 1, -45, 8, 26, -13, 25, 29, -12, -16, 6, 2, 21, -40, -4, 7, 19, 18, 35, 14, -46, -27, -20, 31, -15, 5, -42, -32, 24, 43, 33, 30, 10, -37}

    Returns: {9, 49, 8, 48, 12, 47, 14, 46, 36, 45, 18, 16, 44, 18, 43, 36, 42, 0, 36, 42, 0, 1, 41, 0, 40, 29, 39, 6, 7, 38, 6, 9, 37, 6, 36, 11, 34, 35, 11, 34, 6, 33, 14, 18, 32, 14, 31, 29, 30, 12, 23, 29, 12, 4, 28, 12, 9, 27, 12, 20, 26, 12, 22, 25, 12, 24, 16, 13, 23, 16, 22, 15, 21, 4, 7, 20, 4, 19, 18, 6, 3, 17, 6, 16, 0, 6, 16, 0, 6, 15, 0, 11, 14, 0, 13, 6, 11, 10, 8, 9, 5, 8, 4, 7, 6, 4, 5, 1, 4, 0, 2, 3, 0, 2, 1, 0 }

  47. {24, 46, -38, -1, -13, -16, 47, -39, -3, -21, 44, 27, 23, 11, 9, 22, 10, -19, 25, 30, -15, 5, -8, 43, -18, 6, 32, 2, 35, 45, -14, 12, 41, -29, -40, -37, -33, -36, -31, 0, 20, 7, 17, -34, 28, 26, -42, -4}

    Returns: {6, 47, 39, 1, 46, 39, 29, 45, 39, 10, 44, 39, 23, 43, 39, 1, 42, 39, 32, 41, 39, 40, 34, 39, 7, 38, 2, 37, 35, 2, 36, 35, 0, 28, 35, 0, 23, 34, 0, 2, 33, 0, 26, 32, 0, 7, 31, 0, 19, 30, 0, 2, 29, 0, 28, 10, 11, 27, 10, 2, 26, 10, 18, 25, 10, 24, 0, 12, 23, 0, 15, 22, 0, 21, 9, 12, 20, 9, 19, 17, 10, 18, 17, 1, 16, 5, 12, 15, 5, 14, 9, 13, 4, 12, 7, 11, 9, 10, 1, 9, 5, 4, 8, 5, 7, 2, 1, 6, 2, 5, 0, 4, 1, 3, 0 }

  48. {-23, -31, 14, 42, 37, -27, 18, 19, 34, 0, -33, -15, -30, 4, -26, 29, 48, -47, -17, -9, -24, -6, -16, 35, 39, 38, -10, 44, -5, 36, -32, -7, -13, 21, -25, -22, -49, 20, -12, 3, -40, 2, 46, 43, -41, 8, -1, -45, -28, 11}

    Returns: {-1 }

  49. {17, -13, 21, 48, -29, -31, -25, 27, 15, 40, -12, 36, 42, 9, -26, -8, 2, 0, -22, -38, 1, 11, 5, -45, 23, -32, -14, -35, 10, 20, -18, 30, -28, -41, -19, -6, -46, 37, 43, -7, 44, 39, -24, 3, -4, -33, -34, 16, -47}

    Returns: {3, 48, 17, 3, 47, 17, 46, 36, 45, 23, 40, 44, 23, 38, 43, 23, 12, 42, 23, 41, 33, 9, 40, 33, 39, 23, 38, 19, 11, 36, 19, 35, 27, 17, 34, 27, 33, 11, 32, 25, 31, 5, 30, 25, 29, 4, 11, 28, 4, 7, 27, 4, 26, 14, 25, 6, 12, 24, 6, 23, 12, 22, 18, 2, 21, 18, 14, 20, 18, 17, 19, 18, 0, 5, 18, 0, 5, 17, 0, 16, 3, 8, 15, 3, 4, 14, 3, 13, 1, 12, 10, 11, 2, 9, 3, 5, 6, 3, 1, 5, 3, 2, 4, 3, 1, 2, 0 }

