Statistics

Problem Statement for "ShufflingCardsDiv2"

Problem Statement

Fox Ciel likes shuffling cards. She uses a deck with 2N cards, numbered 1 through 2N.
Ciel always uses the same procedure when shuffling. One round of shuffling looks as follows:
  1. She splits the deck into two piles: the top N cards will be pile A, the bottom N cards pile B.
  2. She takes pile A and rearranges the cards it contains arbitrarily.
  3. She takes pile B and rearranges the cards it contains arbitrarily.
  4. She interleaves the cards from the two piles, producing a single deck again. More precisely, if pile A has cards A1,A2,...,AN and pile B has cards B1,B2,...,BN then the new deck will be A1,B1,A2,B2,...,AN,BN. (Note that the first card has to come from pile A.)
For example, let N=2 and suppose that Ciel starts with the sorted deck 1,2,3,4. One possible round of shuffling looks as follows:
  1. She splits the deck into two piles: the cards 1,2 are pile A and the cards 3,4 are pile B.
  2. She rearranges pile A into 1,2. (I.e., she keeps the cards in their current order.)
  3. She rearranges pile B into 4,3.
  4. She merges the two piles, obtaining the deck 1,4,2,3.
In the above example we have shown one of four possible outcomes of the shuffling process. After the first round of shuffling, Ciel could have that deck in one of these four orders:
  • 1,3,2,4
  • 1,4,2,3
  • 2,3,1,4
  • 2,4,1,3
You are given a int[] permutation which contains a permutation of the 2N cards. Ciel's deck is currently sorted: the cards are in the order 1,2,3,...,2N from top to bottom. Ciel wants to make exactly two rounds of shuffling. After the second round the order of cards in her deck should correspond to the given permutation. Return "Possible" (quotes for clarity) if this can be done and "Impossible" otherwise.

Definition

Class:
ShufflingCardsDiv2
Method:
shuffle
Parameters:
int[]
Returns:
String
Method signature:
String shuffle(int[] permutation)
(be sure your method is public)

Constraints

  • permutation will contain between 4 and 200 elements, inclusive.
  • The number of elements in permutation will be even.
  • The elements of permutation will form a permutation of the numbers 1 through 2N, where 2N is the number of elements in permutation.

Examples

  1. {1,2,3,4}

    Returns: "Possible"

    Fox Ciel can make the following two shuffles: {1,2,3,4} -> {1,3,2,4} -> {1,2,3,4}. Note that she cannot simply keep the deck in sorted order, the shuffling procedure does not allow that. Luckily for Ciel, it is possible to shuffle the deck in the first round and to return the cards to their original places in the second round.

  2. {4,3,2,1}

    Returns: "Possible"

  3. {1,3,2,4}

    Returns: "Impossible"

    Ciel can produce this permutation after the first round of shuffling. However, it is not possible to start with a sorted deck and to have this permutation of cards after two rounds of shuffling.

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

    Returns: "Impossible"

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

    Returns: "Possible"

  6. {4,19,57,41,36,30,27,47,18,24,66,16,34,69,83,23,20,55,50,1,33,15,31,21,5,8,37,81,80,49,32,48,52,54,68,59,26,17,70,42,71,35,22,25,28,72,84,51,12,73,64,6,40,45,44,61,85,78,86,62,58,79,67,39,7,9,53,3,77,74,75,43,46,13,76,38,14,82,56,65,29,10,63,11,2,60}

    Returns: "Impossible"

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

    Returns: "Impossible"

  8. {14,49,69,57,87,76,32,20,58,31,79,71,33,55,48,62,93,102,105,72,91,77,1,2,101,35,66,5,90,85,47,99,108,25,64,98,107,96,53,46,7,92,24,18,19,54,106,12,52,4,42,11,30,74,60,44,37,26,38,68,95,56,81,9,45,3,22,82,73,61,36,6,27,70,40,43,78,63,65,39,86,29,80,109,94,59,97,100,51,10,15,84,83,13,75,67,17,8,88,41,28,110,21,103,23,34,50,104,89,16}

    Returns: "Impossible"

