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Problem Statement for "JumpDistancesOnTreeEasy"

Problem Statement

Treeland is a country with n cities, numbered 0 through n-1. Obviously, the topology of Treeland is a tree: there are exactly n-1 bidirectional roads, each connecting two cities in such a way that it is possible to travel from any city to any other city. You are given the description of the road network: the int[] p with n-1 elements. For each valid index i, there is a road that connects the cities i+1 and p[i]. The distance between two cities is the smallest number of roads you need to use in order to travel from one city to the other.

Rabbit Hanako had a trip in Treeland. She started her trip on day 0 in the city x[0] = 0. On each of the following m days she chose a city x[i] (possibly the same as her current city) and traveled there by using the only direct route. Each day she wrote down the distance she traveled - i.e., on day i she wrote down the distance d[i] between the cities x[i-1] and x[i]. After the trip was over, she constructed a set D that contained all values d[i] she wrote down.

For example, if d[1], d[2], ..., d[m] are {1, 0, 0, 1, 3, 5, 0} then the set D will be {0, 1, 3, 5}.

You know that Hanako's trip had the form described above, but you don't know the value m and the values x[i]. You are given a int[] S. Check whether it is possible that S = D. In other words, check whether there are values m and x[1] ... x[m] such that the set of distances D will contain exactly the same elements as the given int[] S.

Return "Possible" if such a trip exists and "Impossible" if it does not.

Definition

Class:
JumpDistancesOnTreeEasy
Method:
isPossible
Parameters:
int[], int[]
Returns:
String
Method signature:
String isPossible(int[] p, int[] S)
(be sure your method is public)

Constraints

  • p will contain between 1 and 50 elements, inclusive.
  • For each i, 0 <= p[i] <= i.
  • S will contain between 1 and 50 elements, inclusive.
  • Each element in S will be between 0 and |p|, inclusive.
  • For each i, S[i] < S[i+1].

Examples

  1. {0,1,1,0,4,4}

    {2,4}

    Returns: "Possible"

    The tree is like: 0 / \ 1 4 / \ / \ 2 3 5 6 One of the possible route is: 0, 2, 3, 6, 5. The distance for each day is {2, 2, 4, 2} so S = {2, 4}.

  2. {0,1,1,0,4,4}

    {1,2,3,4,5}

    Returns: "Impossible"

    The maximal possible distance between any two cities is 4, so you will never have 5 in D.

  3. {0,1,1,0,4,4}

    {3,4}

    Returns: "Impossible"

  4. {0,1,2,3,4,0,6,7,8,9}

    {2,4,6,8,10}

    Returns: "Impossible"

  5. {0}

    {1}

    Returns: "Possible"

  6. {0,1,2,3,4,0,6,7,8,9}

    {2,4,5,6,8,10}

    Returns: "Possible"

  7. {0,1,0,3,2,4,5,4,7,8,9,10,9,11,11,15,14,14,18,18,18,19,21,22,22,22,26,24,26,27,30,29,30,33,34,35,34,36,36,38,39,39,41,42,44,45,46,44,45,49}

    {20,21,22,23,25,28}

    Returns: "Possible"

  8. {0,0,2,1,1,3,4,6,7,9,8,11,10,11,14,14,13,15,17,19,19,18,21,21,22,23,25,25,26,29,27,29,31,30,33,33,34,34,35,37,38,39,42,43,41,43,43,47,46,49}

    {20,21,22,24,32,37}

    Returns: "Possible"

  9. {0,1,1,0,1,3,4,5,5,6,10,9,10,11,12,14,15,16,17,16,18,18,21,21,24,24,25,24,27,26,27,31,29,33,33,33,33,34,37,38,40,40,41,41,44,44,46,45,47,46}

    {20,21,22,23,24,26}

    Returns: "Possible"

  10. {0,1,0,1,3,5,5,4,6,8,10,11,9,11,11,13,14,16,17,18,19,18,22,21,22,22,26,27,26,28,28,28,30,31,32,34,33,34,37,37,37,40,39,41,42,42,45,47,48,46}

    {20,23,24,28,29,30}

    Returns: "Possible"

  11. {0,0,1,3,2,4,6,7,5,8,10,9,9,11,14,12,15,15,15,16,20,20,19,21,22,23,23,25,27,28,29,31,29,30,32,34,33,37,37,36,40,41,39,43,41,43,43,44,47,48}