  50. {-40, -30, -16, 48, -47, -20, 7, 2, 29, -41, 23, -37, 14, -35, 38, -39, -15, -9, 27, 3, 21, 24, -19, 28, 36, -8, 0, 13, -45, 34, -44, 22, 31, -49, -11, -12, -1, -4, -6, 18, -43, 25, 5, 26, -46, -10, -17, 42, -33, -32}

    Returns: {49, 33, 3, 48, 33, 47, 4, 46, 44, 45, 28, 44, 30, 43, 40, 42, 33, 41, 9, 40, 0, 39, 15, 14, 38, 15, 37, 11, 24, 36, 11, 35, 13, 29, 34, 13, 3, 33, 13, 26, 32, 13, 31, 26, 30, 1, 8, 29, 1, 23, 28, 1, 18, 27, 1, 3, 25, 1, 21, 24, 1, 10, 23, 1, 22, 13, 20, 21, 13, 20, 5, 1, 19, 5, 18, 0, 4, 17, 0, 16, 2, 0, 15, 2, 12, 14, 2, 5, 13, 2, 11, 12, 2, 11, 8, 10, 0, 8, 10, 0, 4, 9, 0, 3, 8, 0, 6, 7, 0, 6, 2, 5, 4, 0, 3, 4, 0, 3, 1, 2, 0 }

  51. {32, -25, 0, 12, -4, 48, 7, 38, 42, -23, -34, 35, 49, 3, 40, 24, -47, 18, -11, -45, 16, -43, -8, -6, 5, -41, -36, -37, 9, 30, 15, -46, 22, 39, -19, 44, -33, 31, -10, 20, 21, 14, 17, 1, -27, 26, 2, 28, 13, -29}

    Returns: {12, 49, 2, 5, 48, 2, 47, 16, 46, 31, 45, 19, 35, 44, 19, 43, 21, 8, 42, 21, 41, 25, 14, 40, 25, 33, 39, 25, 7, 38, 25, 37, 27, 36, 26, 11, 35, 26, 34, 10, 27, 33, 10, 0, 32, 10, 31, 25, 29, 30, 25, 12, 29, 25, 28, 2, 27, 11, 10, 26, 11, 25, 1, 15, 24, 1, 23, 9, 22, 0, 21, 14, 20, 2, 19, 10, 17, 18, 10, 17, 8, 16, 14, 12, 15, 14, 1, 0, 14, 1, 13, 5, 3, 12, 5, 11, 10, 0, 7, 10, 0, 9, 5, 8, 0, 6, 7, 0, 6, 1, 0, 6, 1, 5, 3, 4, 0, 3, 4, 0, 3, 1, 0, 3, 1, 0, 2, 1, 0 }

  52. {32, 29, 7, 36, -27, -43, -45, -17, -12, 9, 4, -11, -8, 0, 44, -14, 23, -33, -22, -30, -39, -13, 3, -40, -25, -46, -18, 6, 26, 10, -38, -24, 1, -2, 19, -20, 35, -16, 41, -15, 28, -31, -5, -21, -34, 37, -42}

    Returns: {46, 25, 45, 6, 14, 44, 6, 43, 5, 13, 42, 5, 38, 41, 5, 40, 23, 39, 20, 38, 30, 37, 25, 3, 36, 25, 35, 3, 14, 34, 3, 33, 17, 0, 32, 17, 31, 20, 30, 19, 1, 29, 19, 28, 5, 27, 4, 26, 19, 25, 24, 0, 17, 24, 0, 16, 23, 0, 22, 18, 6, 21, 18, 20, 19, 14, 4, 18, 14, 17, 7, 16, 4, 7, 15, 4, 7, 14, 4, 6, 13, 4, 12, 8, 11, 0, 8, 11, 0, 10, 1, 4, 8, 1, 2, 7, 1, 6, 5, 0, 1, 5, 0, 4, 1, 3, 0, 2, 1, 0 }

  53. {-35, -30, 6, -7, -17, 38, 4, 10, 18, 16, -23, -12, 41, -14, 33, 19, 29, 15, 48, 42, -22, 3, -40, 36, -20, -5, 11, -8, -9, 21, 45, -28, 24, 0, 39, 37, 2, -44, 32, -13, 46, -47, -34, -31, -27, 25, -43, -26, 1}