  9. {15,106,33,167,63,150,5,93,113,65,81,62,41,149,138,9,6,127,17,58,64,3,139,20,86,71,164,22,169,42,143,37,176,98,27,99,73,83,132,70,130,47,66,10,122,110,156,74,7,77,16,157,124,171,14,136,24,76,54,142,80,161,165,82,96,174,39,95,45,92,158,162,72,38,133,84,32,166,159,67,1,44,100,154,53,134,49,8,172,103,29,51,141,40,90,152,75,163,69,48,89,117,135,68,153,144,148,115,34,13,147,31,123,168,160,4,12,129,120,119,28,85,107,55,145,109,21,175,137,30,50,131,78,26,11,43,146,57,19,56,170,108,102,111,94,105,140,61,52,112,114,18,46,23,59,79,121,87,60,97,2,125,88,118,126,25,36,128,91,151,104,35,116,173,155,101}

    Returns: "Possible"

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

    Returns: "Possible"

  11. {171,32,143,149,190,44,8,91,116,121,139,131,81,102,20,166,183,61,170,155,22,19,154,164,120,178,187,141,31,92,55,70,140,7,63,48,42,110,192,146,85,94,177,111,10,123,86,167,128,5,180,80,119,194,14,15,67,107,46,40,157,90,13,152,2,1,158,25,16,39,41,98,104,174,49,62,109,133,129,57,65,37,150,4,182,78,165,26,82,134,60,59,99,23,156,38,73,189,106,151,186,52,28,43,103,51,3,58,33,191,27,176,169,115,64,50,100,36,75,153,17,147,89,87,66,148,172,130,34,160,69,77,74,11,127,184,79,144,96,108,88,188,112,118,45,21,136,30,35,12,29,159,193,161,9,142,76,24,145,68,54,47,163,97,124,56,175,101,105,137,185,113,95,125,162,6,71,132,181,138,179,114,84,126,168,117,122,72,83,18,135,53,93,173}

    Returns: "Possible"

  12. {56,107,68,105,139,50,47,121,67,33,127,137,98,94,115,55,126,147,91,125,49,146,66,87,75,40,59,24,153,19,89,145,83,138,46,120,60,73,129,69,23,108,122,72,101,12,118,32,134,54,5,71,15,90,84,7,20,70,25,42,156,77,8,160,65,119,82,61,45,48,109,43,103,39,10,114,116,1,124,18,141,111,155,6,130,13,99,88,86,76,27,96,21,152,41,142,9,26,58,144,31,78,64,135,102,36,81,63,57,110,112,28,140,143,131,22,16,157,17,150,62,100,113,151,51,74,136,149,97,80,4,34,35,104,133,106,29,154,2,95,123,11,38,53,92,14,3,30,93,159,148,52,85,128,44,158,117,132,37,79}

    Returns: "Impossible"

  13. {1,3,4,2}

    Returns: "Possible"

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

    Returns: "Impossible"

  15. {84,21,58,57,53,52,54,128,95,91,78,75,129,69,60,98,13,118,79,133,135,37,63,14,68,38,41,49,24,80,110,74,65,73,103,82,3,1,136,30,8,104,101,114,127,77,12,23,111,130,102,43,64,33,4,66,15,10,121,96,122,17,89,29,76,93,119,16,6,120,48,109,138,44,112,7,31,106,134,81,26,100,131,105,2,55,25,126,36,46,20,19,86,92,18,27,107,9,137,34,124,87,50,67,90,72,108,61,70,51,11,117,71,116,94,35,132,125,99,32,62,45,42,5,22,83,47,85,97,115,28,40,59,113,88,56,39,123}

    Returns: "Impossible"

  16. {24,77,112,74,52,50,75,30,114,2,130,55,69,67,100,11,35,107,15,14,119,68,125,110,54,19,73,108,82,28,47,113,76,39,22,109,57,3,17,26,48,16,63,61,23,10,60,37,64,36,20,18,34,90,83,32,96,121,5,94,88,9,59,86,104,105,40,80,58,4,79,46,81,51,62,12,70,101,95,131,132,124,99,118,116,25,43,128,42,13,98,117,122,85,38,1,21,41,106,129,126,84,102,78,49,87,44,45,6,56,91,103,93,89,27,65,33,8,31,97,111,29,123,115,120,127,7,53,71,72,66,92}