    {20,21,25,33,34,36}

    Returns: "Possible"

  12. {0,0,0,3,3,4,5,6,8,8,7,9,10,13,11,15,15,14,16,16,19,18,21,21,24,24,24,24,28,29,30,29,31,31,31,34,36,34,37,37,37,40,39,42,41,45,45,47,48,47}

    {21,22,23,24,27,28}

    Returns: "Possible"

  13. {0,1,2,2,1,3,5,4,5,6,10,10,9,10,13,14,15,16,17,17,18,21,21,22,21,24,23,27,27,28,29,30,31,33,33,35,36,37,35,37,38,41,39,43,42,45,45,47,46,49}

    {22,23,26,27,28,29}

    Returns: "Possible"

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

    {23,25,26,30,32,35}

    Returns: "Possible"

  15. {0,1,1,0,2,5,4,7,5,9,8,11,9,10,12,13,15,17,17,16,18,21,20,20,21,25,25,24,26,28,30,31,29,32,34,33,35,34,38,39,40,38,40,43,41,44,45,47,46,47}

    {20,21,25,26,31,34}

    Returns: "Possible"

  16. {0,1,0,1,4,2,3,5,6,9,7,8,9,11,14,12,15,14,16,17,17,20,22,20,21,23,24,25,27,29,30,31,31,31,33,32,34,36,36,39,37,38,42,42,43,45,43,46,46,46}

    {20,23,24,25,26,27}

    Returns: "Possible"

  17. {0,0,0,3,3,4,5,6,8,6,8,8,11,13,14,12,15,16,17,17,18,20,20,22,21,22,24,25,25,27,30,28,30,31,34,32,36,35,38,39,37,41,42,41,41,42,45,44,48,49}

    {10,11,12,13,14,15,19,20,24,28}

    Returns: "Possible"

  18. {0,0,0,3,2,3,5,4,7,7,7,8,9,12,12,12,16,17,17,16,19,21,22,23,24,25,24,25,27,26,28,30,31,30,32,34,33,37,38,39,37,39,39,42,44,44,44,47,48,47}

    {11,13,15,16,17,19,20,21,22,26}

    Returns: "Possible"

  19. {0,0,2,1,2,2,4,5,7,9,10,10,10,12,13,14,13,17,15,19,19,20,21,22,21,25,25,27,28,28,30,31,30,32,32,33,35,37,37,38,40,40,41,42,41,42,44,46,47,48}

    {11,16,17,18,19,20,21,22,24,26}

    Returns: "Possible"

  20. {0,1,0,3,1,4,3,6,5,7,7,9,11,12,13,14,14,17,15,18,19,21,20,20,22,25,25,27,28,29,29,28,29,30,32,32,36,36,36,38,39,40,40,41,43,43,45,44,48,48}

    {11,15,17,19,22,23,24,25,26,27}

    Returns: "Possible"

  21. {0,0,1,3,1,5,3,4,7,6,8,11,12,10,14,15,15,16,16,16,19,18,22,21,24,23,26,25,25,29,30,28,31,33,33,33,36,37,37,39,40,38,42,43,43,43,44,46,45,46}

    {11,12,13,15,16,18,21,22,24,26}

    Returns: "Possible"

  22. {0,0,0,0,2,5,4,5,6,7,10,8,10,12,11,12,16,14,15,16,19,20,22,21,24,25,23,27,27,29,28,31,30,31,34,33,36,34,37,38,39,39,39,41,43,43,44,47,46,49}

    {10,11,13,15,16,20,22,24,25,28}

    Returns: "Possible"

  23. {0,1,2,0,4,4,4,7,5,6,7,11,12,13,11,14,15,15,18,16,20,21,22,21,23,25,24,26,28,29,27,31,30,33,31,34,36,36,38,39,39,39,42,43,44,43,44,46,46,47}

    {10,11,12,16,18,19,24,25,28,29}

    Returns: "Possible"

  24. {0,1,0,3,2,4,6,5,5,7,9,8,12,10,11,14,16,17,17,19,17,19,19,22,24,24,24,27,28,27,28,30,29,33,34,32,36,34,38,38,39,41,42,40,42,45,45,47,45,47}

    {10,11,12,14,15,17,19,21,23,27}

    Returns: "Possible"