    Returns: {-1 }

  54. {-26, -44, 12, 14, -37, -25, 43, -36, 19, -9, -45, -39, -29, -20, -7, -3, 34, 24, 2, 31, 4, -35, -33, 38, 0, -41, -18, -13, 40, -30, -16, -21, -10, 46, -22, -15, -17, 32, -6, 23, 28, -5, -11, 42, 27, -8, -1, 47}

    Returns: {-1 }

  55. {19, -23, -1, 8, 9, -22, -15, -10, -45, -28, 38, -31, 44, 6, -7, 0, 46, 42, -35, -48, 25, -12, 34, 14, 41, -36, 39, -20, 16, -18, -47, -26, 11, -40, -4, 17, 27, -5, -30, 24, -43, 2, -32, 21, 33, 37, -13, 3, -29}

    Returns: {-1 }

  56. {17, -7, -34, 8, 27, 45, 23, 14, -25, -41, 43, -32, -36, 1, 11, -12, -28, 6, 5, 39, 10, -9, 2, -15, 37, 19, 13, 0, -46, 48, 20, -24, -22, -29, 3, -18, -26, -33, 47, 42, 38, 40, -16, -31, -21, 4, 44, -30, -35}

    Returns: {29, 48, 27, 38, 47, 27, 46, 28, 5, 45, 28, 44, 27, 10, 43, 27, 39, 42, 27, 41, 9, 40, 27, 19, 39, 27, 38, 9, 24, 37, 9, 36, 12, 29, 35, 12, 34, 2, 24, 33, 2, 32, 11, 10, 31, 11, 30, 27, 24, 29, 27, 28, 16, 4, 27, 16, 9, 26, 16, 25, 8, 10, 24, 8, 6, 23, 8, 2, 22, 8, 4, 21, 8, 20, 11, 19, 16, 10, 18, 16, 0, 17, 16, 0, 11, 16, 0, 6, 15, 0, 7, 14, 0, 13, 9, 6, 12, 9, 11, 7, 10, 8, 4, 9, 8, 0, 3, 8, 0, 7, 1, 6, 4, 5, 0, 3, 1, 2, 0, 1, 2, 0 }

  57. {25, 19, 43, -6, 34, -30, -44, -29, -20, 31, -48, -1, -22, -33, 14, 37, -35, -47, 40, -38, 36, -11, -2, 42, 9, -15, -32, 7, 23, 10, 49, -45, -24, 18, -5, -12, -8, -21, 0, -27, -16, -41, -39, -3, 4, -28, 26, 46, 17, -13}

    Returns: {-1 }

  58. {9, 2, -38, 44, 27, 21, -31, 24, -30, -39, 3, -18, -6, -17, -22, 13, 20, -35, -23, 45, -26, -33, 47, 0, 48, -34, -12, 43, -42, 15, 1, -5, -7, -11, 4, -19, 37, -41, 46, -25, 40, -8, 14, 10, -36, 16, -32, 29, 28}

    Returns: {-1 }

  59. {-34, -28, 0, 22, -27, -35, 18, 26, -16, -19, -13, -2, -30, -20, 40, -11, 45, -23, -3, -33, 1, -7, 31, 6, 17, -4, -41, -14, -10, -21, 32, 36, -39, 12, 37, -42, -38, -44, 43, -24, -9, 5, 8, 47, 29, -46, 15, 25}

    Returns: {43, 47, 2, 46, 45, 0, 16, 45, 0, 44, 37, 38, 43, 37, 42, 35, 41, 26, 14, 40, 26, 39, 32, 38, 36, 34, 37, 36, 0, 31, 36, 0, 35, 5, 34, 16, 33, 19, 30, 32, 19, 22, 31, 19, 30, 12, 22, 29, 12, 28, 1, 27, 4, 7, 26, 4, 25, 19, 24, 7, 23, 17, 3, 22, 17, 21, 3, 20, 13, 19, 9, 6, 18, 9, 13, 17, 9, 16, 8, 15, 2, 1, 14, 2, 13, 10, 9, 12, 10, 8, 11, 10, 9, 1, 8, 5, 2, 7, 5, 2, 6, 5, 1, 0, 5, 1, 3, 2, 0 }