    Returns: "Possible"

  17. {150,12,134,164,136,72,11,195,181,95,125,16,139,77,180,198,177,108,93,39,68,111,130,58,70,83,34,167,117,149,115,31,25,153,35,173,110,38,9,156,166,162,48,14,165,122,105,160,76,78,80,37,178,191,140,109,30,102,112,144,189,116,113,159,188,67,158,133,55,123,97,194,69,10,106,128,15,1,51,129,46,21,174,157,49,50,200,53,154,100,126,41,176,24,184,28,143,161,62,79,13,185,40,138,29,36,137,182,170,101,8,33,75,119,59,163,92,145,2,84,81,131,190,27,107,142,179,98,61,18,57,171,71,23,82,91,88,103,121,22,196,114,94,56,186,199,172,96,87,193,44,47,3,120,132,17,42,90,141,187,104,6,52,148,7,127,183,175,73,86,19,152,151,124,89,63,64,32,43,54,4,5,147,169,197,74,155,135,99,66,60,85,45,20,146,118,192,26,65,168}

    Returns: "Impossible"

  18. {62,145,53,98,50,118,17,104,4,78,48,93,77,111,58,113,19,151,14,144,27,140,37,141,16,136,38,134,73,122,56,114,45,153,12,121,70,97,26,106,42,139,63,85,76,86,11,149,68,101,61,110,34,120,15,80,31,124,52,154,7,79,57,152,20,129,51,132,29,142,9,81,30,125,55,99,44,109,36,87,10,96,41,150,75,92,13,100,23,95,49,135,39,94,60,123,74,138,66,128,64,147,18,146,2,90,32,116,22,91,8,143,43,88,47,83,40,117,33,119,3,102,65,137,69,89,59,112,6,126,28,131,54,148,1,108,72,127,25,82,24,115,67,84,46,133,35,107,71,130,21,105,5,103}

    Returns: "Impossible"

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

    Returns: "Impossible"

  20. {24,54,1,63,8,65,22,58,15,48,21,45,17,64,30,76,4,61,7,72,33,79,23,67,37,82,19,68,35,78,40,60,6,57,11,43,31,66,29,70,39,55,38,77,14,49,27,52,12,80,16,46,25,59,9,51,13,71,2,62,32,69,36,81,18,74,3,56,5,53,26,42,34,50,10,73,28,75,41,47,20,44}

    Returns: "Impossible"

  21. {13,63,1,80,24,84,41,51,26,60,39,49,10,87,40,68,14,52,9,62,44,56,5,82,18,75,17,61,7,79,31,65,4,81,21,58,29,71,28,90,8,64,36,77,45,48,32,86,35,89,33,73,15,70,43,85,11,57,23,83,30,67,2,69,34,66,19,74,42,55,20,53,27,54,16,78,22,72,12,47,25,59,6,46,37,50,3,76,38,88}

    Returns: "Impossible"

  22. {15,76,16,71,31,116,20,113,21,98,44,110,41,105,2,86,55,70,52,123,62,90,27,124,58,84,24,119,12,121,18,72,7,69,60,114,1,115,51,78,3,104,40,79,56,118,34,80,22,74,19,63,8,109,30,122,37,101,10,88,43,100,50,108,61,102,59,93,53,77,5,67,28,91,49,99,29,87,57,96,46,95,47,106,32,82,23,81,4,73,11,65,13,85,9,120,17,66,33,75,6,94,36,97,14,112,42,64,48,83,38,107,39,103,26,117,25,111,45,89,35,68,54,92}

    Returns: "Impossible"

  23. {32,73,14,59,5,80,29,87,41,71,42,105,43,70,8,97,2,90,23,65,9,72,15,82,46,93,34,85,13,96,45,106,40,55,37,77,35,103,36,89,44,84,50,99,51,98,48,56,28,61,4,60,18,86,27,74,10,58,6,78,17,81,24,95,19,104,26,54,25,92,1,68,16,102,12,91,20,64,52,69,53,75,49,79,30,94,31,57,3,66,33,63,47,62,38,76,11,67,22,88,7,101,39,83,21,100}

    Returns: "Impossible"