  25. {0,1,2,0,2,2,5,6,6,7,8,11,12,12,13,13,13,17,16,17,18,18,20,20,22,24,25,26,28,29,27,29,30,33,32,35,34,36,36,36,39,40,39,42,42,45,46,47,48,48}

    {10,11,14,16,17,19,20,21,23,24}

    Returns: "Possible"

  26. {0,0,1,1,2,3,3,6,6,6,10,8,12,11,13,13,14,17,15,18,19,21,21,23,24,25,24,26,26,26,27,31,32,33,34,34,36,35,37,39,38,39,39,43,42,42,44,45,47,49}

    {10,12,15,16,17,18,20,24,26,27}

    Returns: "Possible"

  27. {0,0,2,2,1,0,2,1,2,3,2,0,2,0,1,0,1,0,0,0,2,2,3,2,2,1,0,0,2,3,3,0,3,1,1,0,1,3,2,1,2,3,2,1,2,3,0,3,3,2}

    {1,2,4,5}

    Returns: "Possible"

  28. {0,0,0,3,0,1,3,1,2,3,3,3,3,1,3,3,2,3,2,3,3,3,2,3,1,2,3,3,3,1,0,1,3,1,1,0,3,3,0,3,3,1,0,0,1,0,3,1,3,3}

    {1,2,3,4}

    Returns: "Possible"

  29. {0,1,1,3,2,0,2,0,1,3,0,2,2,3,2,1,1,0,1,0,0,2,1,0,1,0,2,3,1,0,3,3,3,2,2,2,2,0,3,1,2,0,3,0,0,1,1,3,1,0}

    {1,2,3,4}

    Returns: "Possible"

  30. {0,0,1,2,1,3,1,3,1,3,3,1,2,3,2,0,3,2,0,2,1,1,2,2,1,0,0,3,2,1,0,2,2,1,0,2,1,3,1,0,1,2,0,3,3,2,1,2,0,0}

    {1,2,3,5}

    Returns: "Possible"

  31. {0,0,2,3,0,2,1,2,2,0,2,2,3,2,3,3,2,1,1,1,1,3,2,2,1,2,1,3,1,2,0,0,2,3,1,3,0,0,0,2,2,3,1,2,3,2,3,2,0,2}

    {1,2,3,4}

    Returns: "Possible"

  32. {0,1,2,2,2,2,3,2,0,2,0,3,2,3,2,1,2,1,3,1,3,1,1,1,2,2,0,2,1,3,0,3,2,3,2,2,1,0,0,3,0,0,1,2,3,1,3,1,2,0}

    {1,2,3,5}

    Returns: "Possible"

  33. {0,0,1,3,1,3,0,0,2,3,0,1,2,0,3,3,3,0,2,3,0,1,2,1,2,0,2,3,0,2,1,1,1,3,2,3,1,0,1,3,0,0,3,2,1,0,2,0,2,1}

    {1,3,4,5}

    Returns: "Possible"

  34. {0,1,2,1,0,3,3,1,0,2,2,2,0,1,3,1,2,3,3,3,3,0,2,0,3,3,3,2,2,2,0,3,0,2,3,3,3,0,2,3,2,3,2,1,2,0,2,3,2,2}

    {1,2,3,4}

    Returns: "Possible"

  35. {0,1,0,3,1,3,3,0,1,0,3,0,1,2,1,0,2,0,3,3,3,2,0,3,2,1,2,2,0,2,1,0,1,3,1,0,3,1,1,0,2,0,1,3,2,2,3,3,1,1}

    {1,2,3,5}

    Returns: "Possible"

  36. {0,0,2,2,3,1,1,3,0,3,1,2,3,0,3,3,0,3,1,1,2,3,3,3,3,0,3,2,2,3,3,2,2,3,3,1,2,3,0,0,3,0,3,0,3,0,2,1,1,2}

    {2,3,4,5}

    Returns: "Possible"

  37. {0,0,1,3,3,0,1,0,0,7,1,10,4,8,11,14,15,1,5,10,15,3,1,0,3,18,0,12,3,27,12,11,5,4,2,25,18,20,4,30,36,21,19,9,11,8,17,17,7,23}

    {3,4,6,10}

    Returns: "Impossible"

  38. {0,0,2,0,0,2,2,6,5,5,6,3,2,9,2,6,9,6,13,10,5,1,2,10,18,8,11,0,10,3,9,20,23,3,28,9,31,24,23,28,4,14,9,26,10,31,22,9,26,3}