  60. {-14, -27, -34, 37, -12, 23, 35, 38, 25, 41, 29, -11, -42, -18, 32, 9, -44, -40, 8, 19, 39, 21, 22, 7, 5, 31, 2, 17, 0, -13, -24, -16, -43, 15, 28, -1, 30, -10, 6, 46, -45, 33, -36, 26, 3, -4, -20}

    Returns: {-1 }

  61. {-13, -1, 3, 15, 44, 12, -5, -34, -43, -37, -32, -39, -42, -23, -17, -40, -19, 6, -30, 10, -38, -45, -33, 35, -28, 21, -11, 29, 0, 31, 25, 22, -41, 46, 20, -27, -24, -18, 8, 16, 4, -9, 2, 7, 36, 14, 26}

    Returns: {33, 46, 28, 45, 21, 4, 44, 21, 43, 8, 42, 12, 41, 32, 40, 15, 39, 11, 38, 20, 37, 9, 36, 4, 23, 35, 4, 34, 7, 33, 22, 32, 10, 29, 31, 10, 30, 18, 27, 29, 18, 28, 24, 23, 27, 24, 7, 26, 24, 25, 10, 9, 24, 10, 23, 13, 10, 22, 13, 9, 21, 13, 20, 4, 19, 16, 18, 13, 17, 14, 16, 15, 0, 3, 15, 0, 13, 3, 5, 12, 3, 7, 11, 3, 10, 4, 9, 5, 7, 8, 5, 7, 4, 0, 6, 4, 0, 5, 4, 0, 3, 4, 0, 2, 3, 0, 2, 1, 0, 2, 1, 0 }

  62. {-28, 15, 38, 41, -24, -12, 0, 29, -11, 35, -17, 27, -30, 25, 6, 9, 8, -39, -22, 46, 32, 44, 4, 34, 21, -16, -7, 18, 26, -5, -1, -10, -33, -23, -20, -31, 13, 43, -2, -19, 14, -45, -37, -42, 3, -40, -36}

    Returns: {-1 }

  63. {26, 28, -20, 21, -38, -17, -42, 4, 16, -39, 34, 10, 3, 19, -29, 1, 15, 23, 6, 11, 8, 22, 5, 46, 41, 18, -2, -35, -45, 9, 24, -30, -27, 7, 14, -32, -47, -43, 0, -44, -33, -36, -13, -40, -25, -37, -31, -12}

    Returns: {-1 }

  64. {22, -48, 15, 26, 34, 43, 21, 23, -30, -42, -49, -33, -24, -8, -11, 7, 19, -12, 1, 35, -38, -25, 0, 4, -18, 5, -6, 27, -45, -36, -13, 40, 39, 29, 47, -10, -31, -16, 3, -46, 17, 37, -32, -44, 41, -28, 9, -2, -14, 20}

    Returns: {-1 }

  65. {15, 45, 11, 33, 10, -3, -5, -1, 0, 19, -17, -30, -12, 2, -18, 20, -39, -29, -26, -41, 32, -31, 46, -23, 16, 6, -8, -21, -24, 38, -42, 40, -43, 14, -7, 4, 34, 36, -35, 9, 27, -25, 44, 13, -28, -22, 37}

    Returns: {22, 46, 8, 1, 45, 8, 42, 44, 8, 43, 32, 42, 30, 41, 19, 31, 40, 19, 39, 16, 29, 38, 16, 37, 22, 36, 16, 29, 35, 16, 34, 22, 3, 33, 22, 20, 32, 22, 31, 21, 30, 11, 29, 17, 20, 28, 17, 22, 27, 17, 26, 18, 25, 21, 20, 24, 21, 23, 0, 21, 23, 0, 1, 22, 0, 21, 1, 15, 20, 1, 9, 19, 1, 18, 14, 17, 10, 15, 16, 10, 15, 0, 14, 3, 13, 8, 12, 0, 8, 12, 0, 2, 11, 0, 4, 10, 0, 7, 4, 1, 6, 4, 1, 5, 4, 2, 1, 3, 2, 0, 1, 2, 0 }