  24. {8,39,16,34,20,56,21,50,29,37,28,45,13,55,18,48,19,49,10,32,11,53,12,54,23,33,27,38,2,43,14,36,5,44,15,46,25,31,22,52,4,57,3,40,24,47,17,60,30,51,6,35,9,41,1,42,7,58,26,59}

    Returns: "Impossible"

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

    Returns: "Impossible"

  26. {29,72,18,61,9,71,44,90,21,68,26,91,34,78,35,96,43,67,3,84,47,62,27,55,42,49,48,92,5,83,41,52,1,79,19,64,7,85,36,53,23,77,16,75,46,86,12,74,33,80,20,54,22,87,39,95,4,50,2,57,6,51,11,60,8,56,15,66,14,76,28,65,32,69,30,73,31,89,37,88,45,82,25,94,38,58,17,93,13,81,24,63,40,59,10,70}

    Returns: "Impossible"

  27. {5,167,46,168,60,154,9,128,63,99,13,109,10,111,56,153,24,89,15,150,22,87,54,118,7,134,79,130,4,129,69,137,39,117,41,101,28,170,27,143,86,135,53,138,33,166,84,162,71,97,18,116,65,96,14,113,50,160,73,140,17,147,12,169,43,156,59,92,47,93,51,149,45,95,3,165,37,121,82,152,6,141,85,94,62,88,35,145,74,120,61,98,29,103,2,171,67,131,40,110,44,102,66,123,78,163,68,172,21,158,83,115,23,122,55,100,72,119,19,106,75,107,1,104,11,112,77,105,48,124,80,155,70,144,52,114,31,164,16,132,49,142,58,127,34,161,25,136,8,125,42,157,64,139,26,126,30,90,20,133,38,91,57,159,32,146,81,148,76,108,36,151}

    Returns: "Impossible"

  28. {58,94,62,134,3,133,32,159,81,126,10,153,55,112,15,86,67,109,63,141,7,124,50,140,66,139,75,106,83,115,33,123,2,108,4,130,21,121,61,101,78,145,19,88,16,156,65,135,44,91,64,111,57,97,47,119,60,118,17,122,70,152,79,104,74,96,54,99,36,102,52,110,14,98,49,138,23,105,40,137,11,154,76,117,68,93,35,143,84,120,8,85,37,162,12,163,25,90,13,149,29,129,38,100,39,95,45,113,51,107,46,151,5,165,72,87,34,164,56,157,6,142,18,114,41,127,31,160,42,136,82,125,27,158,80,166,43,132,48,103,77,167,26,128,73,161,28,144,53,146,9,148,22,116,24,92,69,155,59,168,1,89,71,150,20,131,30,147}

    Returns: "Impossible"

  29. {93,189,43,196,6,155,38,109,70,135,4,181,18,165,19,106,64,173,28,115,14,121,82,124,59,108,62,146,20,156,16,123,66,182,41,103,73,168,5,186,17,119,34,134,49,190,88,162,75,133,98,166,89,147,72,101,8,158,40,131,95,111,50,179,25,150,52,127,86,118,53,167,63,192,69,187,78,180,42,148,85,177,67,102,55,137,54,193,83,157,13,178,91,107,65,163,29,195,51,139,74,176,100,184,61,160,60,129,31,112,87,170,1,116,81,171,76,191,12,128,33,183,15,126,23,130,56,172,7,174,3,122,27,136,21,110,11,104,90,154,46,142,24,141,94,185,57,159,92,125,68,200,44,151,2,117,97,164,37,198,30,153,48,188,71,169,79,143,96,120,77,161,35,105,84,145,99,175,80,144,10,114,45,138,58,113,47,199,32,140,36,197,22,149,39,194,9,132,26,152}

    Returns: "Impossible"

  30. {87,12,38,10,98,41,74,9,33,58,51,39,94,89,92,24,26,32,70,13,60,66,34,65,97,62,56,96,80,100,75,28,14,53,71,17,23,84,95,68,63,83,8,99,49,57,55,6,4,64,15,40,44,7,77,52,20,22,72,93,21,30,79,36,31,11,46,90,29,3,78,47,37,61,43,19,67,27,35,48,88,81,1,69,45,91,42,54,50,25,16,5,73,82,59,85,86,76,18,2}