    {2,5,6,10}

    Returns: "Impossible"

  39. {0,1,0,2,2,2,6,2,1,2,5,9,6,2,1,14,9,6,9,1,14,18,5,0,1,13,7,23,25,15,22,25,0,33,12,29,18,29,18,18,8,9,12,15,37,4,8,16,13,0}

    {1,3,6,9}

    Returns: "Impossible"

  40. {0,0,0,1,1,0,2,1,3,0,6,0,4,9,12,10,2,5,16,12,5,18,18,9,6,15,16,4,5,4,11,11,6,3,3,32,16,21,35,8,16,10,8,20,20,7,43,24,32,8}

    {1,4,8,9}

    Returns: "Impossible"

  41. {0,0,0,3,4,2,3,1,0,2,7,11,8,9,8,0,4,1,17,7,16,11,1,23,23,5,20,0,1,18,24,9,11,27,23,4,21,28,14,10,39,2,10,24,29,39,12,23,29,4}

    {3,7,8,10}

    Returns: "Impossible"

  42. {0,1,2,3,2,2,1,2,1,0,5,8,2,12,5,2,1,4,3,2,4,1,19,20,24,0,12,17,1,19,13,16,10,10,18,24,27,24,15,31,31,29,24,32,26,6,21,43,40,7}

    {1,5,8,10}

    Returns: "Impossible"

  43. {0,0,2,1,1,0,4,5,4,8,0,4,8,5,10,0,11,5,5,14,19,2,5,5,18,20,16,27,0,13,6,27,8,12,18,6,36,22,4,22,34,16,22,34,27,0,20,27,13,6}

    {1,3,4,10}

    Returns: "Impossible"

  44. {0,1,0,3,1,1,1,0,3,7,4,3,4,7,1,1,15,11,6,19,10,11,12,16,7,22,2,8,12,9,1,15,3,1,0,9,10,7,31,6,4,3,7,7,28,32,13,5,48,18}

    {2,4,7,10}

    Returns: "Impossible"

  45. {0,0,0,0,2,2,5,7,2,0,5,2,0,12,0,6,2,16,3,11,7,0,4,16,15,25,14,17,12,20,6,3,0,5,4,3,29,30,29,21,1,6,15,28,14,11,16,15,20,23}

    {5,6,7,10}

    Returns: "Impossible"

  46. {0,1,0,0,1,3,4,1,7,1,1,8,8,11,2,7,6,10,6,18,20,10,6,17,6,12,13,1,3,3,28,5,0,5,18,1,35,3,30,12,19,8,34,34,28,10,16,0,38,7}

    {1,4,5,10}

    Returns: "Impossible"

  47. {0,1,0,0,2,3,4,0,1,6,2,5,11,12,8,14,11,9,14,2,17,19,21,3,16,12,26,0,26,29,30,6,25,5,26,26,33,11,11,5,14,28,32,17,40,29,1,43,40,43}

    {3,6,7,9}

    Returns: "Possible"

  48. {0,1,2,0,4,4,5,5,6,6,7,9,6,2,11,6,10,3,11,6,13,12,21,9,12,1,22,13,4,23,17,10,9,30,5,8,25,4,3,30,7,23,12,13,43,30,36,38,46,6}

    {2,5,8,10}

    Returns: "Possible"

  49. {0,0,2,1,1,2,6,2,7,6,5,11,4,6,3,15,10,8,1,1,1,6,13,11,7,23,14,26,14,17,30,11,20,0,15,7,6,3,15,5,40,19,26,26,15,3,14,47,36,8}

    {1,3,7,9}

    Returns: "Possible"

  50. {0,1,2,0,2,4,1,3,8,1,7,9,5,6,10,15,6,4,10,7,13,15,5,18,15,7,23,26,22,0,16,4,9,31,4,13,18,36,6,30,33,37,5,18,33,39,44,19,36,27}

    {3,4,7,10}

    Returns: "Possible"

  51. {0,0,2,2,2,4,1,7,6,1,10,11,4,7,9,15,14,12,18,14,10,15,5,5,22,18,1,27,9,18,16,17,4,25,10,8,5,9,32,39,20,23,12,9,7,29,19,1,27,13}

    {3,4,6,7}

    Returns: "Possible"

  52. {0,1,1,1,0,4,5,3,5,9,7,11,1,9,2,13,14,14,16,8,4,10,21,2,5,25,20,13,10,7,16,0,2,14,2,31,15,36,2,8,19,20,28,0,28,5,7,21,18,24}