  66. {0, 31, -10, -5, -3, 48, 21, 8, -28, -25, -36, -23, 32, 45, -13, 26, 27, 17, 29, -43, -11, -47, 49, 39, -6, 7, 30, -33, 40, -44, 15, -20, 42, 16, 14, -1, 35, -19, -4, -24, -22, 12, -2, 46, -38, 9, -41, 37, -34, 18 }

    Returns: {22, 49, 0, 5, 48, 0, 47, 21, 43, 46, 21, 13, 45, 21, 44, 29, 43, 19, 32, 42, 19, 41, 29, 28, 40, 29, 23, 39, 29, 21, 38, 29, 37, 0, 36, 10, 35, 0, 5, 34, 0, 33, 27, 12, 32, 27, 1, 31, 27, 26, 30, 27, 18, 29, 27, 28, 8, 16, 27, 8, 15, 26, 8, 25, 9, 23, 24, 9, 23, 11, 16, 22, 11, 6, 21, 11, 1, 20, 11, 19, 18, 0, 16, 18, 0, 16, 1, 0, 16, 1, 14, 5, 1, 13, 5, 11, 12, 5, 0, 11, 5, 10, 2, 1, 9, 2, 7, 8, 2, 1, 6, 2, 5, 3, 1, 4, 3, 0, 1, 3, 0, 2, 1, 0 }

  67. {0, -1, -2, -3, -4 }

    Returns: {4, 1, 0, 4, 1, 3, 0, 1, 3, 0, 2, 1, 0, 2, 1, 0 }

  68. {0, 2, 3, 4, 5, 1 }

    Returns: {4, 5, 0, 3, 4, 0, 2, 3, 0, 1, 2, 0 }

  69. {41, 17, -46, -44, -43, 2, -23, 14, 35, 12, -34, -21, 15, -24, -20, 37, -8, -10, -40, -4, -13, 28, -38, -7, -47, -29, 16, 32, 45, 11, 33, -18, 36, -39, 49, 30, -31, -27, -42, -3, 26, -25, 22, 1, -9, 48, -6, 5, 0, -19 }

    Returns: {34, 49, 48, 0, 45, 48, 0, 47, 24, 46, 2, 28, 45, 2, 44, 3, 43, 4, 42, 38, 41, 28, 40, 18, 39, 33, 38, 22, 15, 37, 22, 32, 36, 22, 8, 35, 22, 34, 10, 30, 33, 10, 27, 32, 10, 31, 27, 30, 8, 29, 25, 21, 28, 25, 15, 27, 25, 21, 26, 25, 0, 15, 25, 0, 24, 13, 23, 6, 22, 4, 21, 11, 20, 14, 6, 19, 14, 10, 18, 14, 1, 17, 14, 4, 16, 14, 12, 15, 14, 0, 7, 14, 0, 11, 13, 0, 9, 12, 0, 11, 8, 1, 10, 8, 2, 9, 8, 0, 4, 8, 0, 4, 7, 0, 4, 6, 0, 2, 5, 0, 4, 1, 0, 4, 1, 0, 3, 1, 2, 0, 1, 2, 0 }

  70. {0, -1, -2 }

    Returns: {2, 1, 0, 2, 1, 0 }

  71. {0, -1, 2, -3, 4 }

    Returns: {3, 1, 0, 3, 1, 0 }

  72. {27, 21, 19, -28, 6, -29, -20, 4, -48, 42, 30, -35, 45, 44, 10, 43, 3, 34, 14, 8, -49, 0, -41, -18, -22, -15, -7, 37, -24, -1, -23, -36, -39, -12, 13, -32, 46, 38, 2, 33, 47, -25, 5, 17, -31, -16, -40, 9, 11, -26 }