    Returns: "Possible"

  31. {14,20,19,6,5,13,15,4,7,8,16,2,3,9,10,18,12,17,1,11}

    Returns: "Possible"

  32. {61,85,14,12,37,47,46,94,97,68,55,19,51,92,84,42,98,4,66,78,77,23,106,86,5,43,49,90,62,18,45,93,38,76,53,63,99,88,64,70,34,33,82,104,52,3,87,22,96,21,57,8,15,58,35,36,102,25,56,27,32,41,29,89,65,103,28,2,44,39,30,13,1,31,101,74,71,10,24,83,26,95,79,107,17,11,7,67,60,80,91,72,20,75,50,16,6,48,100,108,59,73,54,9,81,105,69,40}

    Returns: "Possible"

  33. {122,114,138,119,97,15,24,111,124,54,52,14,126,18,16,36,74,71,112,108,2,136,118,20,17,80,113,25,84,76,63,1,135,56,41,89,13,137,27,48,73,4,39,77,146,140,82,142,131,106,9,32,38,30,58,83,69,49,11,66,90,35,12,93,6,100,55,95,121,43,115,81,57,79,104,144,103,61,147,26,62,91,134,96,101,51,110,87,65,8,133,67,105,50,59,107,5,31,88,22,99,19,72,64,98,47,123,117,45,37,53,116,68,70,34,23,78,21,3,29,130,145,28,46,7,75,42,109,44,141,128,148,40,94,86,10,129,85,143,60,33,120,125,132,102,92,139,127}

    Returns: "Possible"

  34. {83,61,65,47,37,91,41,81,17,32,95,86,78,31,62,89,59,79,92,19,98,23,73,88,6,13,12,58,11,8,54,104,75,1,93,77,42,51,85,53,38,7,97,10,44,94,74,87,48,102,40,55,25,45,16,2,63,68,64,100,24,3,21,80,33,67,50,66,34,14,72,39,76,71,57,70,20,101,90,27,56,60,46,96,15,30,4,26,29,43,82,49,9,22,69,52,5,18,103,84,99,35,28,36}

    Returns: "Possible"

  35. {31,200,58,112,1,71,192,189,15,99,60,9,42,121,152,29,178,40,49,20,124,97,135,95,182,63,115,28,78,181,157,158,165,35,126,53,73,34,45,160,14,196,98,156,166,174,116,194,172,143,12,199,118,148,173,117,108,4,154,36,93,125,19,187,51,129,110,101,37,159,6,76,83,68,5,161,134,176,132,107,111,127,64,179,102,180,149,2,183,138,25,66,100,86,10,70,123,43,137,103,27,67,144,90,79,171,170,30,136,141,122,23,17,153,91,184,82,74,119,177,94,62,72,41,113,3,150,16,44,92,96,120,140,128,21,175,52,89,75,190,54,131,139,197,145,188,55,81,80,47,185,65,50,162,56,142,114,61,11,69,164,198,77,57,84,155,193,146,106,147,8,13,59,130,104,88,151,24,191,26,32,39,169,168,22,85,105,163,167,46,87,48,133,38,18,7,186,195,109,33}

    Returns: "Possible"

  36. {22,123,88,112,56,29,107,69,55,110,7,20,77,101,25,72,13,70,133,113,122,115,31,102,86,80,92,68,63,111,119,33,103,1,15,85,57,97,52,5,23,109,3,105,98,126,114,138,81,45,18,41,124,39,91,95,24,87,131,44,36,62,99,10,129,74,130,14,16,30,134,42,11,21,96,120,132,4,127,26,89,32,135,43,137,93,48,116,61,9,50,8,27,79,28,46,83,6,82,53,84,35,37,106,58,59,64,128,38,65,118,100,66,17,51,121,90,76,60,94,54,78,117,136,12,2,73,49,125,19,67,104,71,75,34,47,40,108}

    Returns: "Possible"