    {2,3,6,7}

    Returns: "Possible"

  53. {0,0,0,0,2,4,0,5,7,4,3,6,10,8,7,4,2,13,2,13,19,8,14,13,4,4,1,1,10,15,4,12,28,30,30,8,17,29,2,32,32,26,12,40,28,43,25,1,9,21}

    {3,4,9,10}

    Returns: "Possible"

  54. {0,1,2,0,0,1,1,3,0,3,2,6,4,0,12,11,9,11,14,8,3,10,16,8,7,10,5,2,20,6,9,10,19,28,23,14,30,32,11,31,14,2,25,1,10,22,16,43,29,41}

    {1,4,5,9}

    Returns: "Possible"

  55. {0,0,0,0,0,1,4,1,5,3,4,11,2,5,6,4,6,2,6,19,6,6,17,14,10,22,2,25,18,5,4,25,32,31,18,2,24,5,30,15,30,34,40,7,27,5,24,45,42,40}

    {3,6,7,9}

    Returns: "Possible"

  56. {0,0,2,2,3,1,1,0,7,8,2,2,2,5,1,8,3,12,15,0,0,17,8,4,9,8,11,7,18,4,26,31,17,24,12,5,0,20,32,16,40,21,29,33,25,35,42,1,2,21}

    {1,8,9,10}

    Returns: "Possible"

  57. {0,1,1,2,0,4,0,7,0,8,4,7,6,6,11,11,11,6,3,12,15,7,17,5,8,6}

    {2}

    Returns: "Possible"

  58. {0,1,0,1,4,0,1,4,5,5,0}

    {3}

    Returns: "Possible"

  59. {0,1,2,1,0,4}

    {3}

    Returns: "Possible"

  60. {0,0,2,0,4,2,3,0}

    {1}

    Returns: "Possible"

  61. {0,0,2,0,1,1,3,1,4,5,2,9,1,5,4,3,3,0,7,7,3,13,11,14,8,19,18,10,13,20,13,16,18,21,20}

    {2,4,6}

    Returns: "Possible"

  62. {0,1,2,2,0,5,5,3,6,4,2,7,1,10,6,0,2,14,10,9,12,11,13,11}

    {1,2}

    Returns: "Possible"

  63. {0,0,2,1,0,3,0,4,2,2,1,6,2,7,8,3,1,10,10,1}

    {4,7}

    Returns: "Possible"

  64. {0}

    {1}

    Returns: "Possible"

  65. {0,0,1,3,1,3,6,7,3,6,6,10,12,4,12,5,16,14,9,6,20,16,7,15,23,11,23,20,18,28,20,27,17,26,20,24,24}

    {7,8,9}

    Returns: "Possible"

  66. {0,1,1}

    {1}

    Returns: "Possible"

  67. {0,0,1}

    {2}

    Returns: "Possible"

  68. {0,0,1,0,2}

    {1}

    Returns: "Possible"

  69. {0,1,2,3,0,4,3,6,6,6}

    {6}

    Returns: "Possible"

  70. {0,0,0,3,2,5,3,5,8,8,10,11,11}

    {2}

    Returns: "Possible"

  71. {0,1,0,2,0,1,4,2,8,9,5,4,8,12,1,10,14,2,7,2,5,1,14,18,18,19,22,22,28,22,16,31,14,10,18,35,17,16,16,16,36,27,19,28,30,38,31,33,34}

    {4,5,6}

    Returns: "Possible"

  72. {0,1,2,3,4,4,5,6,7,9,10,11,12,13,13}

    {11}

    Returns: "Possible"

  73. {0,1,0,3,4,3,2,6,7,9}

    {3}

    Returns: "Possible"

  74. {0,1,2,1,0,2,1,6,4,8,7,0,7,1,8,15,14,6,9,16,4,3,1,9,15,19,20,1,21,8,19,10,16,25,13,24,25,13,22,15,21,19,22,18,25,22,23,23,22,25}

    {6,7,8,9,10}

    Returns: "Possible"

  75. {0,0,1,2,2,1,5,3,6,5,9,11,8,13,11,14,13,13,13,18,19,20,18,19,24,20,21,25}

    {2}

    Returns: "Possible"

