Statistics

Problem Statement for "CubesOnATable"

Problem Statement

You have exactly 150 unit cubes. You also have a small square table. The horizontal surface of the table is divided into a grid of 10x10 unit squares. Let's label the cells of this grid (0,0) through (9,9).

We can now naturally extend the 2-dimensional grid into a 3-dimensional grid of unit cube cells going upwards from the table. Each cell of this grid will have coordinates (x,y,z) with 0 <= x,y <= 9 and with 0 <= z. (Cells with z = 0 touch the surface of the table.)

Place some of your cubes onto the table, as follows:

  • Each cube must exactly fill one of the cube cells of the grid defined above.
  • The set of cubes must be stable. That is, if you have a cube at (x,y,z+1), you must also have a cube at (x,y,z).
  • The total surface area of your creation must be surface. A face of a cube counts as surface if and only if it has a cube on one side and air on the other side.

If there is no solution, return an empty int[]. If your solution consists of cubes (x1,y1,z1), (x2,y2,z2), and so on, return the following int[]: { x1, y1, z1, x2, y2, z2, ... }. If there are multiple solutions, you may construct and return any of them. The order of cubes in your output may be arbitrary.

Definition

Class:
CubesOnATable
Method:
placeCubes
Parameters:
int
Returns:
int[]
Method signature:
int[] placeCubes(int surface)
(be sure your method is public)

Notes

  • By definition, faces that touch the table do not count as surface.

Constraints

  • surface will be between 1 and 500, inclusive.

Examples

  1. 5

    Returns: {0, 0, 0 }

    A single cube placed anywhere on the table will have a surface area of 5.

  2. 20

    Returns: {5, 5, 0, 5, 5, 1, 5, 6, 0, 5, 6, 1, 6, 5, 0, 6, 5, 1, 6, 6, 0, 6, 6, 1 }

    A 2x2x2 cube built from eight unit cubes has surface area 20.

  3. 25

    Returns: {0, 0, 0, 2, 2, 0, 4, 4, 0, 6, 6, 0, 8, 8, 0 }

    Five completely disjoint unit cubes, each sitting somewhere on the table.

  4. 32

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

    A staircase: four adjacent columns consisting of 1, 2, 3, and 4 cubes.

  5. 1

    Returns: { }

  6. 2

    Returns: { }

  7. 3

    Returns: { }

  8. 4

    Returns: { }

  9. 6

    Returns: { }

  10. 7

    Returns: { }

  11. 8

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

  12. 9

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

  13. 10

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

  14. 11

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

  15. 12

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

  16. 13

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

  17. 14

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

  18. 15

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

  19. 16

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

  20. 17

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

  21. 18

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

  22. 19

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

  23. 20

    Returns: {5, 5, 0, 5, 5, 1, 5, 6, 0, 5, 6, 1, 6, 5, 0, 6, 5, 1, 6, 6, 0, 6, 6, 1 }

  24. 500

    Returns: {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121, 0, 0, 122, 0, 0, 123 }

  25. 499

    Returns: {1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121, 0, 0, 122 }

  26. 498

    Returns: {2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121, 0, 0, 122 }

  27. 497

    Returns: {0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121, 0, 0, 122, 0, 0, 123 }

  28. 496

    Returns: {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121, 0, 0, 122 }

  29. 495

    Returns: {1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121 }

  30. 494

    Returns: {2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103, 0, 0, 104, 0, 0, 105, 0, 0, 106, 0, 0, 107, 0, 0, 108, 0, 0, 109, 0, 0, 110, 0, 0, 111, 0, 0, 112, 0, 0, 113, 0, 0, 114, 0, 0, 115, 0, 0, 116, 0, 0, 117, 0, 0, 118, 0, 0, 119, 0, 0, 120, 0, 0, 121 }

  31. 123

    Returns: {1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28 }

  32. 172

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

  33. 210

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

  34. 211

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

  35. 212

    Returns: {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51 }

  36. 213

    Returns: {0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52 }

  37. 297

    Returns: {0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73 }

  38. 344

    Returns: {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84 }

  39. 392

    Returns: {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96 }

  40. 423

    Returns: {1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0, 0, 32, 0, 0, 33, 0, 0, 34, 0, 0, 35, 0, 0, 36, 0, 0, 37, 0, 0, 38, 0, 0, 39, 0, 0, 40, 0, 0, 41, 0, 0, 42, 0, 0, 43, 0, 0, 44, 0, 0, 45, 0, 0, 46, 0, 0, 47, 0, 0, 48, 0, 0, 49, 0, 0, 50, 0, 0, 51, 0, 0, 52, 0, 0, 53, 0, 0, 54, 0, 0, 55, 0, 0, 56, 0, 0, 57, 0, 0, 58, 0, 0, 59, 0, 0, 60, 0, 0, 61, 0, 0, 62, 0, 0, 63, 0, 0, 64, 0, 0, 65, 0, 0, 66, 0, 0, 67, 0, 0, 68, 0, 0, 69, 0, 0, 70, 0, 0, 71, 0, 0, 72, 0, 0, 73, 0, 0, 74, 0, 0, 75, 0, 0, 76, 0, 0, 77, 0, 0, 78, 0, 0, 79, 0, 0, 80, 0, 0, 81, 0, 0, 82, 0, 0, 83, 0, 0, 84, 0, 0, 85, 0, 0, 86, 0, 0, 87, 0, 0, 88, 0, 0, 89, 0, 0, 90, 0, 0, 91, 0, 0, 92, 0, 0, 93, 0, 0, 94, 0, 0, 95, 0, 0, 96, 0, 0, 97, 0, 0, 98, 0, 0, 99, 0, 0, 100, 0, 0, 101, 0, 0, 102, 0, 0, 103 }

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