  37. {26,11,75,132,111,2,4,54,46,12,47,10,80,64,105,73,25,91,114,6,36,88,99,3,43,34,19,100,14,104,121,7,139,5,79,41,145,24,49,117,87,106,67,101,20,13,28,142,131,78,122,17,140,113,107,102,51,85,118,8,110,116,71,68,98,33,65,44,61,128,39,18,16,45,74,59,50,97,86,125,137,81,63,133,52,120,15,58,48,21,123,109,127,76,136,115,69,112,37,124,135,138,82,96,92,77,143,103,72,30,60,9,83,55,62,89,93,22,130,146,32,84,56,144,38,90,94,108,57,119,141,42,40,1,134,27,29,66,95,35,126,129,70,23,31,53}

    Returns: "Possible"

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

    Returns: "Possible"

  39. {52,126,43,134,9,47,1,61,12,63,82,132,100,86,26,87,30,13,16,110,37,17,91,95,125,104,72,113,19,39,5,71,6,85,10,7,31,84,22,74,80,121,34,4,93,49,15,24,109,127,96,58,119,29,11,76,112,73,32,102,3,111,89,59,51,20,67,101,99,36,64,14,116,28,23,83,117,8,41,35,66,65,88,105,118,69,92,98,131,70,97,45,2,79,81,25,124,108,115,54,40,57,77,128,46,94,120,50,106,122,44,42,107,103,33,27,114,18,48,38,133,130,53,78,90,56,123,75,68,62,60,55,129,21}

    Returns: "Possible"

  40. {1,7,5,3,4,10,9,8,6,2}

    Returns: "Possible"

  41. {97,168,161,110,108,137,29,187,77,152,94,135,166,123,25,141,99,5,156,130,48,153,27,173,122,10,24,114,149,36,33,57,16,111,167,78,62,35,22,184,71,188,20,185,76,89,60,180,12,95,197,150,64,112,160,90,176,193,49,138,146,7,133,26,120,69,194,145,104,91,118,177,39,38,45,55,119,23,88,109,58,132,93,96,102,51,101,113,191,164,186,125,147,40,30,106,127,19,121,178,128,134,56,21,28,107,92,68,124,17,85,59,158,131,182,140,15,70,155,82,126,143,115,9,116,8,43,72,151,6,170,61,103,100,79,66,50,154,162,192,174,1,165,37,86,190,163,46,196,105,139,34,54,181,157,171,117,148,13,129,3,189,84,159,172,14,73,2,195,4,198,75,175,80,44,32,11,41,142,52,136,42,31,144,63,18,98,179,65,47,67,53,74,169,87,83,81,183}

    Returns: "Possible"

  42. {7,4,9,2,8,5,6,3,10,1}

    Returns: "Impossible"

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

    Returns: "Impossible"

  44. {105,10,83,37,94,27,67,50,95,31,93,36,98,51,96,25,99,33,73,53,103,8,106,30,80,3,91,52,59,48,70,39,78,42,74,9,101,38,72,28,56,12,92,23,82,20,102,24,104,32,62,46,66,41,88,26,57,43,85,21,64,11,58,16,54,45,89,6,90,1,79,29,63,49,75,5,68,15,86,18,81,34,77,35,71,13,65,19,61,22,87,40,60,47,69,44,84,14,97,2,76,7,55,17,100,4}

    Returns: "Impossible"

  45. {123,62,107,20,97,9,111,39,113,12,102,45,80,11,77,58,93,8,74,27,83,19,96,25,79,16,106,36,101,35,92,56,124,1,88,50,94,5,91,33,76,44,126,47,115,37,90,41,68,54,67,4,70,31,82,26,87,34,105,52,71,43,109,40,86,49,66,10,116,38,120,29,95,17,110,15,85,55,98,32,99,60,78,53,73,63,89,61,72,24,114,6,104,46,125,7,119,22,118,13,121,18,64,48,81,21,69,3,103,59,84,28,108,30,65,51,122,23,100,57,112,42,117,14,75,2}

    Returns: "Impossible"

  46. {62,23,57,4,38,10,46,30,45,7,32,31,58,22,36,1,41,21,61,6,39,11,40,18,53,19,60,24,48,14,50,17,44,15,37,20,56,29,34,5,42,28,59,12,33,9,49,13,55,8,35,3,52,27,54,25,43,2,47,16,51,26}

    Returns: "Impossible"