  76. {0,0,1,2,2,0,3,7,1,7,7,2,8,5,13,3,11,15,16,6,6,11,10,13,10,2,16,15}

    {6}

    Returns: "Possible"

  77. {0,1,1,2,2,0,2,5,0,4,10,5,8,11,13,11,11,6,14,14,15,14,11,18,23,15,13,16,15,28,24,21,26,29,27,28,28,26}

    {3,4,5}

    Returns: "Possible"

  78. {0,0,2,0,0,3,2,3,6,2,8,11,11,0,11,15,10,7,8,11,7,21,17,15,14,23,20,20,20}

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

    Returns: "Possible"

  79. {0,1,0,3,1,3,4,2,1,8,4,9,10,11,4,2,11,4,6,7,13,13,4,22,19,22,21,4,18,15,12,9,16,18,13,15,23}

    {1}

    Returns: "Possible"

  80. {0}

    {1}

    Returns: "Possible"

  81. {0,0,2,3,3,3,6,3,1,3,7,1,4,13,11,0,4,15,6,3,1,18,6,15,23,6,23,23,18,20,21,20,16,15}

    {7,8}

    Returns: "Possible"

  82. {0}

    {1}

    Returns: "Possible"

  83. {0,0,1,3,0,1,0,0,4}

    {1,2}

    Returns: "Possible"

  84. {0,0,1,1,4,5,2,5,7,5,6}

    {1}

    Returns: "Possible"

  85. {0,0,1,2}

    {1,2}

    Returns: "Possible"

  86. {0,1,1,1,1}

    {2}

    Returns: "Possible"

  87. {0,1,0,3,4,5,6,1,4,5,8,7,11,9,12,8,10,1,18,9,15,13,1,13,13,9,14,23,17,26,2,9,3,11,4,19,30,9,16,27,32,27,17,33,22,39,36}

    {14,15,16,19,33}

    Returns: "Impossible"

  88. {0,0,0,1,2,5,4,3,2,6,3,1,11,12,13,11,5,16,12,12,17,3,12,3,14,20,25,19,11,26,12,9,21,15,28,17,30,20,16,25,20,19,29,31,24}

    {10,12,14,16,17,18,22,23,25,26,28}

    Returns: "Impossible"

  89. {0,0,2,2,3,1,1,2,7,2,7,10,3,12,8,4,8,14,1,17,11,7,7,17,22,5,0,3,5,9,14,25,32,25,33,23,29,15,36,36,1,18,33,40,36}

    {36,37,38,39,40,41}

    Returns: "Impossible"

  90. {0,0,2,1,1,3,4,7,7,1,8,3,1,3,12,7,1,11,14,4,3,12,22,6,12,16,10,25,25,12,30}

    {7,9,10,11,15,18,20}

    Returns: "Impossible"

  91. {0,0,2,0}

    {4}

    Returns: "Impossible"

  92. {0,1,1,2,3,0,0,7,6,6,8,7,8,4,8,13,8,3,10,11,4,8,17,17,10,17,10,12,19,19,16,15}

    {15}

    Returns: "Impossible"

  93. {0,1,0,3,0,1,0,5,5,9,4}

    {10}

    Returns: "Impossible"

  94. {0,1,1,1,1,0,3,0,6,4,7,6,7,7,1}

    {8}

    Returns: "Impossible"

  95. {0,0,1,2,2,3,4,5,8,5,5,2,5,11,11,11,6,9,9,14,13}

    {9,10}

    Returns: "Impossible"

  96. {0,1,1,2,0,2}

    {5}

    Returns: "Impossible"

  97. {0,0,1,1,0,0,3,7,7,2,9,6,3,3,9,7,8,7,1,7,9,1,9,22,20,0,16,16,26,17,21,14,8,7,26,26}

    {18,20,21}

    Returns: "Impossible"

  98. {0,1,2,2,1,2,0,0,8,3,4,9,5,8,1,6,12,4,15,4,6,6,13,11,21,17,11,19,16,16,11,17,12}

    {19,20}

    Returns: "Impossible"

  99. {0,1,2,2,3,1,0,5,1,2,9,7,5,4,2,0,5,6,13,11,5,17,19,19,24,14,24,13,18,24,28,17,30,22,18,19,31,28,33,33}

    {8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}

    Returns: "Impossible"

  100. {0,0,2,2,3,4,1,4,0,8,9,4,12,1,12,12,1,11,6,5,10,12,17,14,6,15,8,20,23,21,20,14,23,22,22,23,22,21,24,25,23,25,25,25}

    {35}

    Returns: "Impossible"

  101. {0,1,1,1,2,1,0,7,4,9,8,2,2,12,12,13,11,7,8,11,18,21,17,16,15,17,21,18,22,23}

    {6,7,8,9,10,11,12,13,14,15,16,17,19,20}

    Returns: "Impossible"

  102. {0,1,0,0,3,5,5,5,4,5,4,3,11,5,6,14,6,17,0,0,1,20,4,17,11,9,3,25,25,21,11,28,26,17,5,19,25,9,12,20,13,21,20,17,24,17,22}

    {14}

    Returns: "Impossible"

  103. {0,1,2,0,0,0,3,3,4,6,6,8,2,7,2,8,2,5,16,11,14,20,9,18,16,13,12,25,26,24,24,19,23,21,24,26,23,23,23,28,29}

    {12,13,14,16,17,18,19,20,21,22,24,25,26,28,29,30,31,33}

    Returns: "Impossible"

  104. {0,0}

    {2}

    Returns: "Impossible"

  105. {0,0,0}

    {3}

    Returns: "Impossible"

  106. {0,0,0,3,0,3,2,1,8,1,9,9,0,12,14,9,15,8,10,0,20,20,11,15,11,25,4,15,1,19,18,11,17,31,15,31,30,15,19,1}

    {8,9,12,13,14,15,16,17,19,20,21,22,23,24,25,26,28}

    Returns: "Impossible"

  107. {0,0,2,3,0,3,0,7,4,5,8,5,7,13,8,9,16,14}

    {10,12}

    Returns: "Impossible"

  108. {0,1,2,2,4,5,5,6,6,7,7,10,11,10,11,15,16,15,15,16}

    {10,14}

    Returns: "Impossible"

  109. {0,1,0,0,1,1,2,2,4,2,6,5,5}

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

    Returns: "Impossible"

  110. {0,0,2,3,1,0,0,2,8,0,7,8,10,1,2,9,4,8,14,15,17,11,17,23,0,0,20,16,12,18,5}

    {14,15,16,19}

    Returns: "Impossible"

  111. {0,1,1,2,1,1,3,0,4,7,8,7,8,13,12,15,0,10,16,1,12,12,8,7,13,7,0,23,16,4,2,12,10,15,23,21,12,17,36,18,25,19,14,27,34,28,46,27,46}

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

    Returns: "Impossible"

  112. {0,0,1,0,3,4,1,6,5,6,3,8,1,6,0}

    {5,6,7,8,9,12,13,15}

    Returns: "Impossible"

  113. {0,1,2,2,2,1,6,3,5,4,8,10,2,4,13,4,15,17,17,16,18,10,12,22,16,17,16,21,18,21,22,21,21}

    {7,10}

    Returns: "Impossible"

  114. {0,1,1,0,0,5,6,4,5,1,5,4,11,0,11,13,16,3,17,11,6,3,5,8,17,20,2,16,14,4,18,19,7,18,21,20,12,14,26,3,19,17,9,31,29,18,27,29}

    {9,10,11,12,13,14,15,16,17,18,19,20,21,24,25,26,27,28}

    Returns: "Impossible"

  115. {0,0,2,3,0,4,4,6,0,4,6,7,5,8,10,11,10,12,13,16,20,19,14,17,22,21,20,23,26,24,22,27,32,28,31,27,33,34,30,32,37,36,37,36,37}

    {29,32,33,34,35}

    Returns: "Impossible"

  116. {0,1,0,0,2,2,4,7,2,8,1,0,9,7,2,6,9,13,9,19,6,20,17,21,6,24,11,25,7,7,6,8}

    {8,9}

    Returns: "Impossible"

  117. {0 }

    {0 }

    Returns: "Possible"

  118. {0, 0 }

    {2 }

    Returns: "Impossible"

  119. {0, 0, 2, 3 }

    {2, 3, 4 }

    Returns: "Possible"

  120. {0, 1, 1, 2, 3, 3 }

    {4 }

    Returns: "Impossible"

  121. {0, 1, 2 }

    {2, 3 }

    Returns: "Possible"

  122. {0, 1, 1, 0, 4, 4 }

    {3, 4 }

    Returns: "Impossible"

  123. {0, 1, 2 }

    {2 }

    Returns: "Possible"

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