    Returns: {49, 20, 48, 8, 40, 47, 8, 36, 46, 8, 12, 45, 8, 13, 44, 8, 15, 43, 8, 9, 42, 8, 41, 22, 36, 40, 22, 39, 32, 37, 38, 32, 27, 37, 32, 36, 31, 35, 11, 17, 34, 11, 33, 22, 31, 32, 22, 13, 31, 22, 10, 30, 22, 29, 5, 28, 3, 0, 27, 3, 21, 26, 3, 8, 25, 3, 5, 24, 3, 10, 23, 3, 5, 22, 3, 1, 21, 3, 20, 6, 2, 19, 6, 10, 18, 6, 17, 15, 12, 16, 15, 0, 8, 15, 0, 14, 10, 6, 13, 10, 11, 12, 10, 3, 11, 10, 0, 6, 9, 0, 8, 2, 7, 1, 4, 6, 1, 5, 4, 2, 3, 0, 2, 3, 0 }

  73. {0, 1, -2, -4, -3, -8, 7, 6, -5 }

    Returns: {8, 5, 6, 7, 5, 6, 0, 5, 6, 0, 4, 3, 1, 0, 3, 1, 2, 0, 1, 2, 0 }

  74. {0, -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 }

    Returns: {49, 1, 0, 49, 1, 0 }

  75. {0, 49, -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 }

    Returns: {1, 49, 0, 1, 48, 0, 1, 47, 0, 1, 46, 0, 1, 45, 0, 1, 44, 0, 1, 43, 0, 1, 42, 0, 1, 41, 0, 1, 40, 0, 1, 39, 0, 1, 38, 0, 1, 37, 0, 1, 36, 0, 1, 35, 0, 1, 34, 0, 1, 33, 0, 1, 32, 0, 1, 31, 0, 1, 30, 0, 1, 29, 0, 1, 28, 0, 1, 27, 0, 1, 26, 0, 1, 25, 0, 1, 24, 0, 1, 23, 0, 1, 22, 0, 1, 21, 0, 1, 20, 0, 1, 19, 0, 1, 18, 0, 1, 17, 0, 1, 16, 0, 1, 15, 0, 1, 14, 0, 1, 13, 0, 1, 12, 0, 1, 11, 0, 1, 10, 0, 1, 9, 0, 1, 8, 0, 1, 7, 0, 1, 6, 0, 1, 5, 0, 1, 4, 0, 1, 3, 0, 1, 2, 0 }

  76. {0, -1, -2, -3, 4 }

    Returns: {-1 }

  77. {-7, 10, 18, -8, 15, -19, -6, 3, -20, -17, -13, -4, 12, 0, -9, -16, -5, 2, -1, 11, 14 }

    Returns: {-1 }

  78. {-2, -1, 0 }

    Returns: {-1 }

  79. {0, -48, 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 }

    Returns: {48, 1, 47, 0, 46, 1, 45, 0, 44, 1, 43, 0, 42, 1, 41, 0, 40, 1, 39, 0, 38, 1, 37, 0, 36, 1, 35, 0, 34, 1, 33, 0, 32, 1, 31, 0, 30, 1, 29, 0, 28, 1, 27, 0, 26, 1, 25, 0, 24, 1, 23, 0, 22, 1, 21, 0, 20, 1, 19, 0, 18, 1, 17, 0, 16, 1, 15, 0, 14, 1, 13, 0, 12, 1, 11, 0, 10, 1, 9, 0, 8, 1, 7, 0, 6, 1, 5, 0, 4, 1, 3, 0, 2, 1, 0 }

  80. {-2, 9, 10, 1, 6, 15, 11, 7, -5, 13, -20, -14, 3, 12, -19, 18, -8, 4, -17, 0, -16 }

    Returns: {20, 10, 19, 14, 15, 18, 14, 15, 17, 14, 16, 10, 5, 15, 10, 14, 11, 9, 13, 11, 12, 9, 6, 11, 9, 2, 10, 9, 0, 1, 9, 0, 2, 8, 0, 4, 6, 0, 2, 5, 0, 4, 2, 0, 3, 2, 1, 0 }

  81. {-2, 0, 1, -3 }

    Returns: {3, 0, 1, 3, 0, 2, 1, 0 }

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