  47. {85,8,78,2,68,47,71,37,89,53,90,41,104,9,94,51,98,49,69,1,77,40,75,43,81,36,59,44,67,18,103,12,58,23,91,42,54,34,99,20,100,15,57,6,96,13,61,27,65,17,55,24,70,10,64,26,95,5,86,25,73,21,101,52,83,30,105,38,97,4,80,7,87,14,88,45,76,22,63,48,93,31,56,11,92,28,74,19,60,46,62,33,79,32,82,35,102,50,72,29,66,3,106,16,84,39}{85,8,78,2,68,47,71,37,89,53,90,41,104,9,94,51,98,49,69,1,77,40,75,43,81,36,59,44,67,18,103,12,58,23,91,42,54,34,99,20,100,15,57,6,96,13,61,27,65,17,55,24,70,10,64,26,95,5,86,25,73,21,101,52,83,30,105,38,97,4,80,7,87,14,88,45,76,22,63,48,93,31,56,11,92,28,74,19,60,46,62,33,79,32,82,35,102,50,72,29,66,3,106,16,84,39}

    Returns: "Impossible"

  48. {78,31,69,16,51,47,83,44,71,36,90,35,88,18,70,29,64,21,68,34,75,2,93,26,62,20,50,5,80,7,73,17,79,13,87,27,55,38,82,3,53,32,59,49,74,1,57,11,52,24,81,30,67,39,60,43,61,33,89,12,97,4,66,8,86,46,76,48,94,37,92,22,63,19,84,9,56,10,54,25,96,41,85,42,95,45,91,40,65,15,72,28,98,6,77,14,58,23}

    Returns: "Impossible"

  49. {100,46,137,8,141,14,102,30,124,1,145,60,98,2,94,4,135,17,81,49,138,56,109,42,106,6,88,68,79,69,77,3,139,48,117,20,143,44,126,50,123,65,144,18,125,51,110,66,132,41,101,32,87,53,78,71,92,52,74,11,107,24,128,57,95,58,111,37,82,59,76,45,122,70,85,28,115,19,134,38,105,22,112,5,130,64,90,29,114,9,136,63,118,73,104,55,113,25,84,39,75,12,121,54,127,34,131,31,119,21,99,47,97,10,83,72,103,61,93,7,116,40,96,15,120,43,108,35,91,23,129,67,80,36,86,13,140,16,146,62,133,26,142,33,89,27}

    Returns: "Impossible"

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

    Returns: "Impossible"

  51. {66,14,64,3,57,22,53,6,51,15,44,32,70,9,41,35,68,13,63,12,46,8,37,23,58,27,42,2,67,26,56,34,69,16,43,19,39,31,45,7,59,10,49,4,65,20,48,21,52,5,55,18,62,24,60,28,54,11,38,33,61,25,40,17,36,1,47,29,50,30}

    Returns: "Impossible"

  52. {162,84,171,69,119,38,113,83,114,68,169,1,133,13,121,94,111,8,185,35,137,87,160,78,109,20,108,14,170,33,136,30,117,82,102,74,140,61,148,60,149,50,179,31,186,64,116,66,129,23,105,76,96,27,159,7,138,45,155,10,181,67,115,36,97,34,112,44,135,41,150,88,151,72,187,59,152,93,153,51,99,19,146,65,141,42,172,25,182,79,103,58,122,6,118,71,163,40,178,43,126,57,154,3,110,95,176,16,164,22,156,90,123,2,134,75,144,37,106,77,143,46,130,4,127,55,161,54,124,49,190,53,120,86,168,70,189,91,174,73,165,81,104,12,184,15,131,11,180,48,188,18,157,21,158,92,145,26,139,85,147,80,175,24,100,29,142,89,166,47,101,62,125,9,177,32,98,5,173,39,167,17,183,63,107,52,132,28,128,56}

    Returns: "Impossible"

