Statistics

Problem Statement for "BipartiteConstruction"

Problem Statement

You are given a single int K. Your task is to construct any bipartite graph with the following properties:
  • The graph must contain n white and n black vertices, where n is between 1 and 20, inclusive. The white vertices must be numbered 0 through n-1, and the black vertices must also be numbered 0 through n-1.
  • The graph must contain between 0 and 120 edges, inclusive.
  • Each edge of the graph must connect a white and a black vertex.
  • The number of different perfect matchings in the graph must be exactly K. Note that a perfect matching in a graph is a set of edges of the graph that contains each vertex exactly once.
Note that each pair of differently-colored vertices may be connected by arbitrarily many edges. These edges are all considered distinct.
Return a int[] with the description of the graph you constructed. This int[] should have m+1 elements, where m is the number of edges in your graph. Element 0 of the return value should be n. Each of the other elements should encode one edge of your graph. An edge that connects the i-th white vertex and the j-th black vertex is encoded as the integer (i*n + j).
It is guaranteed that for the given constraints a solution always exists. If there are multiple solutions, you may return any of them.

Definition

Class:
BipartiteConstruction
Method:
construct
Parameters:
int
Returns:
int[]
Method signature:
int[] construct(int K)
(be sure your method is public)

Notes

  • A perfect matching in a graph is a set of edges of the graph that contains each vertex exactly once.

Constraints

  • K will be between 0 and 1,000,000,000, inclusive.

Examples

  1. 2

    Returns: {3, 8, 1, 7, 4, 3, 0 }

    The edges are (2,2), (0,1), (2,1), (1,1), (1,0), (0,0). It has two different perfect matchings: {(2,2), (0,1), (1,0)} and {(2,2), (1,1), (0,0)}.

  2. 5

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

    This return value describes a graph with a single white vertex and a single black vertex. These vertices are connected by five distinct edges. Each of these edges forms a perfect matching in our graph.

  3. 0

    Returns: {2, 1, 0 }

  4. 2333333

    Returns: {20, 93, 195, 195, 211, 87, 114, 369, 390, 216, 195, 305, 17, 370, 356, 308, 150, 263, 20, 153, 331, 79, 344, 108, 114, 257, 245, 289, 211, 388, 388, 359, 293, 263, 219, 131, 201, 293, 279, 204, 97, 367, 90, 279, 308, 324, 323, 359, 338, 63, 26, 318, 218, 226, 164, 361, 276, 388, 343, 149, 17, 336, 88, 161, 76, 237, 136, 278, 302, 107, 271, 15, 382, 45, 338, 264, 78, 150, 220, 341, 180, 20, 252, 94, 114, 161 }

  5. 555

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 18, 17, 16, 16, 14, 14 }

  6. 1

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19 }

  7. 3

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18 }

  8. 4

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18 }

  9. 6

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 18 }

  10. 7

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 18 }

  11. 8

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 18 }

  12. 11

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 17 }

  13. 23

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 17, 17 }

  14. 41

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 17, 16 }

  15. 199

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 17, 16, 15, 15 }

  16. 397

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 17, 17, 16, 16, 15, 14 }

  17. 997

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 18, 17, 17, 14, 13 }

  18. 9973

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 17, 14, 14, 13, 12, 11 }

  19. 99991

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 17, 16, 15, 13, 13, 10, 10, 9 }

  20. 999983

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 17, 16, 14, 14, 12, 11, 11, 10, 10, 9, 8, 8, 7 }

  21. 9764981

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 18, 17, 17, 12, 10, 8, 5, 5 }

  22. 97999949

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 17, 17, 16, 16, 15, 15, 14, 12, 12, 11, 11, 10, 8, 7, 6, 5, 5, 3, 3 }

  23. 999899987

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 17, 17, 15, 15, 14, 14, 13, 12, 10, 9, 8, 5, 5, 3, 3, 2, 1, 1 }

  24. 536870910

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 17, 17, 16, 16, 14, 13, 13, 12, 11, 11, 10, 10, 9, 7, 7, 5, 4, 2, 1 }

  25. 387420486

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 18, 17, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2 }

  26. 268435452

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 17, 17, 16, 16, 15, 13, 12, 12, 11, 11, 10, 10, 7, 5, 5, 2, 2 }

  27. 244140620

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 16, 16, 15, 15, 14, 14, 13, 12, 12, 11, 10, 8, 4, 4, 3, 3, 2 }

  28. 362797050

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 17, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 7, 6, 6, 4, 3, 3, 2, 2 }

  29. 282475242

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 16, 16, 15, 12, 12, 10, 10, 9, 8, 5, 5, 4, 2, 2 }

  30. 988805850

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 18, 17, 17, 16, 15, 15, 14, 13, 13, 12, 11, 10, 9, 9, 8, 6, 6, 5, 5, 4, 4, 3, 2, 1, 1 }

  31. 386889036

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 18, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2 }

  32. 250609656

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 16, 15, 14, 14, 13, 12, 12, 9, 9, 8, 6, 5, 4, 4, 3, 3, 2 }

  33. 242105620

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 17, 17, 15, 14, 12, 12, 9, 9, 8, 7, 7, 6, 5, 5, 4, 3, 3, 2 }

  34. 362789238

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 17, 16, 15, 15, 13, 12, 12, 11, 10, 10, 9, 9, 8, 7, 6, 6, 4, 3, 3, 2, 2 }

  35. 241278884

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 18, 17, 17, 16, 14, 12, 12, 7, 6, 5, 5, 4, 3, 3, 2 }

  36. 1000000000

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 15, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  37. 999999999

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 15, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  38. 999999998

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 18, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  39. 999999997

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 18, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  40. 999999996

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 18, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  41. 999999995

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 18, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  42. 999999994

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  43. 999999993

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 18, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  44. 999999992

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  45. 999999991

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  46. 999999990

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 17, 17, 16, 16, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  47. 435546886

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 13, 13, 9, 9, 8, 5, 3, 1 }

  48. 999999937

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 17, 17, 13, 12, 12, 8, 8, 5, 5, 3, 3, 2, 1, 1 }

  49. 805306367

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 19, 17, 17, 16, 16, 15, 15, 14, 12, 11, 11, 10, 10, 9, 9, 6, 4, 4, 1, 1 }

  50. 42424243

    Returns: {20, 21, 21, 21, 20, 42, 42, 42, 41, 63, 63, 63, 62, 84, 84, 84, 83, 105, 105, 105, 104, 126, 126, 126, 125, 147, 147, 147, 146, 168, 168, 168, 167, 189, 189, 189, 188, 210, 210, 210, 209, 231, 231, 231, 230, 252, 252, 252, 251, 273, 273, 273, 272, 294, 294, 294, 293, 315, 315, 315, 314, 336, 336, 336, 335, 357, 357, 357, 356, 378, 378, 378, 377, 399, 399, 399, 398, 19, 18, 18, 15, 13, 11, 10, 9, 8, 8, 7, 6, 6, 5, 5, 4, 4 }

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