  53. {144,91,164,15,151,48,158,2,102,98,140,78,185,9,182,95,131,1,122,75,189,72,103,35,178,65,167,59,129,23,190,18,157,21,130,36,172,39,100,20,111,28,146,4,120,76,128,51,180,33,127,83,181,96,121,73,118,13,107,82,104,90,132,38,186,99,196,79,108,68,197,5,150,10,142,47,179,70,137,25,109,50,184,58,155,54,145,94,110,37,163,56,156,27,124,19,161,85,154,97,114,80,175,87,176,16,173,69,192,46,126,14,143,64,165,61,139,34,159,3,113,53,187,7,135,31,106,49,170,17,188,67,134,8,162,41,116,55,195,30,198,84,105,32,149,26,174,40,125,11,183,60,168,92,148,62,169,63,112,71,152,22,141,45,101,89,117,44,193,12,153,29,123,6,166,43,177,81,115,24,136,66,191,93,160,52,147,57,133,77,171,86,119,74,194,42,138,88}

    Returns: "Impossible"

  54. {1, 4, 2, 5, 3, 6 }

    Returns: "Impossible"

  55. {3, 2, 4, 1 }

    Returns: "Impossible"

  56. {8, 5, 4, 9, 1, 7, 6, 10, 3, 2 }

    Returns: "Possible"

  57. {4, 2, 3, 1 }

    Returns: "Impossible"

  58. {1, 2, 4, 3, 5, 6 }

    Returns: "Impossible"

  59. {2, 3, 1, 4 }

    Returns: "Impossible"

  60. {1, 2, 3, 4 }

    Returns: "Possible"

  61. {1, 3, 2, 4 }

    Returns: "Impossible"

  62. {1, 4, 2, 3 }

    Returns: "Impossible"

  63. {1, 3, 4, 5, 2, 6 }

    Returns: "Possible"

  64. {1, 4, 3, 2 }

    Returns: "Possible"

  65. {5, 1, 2, 6, 3, 7, 4, 8 }

    Returns: "Impossible"

  66. {1, 3, 6, 4, 7, 5, 8, 2 }

    Returns: "Impossible"

  67. {6, 5, 4, 3, 2, 1 }

    Returns: "Impossible"

  68. {8, 5, 4, 9, 6, 7, 1, 10, 3, 2 }

    Returns: "Possible"

  69. {8, 3, 2, 6, 5, 4, 1, 7 }

    Returns: "Possible"

  70. {5, 1, 3, 4, 6, 2 }

    Returns: "Impossible"

  71. {5, 1, 6, 2, 7, 3, 8, 4 }

    Returns: "Impossible"

  72. {1, 3, 5, 2, 4, 6 }

    Returns: "Impossible"

  73. {1, 9, 6, 3, 7, 10, 8, 4, 2, 5 }

    Returns: "Impossible"

  74. {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, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 }

    Returns: "Possible"

  75. {2, 4, 6, 8, 1, 3, 5, 7 }

    Returns: "Possible"

  76. {5, 1, 6, 2, 7, 3, 4, 8 }

    Returns: "Impossible"

  77. {1, 3, 5, 4, 6, 2 }

    Returns: "Impossible"

  78. {8, 5, 4, 9, 1, 7, 2, 10, 3, 6 }

    Returns: "Impossible"

  79. {4, 1, 3, 2 }

    Returns: "Impossible"

  80. {1, 2, 5, 3, 6, 4 }

    Returns: "Impossible"

  81. {1, 3, 4, 5, 6, 2 }

    Returns: "Impossible"

  82. {3, 4, 1, 2 }

    Returns: "Possible"

  83. {1, 3, 5, 6, 2, 8, 4, 7 }

    Returns: "Impossible"

  84. {1, 2, 3, 4, 8, 5, 9, 6, 10, 7 }

    Returns: "Impossible"

  85. {1, 3, 4, 2, 5, 6 }

    Returns: "Impossible"

  86. {1, 5, 3, 7, 6, 2, 8, 4 }

    Returns: "Possible"

  87. {1, 5, 3, 4, 2, 6, 7, 8 }

    Returns: "Impossible"

  88. {200, 19, 198, 197, 196, 195, 194, 193, 192, 191, 190, 189, 188, 187, 186, 185, 184, 183, 182, 181, 180, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 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, 199, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

    Returns: "Possible"

  89. {4, 3, 1, 2, 5, 6 }

    Returns: "Impossible"

  90. {6, 7, 5, 3, 1, 4, 2, 8 }

    Returns: "Possible"

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: