Statistics

Problem Statement for "TAASquares"

Problem Statement

Given a matrix, we will use the term lines to denote both rows and columns of that matrix. For example, a 5x5 matrix has ten lines.

A ternary almost-antimagic square (TAA square) is a square matrix with the following properties:

  • Each cell contains one of the digits 0, 1, 2.
  • The set containing the sums of all individual lines in the matrix has as many (distinct) elements as possible.

Given N, construct and return any N x N TAA square as a String[].

Definition

Class:
TAASquares
Method:
construct
Parameters:
int
Returns:
String[]
Method signature:
String[] construct(int N)
(be sure your method is public)

Constraints

  • N will be between 1 and 50, inclusive.

Examples

  1. 4

    Returns: {"2212", "2002", "0002", "2102" }

    The row sums are 7, 4, 2, and 5. The column sums are 6, 3, 1, and 8. All eight values are distinct.

  2. 5

    Returns: {"12222", "00012", "02221", "00110", "00122" }

    There are nine distinct line sums. In particular, row 2 is 0+2+2+2+1 = 7 and column 4 is 2+2+1+0+2 = 7.

  3. 1

    Returns: {"1" }

    The only row has sum 1 and the only column has sum 1. Clearly, the row sum must be the same as the column sum so you cannot do better.

  4. 2

    Returns: {"00", "12" }

  5. 3

    Returns: {"000", "012", "122" }

  6. 6

    Returns: {"000000", "000002", "000022", "001222", "012222", "122222" }

  7. 7

    Returns: {"0000000", "0000002", "0000022", "0001222", "0012222", "0122222", "1222222" }

  8. 8

    Returns: {"00000000", "00000002", "00000022", "00000222", "00012222", "00122222", "01222222", "12222222" }

  9. 9

    Returns: {"000000000", "000000002", "000000022", "000000222", "000012222", "000122222", "001222222", "012222222", "122222222" }

  10. 10

    Returns: {"0000000000", "0000000002", "0000000022", "0000000222", "0000002222", "0000122222", "0001222222", "0012222222", "0122222222", "1222222222" }

  11. 11

    Returns: {"00000000000", "00000000002", "00000000022", "00000000222", "00000002222", "00000122222", "00001222222", "00012222222", "00122222222", "01222222222", "12222222222" }

  12. 12

    Returns: {"000000000000", "000000000002", "000000000022", "000000000222", "000000002222", "000000022222", "000001222222", "000012222222", "000122222222", "001222222222", "012222222222", "122222222222" }

  13. 13

    Returns: {"0000000000000", "0000000000002", "0000000000022", "0000000000222", "0000000002222", "0000000022222", "0000001222222", "0000012222222", "0000122222222", "0001222222222", "0012222222222", "0122222222222", "1222222222222" }

  14. 14

    Returns: {"00000000000000", "00000000000002", "00000000000022", "00000000000222", "00000000002222", "00000000022222", "00000000222222", "00000012222222", "00000122222222", "00001222222222", "00012222222222", "00122222222222", "01222222222222", "12222222222222" }

  15. 15

    Returns: {"000000000000000", "000000000000002", "000000000000022", "000000000000222", "000000000002222", "000000000022222", "000000000222222", "000000012222222", "000000122222222", "000001222222222", "000012222222222", "000122222222222", "001222222222222", "012222222222222", "122222222222222" }

  16. 16

    Returns: {"0000000000000000", "0000000000000002", "0000000000000022", "0000000000000222", "0000000000002222", "0000000000022222", "0000000000222222", "0000000002222222", "0000000122222222", "0000001222222222", "0000012222222222", "0000122222222222", "0001222222222222", "0012222222222222", "0122222222222222", "1222222222222222" }

  17. 17

    Returns: {"00000000000000000", "00000000000000002", "00000000000000022", "00000000000000222", "00000000000002222", "00000000000022222", "00000000000222222", "00000000002222222", "00000000122222222", "00000001222222222", "00000012222222222", "00000122222222222", "00001222222222222", "00012222222222222", "00122222222222222", "01222222222222222", "12222222222222222" }

  18. 18

    Returns: {"000000000000000000", "000000000000000002", "000000000000000022", "000000000000000222", "000000000000002222", "000000000000022222", "000000000000222222", "000000000002222222", "000000000022222222", "000000001222222222", "000000012222222222", "000000122222222222", "000001222222222222", "000012222222222222", "000122222222222222", "001222222222222222", "012222222222222222", "122222222222222222" }

  19. 19

    Returns: {"0000000000000000000", "0000000000000000002", "0000000000000000022", "0000000000000000222", "0000000000000002222", "0000000000000022222", "0000000000000222222", "0000000000002222222", "0000000000022222222", "0000000001222222222", "0000000012222222222", "0000000122222222222", "0000001222222222222", "0000012222222222222", "0000122222222222222", "0001222222222222222", "0012222222222222222", "0122222222222222222", "1222222222222222222" }

  20. 20

    Returns: {"00000000000000000000", "00000000000000000002", "00000000000000000022", "00000000000000000222", "00000000000000002222", "00000000000000022222", "00000000000000222222", "00000000000002222222", "00000000000022222222", "00000000000222222222", "00000000012222222222", "00000000122222222222", "00000001222222222222", "00000012222222222222", "00000122222222222222", "00001222222222222222", "00012222222222222222", "00122222222222222222", "01222222222222222222", "12222222222222222222" }

  21. 21

    Returns: {"000000000000000000000", "000000000000000000002", "000000000000000000022", "000000000000000000222", "000000000000000002222", "000000000000000022222", "000000000000000222222", "000000000000002222222", "000000000000022222222", "000000000000222222222", "000000000012222222222", "000000000122222222222", "000000001222222222222", "000000012222222222222", "000000122222222222222", "000001222222222222222", "000012222222222222222", "000122222222222222222", "001222222222222222222", "012222222222222222222", "122222222222222222222" }

  22. 22

    Returns: {"0000000000000000000000", "0000000000000000000002", "0000000000000000000022", "0000000000000000000222", "0000000000000000002222", "0000000000000000022222", "0000000000000000222222", "0000000000000002222222", "0000000000000022222222", "0000000000000222222222", "0000000000002222222222", "0000000000122222222222", "0000000001222222222222", "0000000012222222222222", "0000000122222222222222", "0000001222222222222222", "0000012222222222222222", "0000122222222222222222", "0001222222222222222222", "0012222222222222222222", "0122222222222222222222", "1222222222222222222222" }

  23. 23

    Returns: {"00000000000000000000000", "00000000000000000000002", "00000000000000000000022", "00000000000000000000222", "00000000000000000002222", "00000000000000000022222", "00000000000000000222222", "00000000000000002222222", "00000000000000022222222", "00000000000000222222222", "00000000000002222222222", "00000000000122222222222", "00000000001222222222222", "00000000012222222222222", "00000000122222222222222", "00000001222222222222222", "00000012222222222222222", "00000122222222222222222", "00001222222222222222222", "00012222222222222222222", "00122222222222222222222", "01222222222222222222222", "12222222222222222222222" }

  24. 24

    Returns: {"000000000000000000000000", "000000000000000000000002", "000000000000000000000022", "000000000000000000000222", "000000000000000000002222", "000000000000000000022222", "000000000000000000222222", "000000000000000002222222", "000000000000000022222222", "000000000000000222222222", "000000000000002222222222", "000000000000022222222222", "000000000001222222222222", "000000000012222222222222", "000000000122222222222222", "000000001222222222222222", "000000012222222222222222", "000000122222222222222222", "000001222222222222222222", "000012222222222222222222", "000122222222222222222222", "001222222222222222222222", "012222222222222222222222", "122222222222222222222222" }

  25. 25

    Returns: {"0000000000000000000000000", "0000000000000000000000002", "0000000000000000000000022", "0000000000000000000000222", "0000000000000000000002222", "0000000000000000000022222", "0000000000000000000222222", "0000000000000000002222222", "0000000000000000022222222", "0000000000000000222222222", "0000000000000002222222222", "0000000000000022222222222", "0000000000001222222222222", "0000000000012222222222222", "0000000000122222222222222", "0000000001222222222222222", "0000000012222222222222222", "0000000122222222222222222", "0000001222222222222222222", "0000012222222222222222222", "0000122222222222222222222", "0001222222222222222222222", "0012222222222222222222222", "0122222222222222222222222", "1222222222222222222222222" }

  26. 26

    Returns: {"00000000000000000000000000", "00000000000000000000000002", "00000000000000000000000022", "00000000000000000000000222", "00000000000000000000002222", "00000000000000000000022222", "00000000000000000000222222", "00000000000000000002222222", "00000000000000000022222222", "00000000000000000222222222", "00000000000000002222222222", "00000000000000022222222222", "00000000000000222222222222", "00000000000012222222222222", "00000000000122222222222222", "00000000001222222222222222", "00000000012222222222222222", "00000000122222222222222222", "00000001222222222222222222", "00000012222222222222222222", "00000122222222222222222222", "00001222222222222222222222", "00012222222222222222222222", "00122222222222222222222222", "01222222222222222222222222", "12222222222222222222222222" }

  27. 27

    Returns: {"000000000000000000000000000", "000000000000000000000000002", "000000000000000000000000022", "000000000000000000000000222", "000000000000000000000002222", "000000000000000000000022222", "000000000000000000000222222", "000000000000000000002222222", "000000000000000000022222222", "000000000000000000222222222", "000000000000000002222222222", "000000000000000022222222222", "000000000000000222222222222", "000000000000012222222222222", "000000000000122222222222222", "000000000001222222222222222", "000000000012222222222222222", "000000000122222222222222222", "000000001222222222222222222", "000000012222222222222222222", "000000122222222222222222222", "000001222222222222222222222", "000012222222222222222222222", "000122222222222222222222222", "001222222222222222222222222", "012222222222222222222222222", "122222222222222222222222222" }

  28. 28

    Returns: {"0000000000000000000000000000", "0000000000000000000000000002", "0000000000000000000000000022", "0000000000000000000000000222", "0000000000000000000000002222", "0000000000000000000000022222", "0000000000000000000000222222", "0000000000000000000002222222", "0000000000000000000022222222", "0000000000000000000222222222", "0000000000000000002222222222", "0000000000000000022222222222", "0000000000000000222222222222", "0000000000000002222222222222", "0000000000000122222222222222", "0000000000001222222222222222", "0000000000012222222222222222", "0000000000122222222222222222", "0000000001222222222222222222", "0000000012222222222222222222", "0000000122222222222222222222", "0000001222222222222222222222", "0000012222222222222222222222", "0000122222222222222222222222", "0001222222222222222222222222", "0012222222222222222222222222", "0122222222222222222222222222", "1222222222222222222222222222" }

  29. 29

    Returns: {"00000000000000000000000000000", "00000000000000000000000000002", "00000000000000000000000000022", "00000000000000000000000000222", "00000000000000000000000002222", "00000000000000000000000022222", "00000000000000000000000222222", "00000000000000000000002222222", "00000000000000000000022222222", "00000000000000000000222222222", "00000000000000000002222222222", "00000000000000000022222222222", "00000000000000000222222222222", "00000000000000002222222222222", "00000000000000122222222222222", "00000000000001222222222222222", "00000000000012222222222222222", "00000000000122222222222222222", "00000000001222222222222222222", "00000000012222222222222222222", "00000000122222222222222222222", "00000001222222222222222222222", "00000012222222222222222222222", "00000122222222222222222222222", "00001222222222222222222222222", "00012222222222222222222222222", "00122222222222222222222222222", "01222222222222222222222222222", "12222222222222222222222222222" }

  30. 30

    Returns: {"000000000000000000000000000000", "000000000000000000000000000002", "000000000000000000000000000022", "000000000000000000000000000222", "000000000000000000000000002222", "000000000000000000000000022222", "000000000000000000000000222222", "000000000000000000000002222222", "000000000000000000000022222222", "000000000000000000000222222222", "000000000000000000002222222222", "000000000000000000022222222222", "000000000000000000222222222222", "000000000000000002222222222222", "000000000000000022222222222222", "000000000000001222222222222222", "000000000000012222222222222222", "000000000000122222222222222222", "000000000001222222222222222222", "000000000012222222222222222222", "000000000122222222222222222222", "000000001222222222222222222222", "000000012222222222222222222222", "000000122222222222222222222222", "000001222222222222222222222222", "000012222222222222222222222222", "000122222222222222222222222222", "001222222222222222222222222222", "012222222222222222222222222222", "122222222222222222222222222222" }

  31. 31

    Returns: {"0000000000000000000000000000000", "0000000000000000000000000000002", "0000000000000000000000000000022", "0000000000000000000000000000222", "0000000000000000000000000002222", "0000000000000000000000000022222", "0000000000000000000000000222222", "0000000000000000000000002222222", "0000000000000000000000022222222", "0000000000000000000000222222222", "0000000000000000000002222222222", "0000000000000000000022222222222", "0000000000000000000222222222222", "0000000000000000002222222222222", "0000000000000000022222222222222", "0000000000000001222222222222222", "0000000000000012222222222222222", "0000000000000122222222222222222", "0000000000001222222222222222222", "0000000000012222222222222222222", "0000000000122222222222222222222", "0000000001222222222222222222222", "0000000012222222222222222222222", "0000000122222222222222222222222", "0000001222222222222222222222222", "0000012222222222222222222222222", "0000122222222222222222222222222", "0001222222222222222222222222222", "0012222222222222222222222222222", "0122222222222222222222222222222", "1222222222222222222222222222222" }

  32. 32

    Returns: {"00000000000000000000000000000000", "00000000000000000000000000000002", "00000000000000000000000000000022", "00000000000000000000000000000222", "00000000000000000000000000002222", "00000000000000000000000000022222", "00000000000000000000000000222222", "00000000000000000000000002222222", "00000000000000000000000022222222", "00000000000000000000000222222222", "00000000000000000000002222222222", "00000000000000000000022222222222", "00000000000000000000222222222222", "00000000000000000002222222222222", "00000000000000000022222222222222", "00000000000000000222222222222222", "00000000000000012222222222222222", "00000000000000122222222222222222", "00000000000001222222222222222222", "00000000000012222222222222222222", "00000000000122222222222222222222", "00000000001222222222222222222222", "00000000012222222222222222222222", "00000000122222222222222222222222", "00000001222222222222222222222222", "00000012222222222222222222222222", "00000122222222222222222222222222", "00001222222222222222222222222222", "00012222222222222222222222222222", "00122222222222222222222222222222", "01222222222222222222222222222222", "12222222222222222222222222222222" }

  33. 33

    Returns: {"000000000000000000000000000000000", "000000000000000000000000000000002", "000000000000000000000000000000022", "000000000000000000000000000000222", "000000000000000000000000000002222", "000000000000000000000000000022222", "000000000000000000000000000222222", "000000000000000000000000002222222", "000000000000000000000000022222222", "000000000000000000000000222222222", "000000000000000000000002222222222", "000000000000000000000022222222222", "000000000000000000000222222222222", "000000000000000000002222222222222", "000000000000000000022222222222222", "000000000000000000222222222222222", "000000000000000012222222222222222", "000000000000000122222222222222222", "000000000000001222222222222222222", "000000000000012222222222222222222", "000000000000122222222222222222222", "000000000001222222222222222222222", "000000000012222222222222222222222", "000000000122222222222222222222222", "000000001222222222222222222222222", "000000012222222222222222222222222", "000000122222222222222222222222222", "000001222222222222222222222222222", "000012222222222222222222222222222", "000122222222222222222222222222222", "001222222222222222222222222222222", "012222222222222222222222222222222", "122222222222222222222222222222222" }

  34. 34

    Returns: {"0000000000000000000000000000000000", "0000000000000000000000000000000002", "0000000000000000000000000000000022", "0000000000000000000000000000000222", "0000000000000000000000000000002222", "0000000000000000000000000000022222", "0000000000000000000000000000222222", "0000000000000000000000000002222222", "0000000000000000000000000022222222", "0000000000000000000000000222222222", "0000000000000000000000002222222222", "0000000000000000000000022222222222", "0000000000000000000000222222222222", "0000000000000000000002222222222222", "0000000000000000000022222222222222", "0000000000000000000222222222222222", "0000000000000000002222222222222222", "0000000000000000122222222222222222", "0000000000000001222222222222222222", "0000000000000012222222222222222222", "0000000000000122222222222222222222", "0000000000001222222222222222222222", "0000000000012222222222222222222222", "0000000000122222222222222222222222", "0000000001222222222222222222222222", "0000000012222222222222222222222222", "0000000122222222222222222222222222", "0000001222222222222222222222222222", "0000012222222222222222222222222222", "0000122222222222222222222222222222", "0001222222222222222222222222222222", "0012222222222222222222222222222222", "0122222222222222222222222222222222", "1222222222222222222222222222222222" }

  35. 35

    Returns: {"00000000000000000000000000000000000", "00000000000000000000000000000000002", "00000000000000000000000000000000022", "00000000000000000000000000000000222", "00000000000000000000000000000002222", "00000000000000000000000000000022222", "00000000000000000000000000000222222", "00000000000000000000000000002222222", "00000000000000000000000000022222222", "00000000000000000000000000222222222", "00000000000000000000000002222222222", "00000000000000000000000022222222222", "00000000000000000000000222222222222", "00000000000000000000002222222222222", "00000000000000000000022222222222222", "00000000000000000000222222222222222", "00000000000000000002222222222222222", "00000000000000000122222222222222222", "00000000000000001222222222222222222", "00000000000000012222222222222222222", "00000000000000122222222222222222222", "00000000000001222222222222222222222", "00000000000012222222222222222222222", "00000000000122222222222222222222222", "00000000001222222222222222222222222", "00000000012222222222222222222222222", "00000000122222222222222222222222222", "00000001222222222222222222222222222", "00000012222222222222222222222222222", "00000122222222222222222222222222222", "00001222222222222222222222222222222", "00012222222222222222222222222222222", "00122222222222222222222222222222222", "01222222222222222222222222222222222", "12222222222222222222222222222222222" }

  36. 36

    Returns: {"000000000000000000000000000000000000", "000000000000000000000000000000000002", "000000000000000000000000000000000022", "000000000000000000000000000000000222", "000000000000000000000000000000002222", "000000000000000000000000000000022222", "000000000000000000000000000000222222", "000000000000000000000000000002222222", "000000000000000000000000000022222222", "000000000000000000000000000222222222", "000000000000000000000000002222222222", "000000000000000000000000022222222222", "000000000000000000000000222222222222", "000000000000000000000002222222222222", "000000000000000000000022222222222222", "000000000000000000000222222222222222", "000000000000000000002222222222222222", "000000000000000000022222222222222222", "000000000000000001222222222222222222", "000000000000000012222222222222222222", "000000000000000122222222222222222222", "000000000000001222222222222222222222", "000000000000012222222222222222222222", "000000000000122222222222222222222222", "000000000001222222222222222222222222", "000000000012222222222222222222222222", "000000000122222222222222222222222222", "000000001222222222222222222222222222", "000000012222222222222222222222222222", "000000122222222222222222222222222222", "000001222222222222222222222222222222", "000012222222222222222222222222222222", "000122222222222222222222222222222222", "001222222222222222222222222222222222", "012222222222222222222222222222222222", "122222222222222222222222222222222222" }

  37. 37

    Returns: {"0000000000000000000000000000000000000", "0000000000000000000000000000000000002", "0000000000000000000000000000000000022", "0000000000000000000000000000000000222", "0000000000000000000000000000000002222", "0000000000000000000000000000000022222", "0000000000000000000000000000000222222", "0000000000000000000000000000002222222", "0000000000000000000000000000022222222", "0000000000000000000000000000222222222", "0000000000000000000000000002222222222", "0000000000000000000000000022222222222", "0000000000000000000000000222222222222", "0000000000000000000000002222222222222", "0000000000000000000000022222222222222", "0000000000000000000000222222222222222", "0000000000000000000002222222222222222", "0000000000000000000022222222222222222", "0000000000000000001222222222222222222", "0000000000000000012222222222222222222", "0000000000000000122222222222222222222", "0000000000000001222222222222222222222", "0000000000000012222222222222222222222", "0000000000000122222222222222222222222", "0000000000001222222222222222222222222", "0000000000012222222222222222222222222", "0000000000122222222222222222222222222", "0000000001222222222222222222222222222", "0000000012222222222222222222222222222", "0000000122222222222222222222222222222", "0000001222222222222222222222222222222", "0000012222222222222222222222222222222", "0000122222222222222222222222222222222", "0001222222222222222222222222222222222", "0012222222222222222222222222222222222", "0122222222222222222222222222222222222", "1222222222222222222222222222222222222" }

  38. 38

    Returns: {"00000000000000000000000000000000000000", "00000000000000000000000000000000000002", "00000000000000000000000000000000000022", "00000000000000000000000000000000000222", "00000000000000000000000000000000002222", "00000000000000000000000000000000022222", "00000000000000000000000000000000222222", "00000000000000000000000000000002222222", "00000000000000000000000000000022222222", "00000000000000000000000000000222222222", "00000000000000000000000000002222222222", "00000000000000000000000000022222222222", "00000000000000000000000000222222222222", "00000000000000000000000002222222222222", "00000000000000000000000022222222222222", "00000000000000000000000222222222222222", "00000000000000000000002222222222222222", "00000000000000000000022222222222222222", "00000000000000000000222222222222222222", "00000000000000000012222222222222222222", "00000000000000000122222222222222222222", "00000000000000001222222222222222222222", "00000000000000012222222222222222222222", "00000000000000122222222222222222222222", "00000000000001222222222222222222222222", "00000000000012222222222222222222222222", "00000000000122222222222222222222222222", "00000000001222222222222222222222222222", "00000000012222222222222222222222222222", "00000000122222222222222222222222222222", "00000001222222222222222222222222222222", "00000012222222222222222222222222222222", "00000122222222222222222222222222222222", "00001222222222222222222222222222222222", "00012222222222222222222222222222222222", "00122222222222222222222222222222222222", "01222222222222222222222222222222222222", "12222222222222222222222222222222222222" }

  39. 39

    Returns: {"000000000000000000000000000000000000000", "000000000000000000000000000000000000002", "000000000000000000000000000000000000022", "000000000000000000000000000000000000222", "000000000000000000000000000000000002222", "000000000000000000000000000000000022222", "000000000000000000000000000000000222222", "000000000000000000000000000000002222222", "000000000000000000000000000000022222222", "000000000000000000000000000000222222222", "000000000000000000000000000002222222222", "000000000000000000000000000022222222222", "000000000000000000000000000222222222222", "000000000000000000000000002222222222222", "000000000000000000000000022222222222222", "000000000000000000000000222222222222222", "000000000000000000000002222222222222222", "000000000000000000000022222222222222222", "000000000000000000000222222222222222222", "000000000000000000012222222222222222222", "000000000000000000122222222222222222222", "000000000000000001222222222222222222222", "000000000000000012222222222222222222222", "000000000000000122222222222222222222222", "000000000000001222222222222222222222222", "000000000000012222222222222222222222222", "000000000000122222222222222222222222222", "000000000001222222222222222222222222222", "000000000012222222222222222222222222222", "000000000122222222222222222222222222222", "000000001222222222222222222222222222222", "000000012222222222222222222222222222222", "000000122222222222222222222222222222222", "000001222222222222222222222222222222222", "000012222222222222222222222222222222222", "000122222222222222222222222222222222222", "001222222222222222222222222222222222222", "012222222222222222222222222222222222222", "122222222222222222222222222222222222222" }

  40. 40

    Returns: {"0000000000000000000000000000000000000000", "0000000000000000000000000000000000000002", "0000000000000000000000000000000000000022", "0000000000000000000000000000000000000222", "0000000000000000000000000000000000002222", "0000000000000000000000000000000000022222", "0000000000000000000000000000000000222222", "0000000000000000000000000000000002222222", "0000000000000000000000000000000022222222", "0000000000000000000000000000000222222222", "0000000000000000000000000000002222222222", "0000000000000000000000000000022222222222", "0000000000000000000000000000222222222222", "0000000000000000000000000002222222222222", "0000000000000000000000000022222222222222", "0000000000000000000000000222222222222222", "0000000000000000000000002222222222222222", "0000000000000000000000022222222222222222", "0000000000000000000000222222222222222222", "0000000000000000000002222222222222222222", "0000000000000000000122222222222222222222", "0000000000000000001222222222222222222222", "0000000000000000012222222222222222222222", "0000000000000000122222222222222222222222", "0000000000000001222222222222222222222222", "0000000000000012222222222222222222222222", "0000000000000122222222222222222222222222", "0000000000001222222222222222222222222222", "0000000000012222222222222222222222222222", "0000000000122222222222222222222222222222", "0000000001222222222222222222222222222222", "0000000012222222222222222222222222222222", "0000000122222222222222222222222222222222", "0000001222222222222222222222222222222222", "0000012222222222222222222222222222222222", "0000122222222222222222222222222222222222", "0001222222222222222222222222222222222222", "0012222222222222222222222222222222222222", "0122222222222222222222222222222222222222", "1222222222222222222222222222222222222222" }

  41. 41

    Returns: {"00000000000000000000000000000000000000000", "00000000000000000000000000000000000000002", "00000000000000000000000000000000000000022", "00000000000000000000000000000000000000222", "00000000000000000000000000000000000002222", "00000000000000000000000000000000000022222", "00000000000000000000000000000000000222222", "00000000000000000000000000000000002222222", "00000000000000000000000000000000022222222", "00000000000000000000000000000000222222222", "00000000000000000000000000000002222222222", "00000000000000000000000000000022222222222", "00000000000000000000000000000222222222222", "00000000000000000000000000002222222222222", "00000000000000000000000000022222222222222", "00000000000000000000000000222222222222222", "00000000000000000000000002222222222222222", "00000000000000000000000022222222222222222", "00000000000000000000000222222222222222222", "00000000000000000000002222222222222222222", "00000000000000000000122222222222222222222", "00000000000000000001222222222222222222222", "00000000000000000012222222222222222222222", "00000000000000000122222222222222222222222", "00000000000000001222222222222222222222222", "00000000000000012222222222222222222222222", "00000000000000122222222222222222222222222", "00000000000001222222222222222222222222222", "00000000000012222222222222222222222222222", "00000000000122222222222222222222222222222", "00000000001222222222222222222222222222222", "00000000012222222222222222222222222222222", "00000000122222222222222222222222222222222", "00000001222222222222222222222222222222222", "00000012222222222222222222222222222222222", "00000122222222222222222222222222222222222", "00001222222222222222222222222222222222222", "00012222222222222222222222222222222222222", "00122222222222222222222222222222222222222", "01222222222222222222222222222222222222222", "12222222222222222222222222222222222222222" }

  42. 42

    Returns: {"000000000000000000000000000000000000000000", "000000000000000000000000000000000000000002", "000000000000000000000000000000000000000022", "000000000000000000000000000000000000000222", "000000000000000000000000000000000000002222", "000000000000000000000000000000000000022222", "000000000000000000000000000000000000222222", "000000000000000000000000000000000002222222", "000000000000000000000000000000000022222222", "000000000000000000000000000000000222222222", "000000000000000000000000000000002222222222", "000000000000000000000000000000022222222222", "000000000000000000000000000000222222222222", "000000000000000000000000000002222222222222", "000000000000000000000000000022222222222222", "000000000000000000000000000222222222222222", "000000000000000000000000002222222222222222", "000000000000000000000000022222222222222222", "000000000000000000000000222222222222222222", "000000000000000000000002222222222222222222", "000000000000000000000022222222222222222222", "000000000000000000001222222222222222222222", "000000000000000000012222222222222222222222", "000000000000000000122222222222222222222222", "000000000000000001222222222222222222222222", "000000000000000012222222222222222222222222", "000000000000000122222222222222222222222222", "000000000000001222222222222222222222222222", "000000000000012222222222222222222222222222", "000000000000122222222222222222222222222222", "000000000001222222222222222222222222222222", "000000000012222222222222222222222222222222", "000000000122222222222222222222222222222222", "000000001222222222222222222222222222222222", "000000012222222222222222222222222222222222", "000000122222222222222222222222222222222222", "000001222222222222222222222222222222222222", "000012222222222222222222222222222222222222", "000122222222222222222222222222222222222222", "001222222222222222222222222222222222222222", "012222222222222222222222222222222222222222", "122222222222222222222222222222222222222222" }

  43. 43

    Returns: {"0000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000002", "0000000000000000000000000000000000000000022", "0000000000000000000000000000000000000000222", "0000000000000000000000000000000000000002222", "0000000000000000000000000000000000000022222", "0000000000000000000000000000000000000222222", "0000000000000000000000000000000000002222222", "0000000000000000000000000000000000022222222", "0000000000000000000000000000000000222222222", "0000000000000000000000000000000002222222222", "0000000000000000000000000000000022222222222", "0000000000000000000000000000000222222222222", "0000000000000000000000000000002222222222222", "0000000000000000000000000000022222222222222", "0000000000000000000000000000222222222222222", "0000000000000000000000000002222222222222222", "0000000000000000000000000022222222222222222", "0000000000000000000000000222222222222222222", "0000000000000000000000002222222222222222222", "0000000000000000000000022222222222222222222", "0000000000000000000001222222222222222222222", "0000000000000000000012222222222222222222222", "0000000000000000000122222222222222222222222", "0000000000000000001222222222222222222222222", "0000000000000000012222222222222222222222222", "0000000000000000122222222222222222222222222", "0000000000000001222222222222222222222222222", "0000000000000012222222222222222222222222222", "0000000000000122222222222222222222222222222", "0000000000001222222222222222222222222222222", "0000000000012222222222222222222222222222222", "0000000000122222222222222222222222222222222", "0000000001222222222222222222222222222222222", "0000000012222222222222222222222222222222222", "0000000122222222222222222222222222222222222", "0000001222222222222222222222222222222222222", "0000012222222222222222222222222222222222222", "0000122222222222222222222222222222222222222", "0001222222222222222222222222222222222222222", "0012222222222222222222222222222222222222222", "0122222222222222222222222222222222222222222", "1222222222222222222222222222222222222222222" }

  44. 44

    Returns: {"00000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000002", "00000000000000000000000000000000000000000022", "00000000000000000000000000000000000000000222", "00000000000000000000000000000000000000002222", "00000000000000000000000000000000000000022222", "00000000000000000000000000000000000000222222", "00000000000000000000000000000000000002222222", "00000000000000000000000000000000000022222222", "00000000000000000000000000000000000222222222", "00000000000000000000000000000000002222222222", "00000000000000000000000000000000022222222222", "00000000000000000000000000000000222222222222", "00000000000000000000000000000002222222222222", "00000000000000000000000000000022222222222222", "00000000000000000000000000000222222222222222", "00000000000000000000000000002222222222222222", "00000000000000000000000000022222222222222222", "00000000000000000000000000222222222222222222", "00000000000000000000000002222222222222222222", "00000000000000000000000022222222222222222222", "00000000000000000000000222222222222222222222", "00000000000000000000012222222222222222222222", "00000000000000000000122222222222222222222222", "00000000000000000001222222222222222222222222", "00000000000000000012222222222222222222222222", "00000000000000000122222222222222222222222222", "00000000000000001222222222222222222222222222", "00000000000000012222222222222222222222222222", "00000000000000122222222222222222222222222222", "00000000000001222222222222222222222222222222", "00000000000012222222222222222222222222222222", "00000000000122222222222222222222222222222222", "00000000001222222222222222222222222222222222", "00000000012222222222222222222222222222222222", "00000000122222222222222222222222222222222222", "00000001222222222222222222222222222222222222", "00000012222222222222222222222222222222222222", "00000122222222222222222222222222222222222222", "00001222222222222222222222222222222222222222", "00012222222222222222222222222222222222222222", "00122222222222222222222222222222222222222222", "01222222222222222222222222222222222222222222", "12222222222222222222222222222222222222222222" }

  45. 45

    Returns: {"000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000002", "000000000000000000000000000000000000000000022", "000000000000000000000000000000000000000000222", "000000000000000000000000000000000000000002222", "000000000000000000000000000000000000000022222", "000000000000000000000000000000000000000222222", "000000000000000000000000000000000000002222222", "000000000000000000000000000000000000022222222", "000000000000000000000000000000000000222222222", "000000000000000000000000000000000002222222222", "000000000000000000000000000000000022222222222", "000000000000000000000000000000000222222222222", "000000000000000000000000000000002222222222222", "000000000000000000000000000000022222222222222", "000000000000000000000000000000222222222222222", "000000000000000000000000000002222222222222222", "000000000000000000000000000022222222222222222", "000000000000000000000000000222222222222222222", "000000000000000000000000002222222222222222222", "000000000000000000000000022222222222222222222", "000000000000000000000000222222222222222222222", "000000000000000000000012222222222222222222222", "000000000000000000000122222222222222222222222", "000000000000000000001222222222222222222222222", "000000000000000000012222222222222222222222222", "000000000000000000122222222222222222222222222", "000000000000000001222222222222222222222222222", "000000000000000012222222222222222222222222222", "000000000000000122222222222222222222222222222", "000000000000001222222222222222222222222222222", "000000000000012222222222222222222222222222222", "000000000000122222222222222222222222222222222", "000000000001222222222222222222222222222222222", "000000000012222222222222222222222222222222222", "000000000122222222222222222222222222222222222", "000000001222222222222222222222222222222222222", "000000012222222222222222222222222222222222222", "000000122222222222222222222222222222222222222", "000001222222222222222222222222222222222222222", "000012222222222222222222222222222222222222222", "000122222222222222222222222222222222222222222", "001222222222222222222222222222222222222222222", "012222222222222222222222222222222222222222222", "122222222222222222222222222222222222222222222" }

  46. 46

    Returns: {"0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000002", "0000000000000000000000000000000000000000000022", "0000000000000000000000000000000000000000000222", "0000000000000000000000000000000000000000002222", "0000000000000000000000000000000000000000022222", "0000000000000000000000000000000000000000222222", "0000000000000000000000000000000000000002222222", "0000000000000000000000000000000000000022222222", "0000000000000000000000000000000000000222222222", "0000000000000000000000000000000000002222222222", "0000000000000000000000000000000000022222222222", "0000000000000000000000000000000000222222222222", "0000000000000000000000000000000002222222222222", "0000000000000000000000000000000022222222222222", "0000000000000000000000000000000222222222222222", "0000000000000000000000000000002222222222222222", "0000000000000000000000000000022222222222222222", "0000000000000000000000000000222222222222222222", "0000000000000000000000000002222222222222222222", "0000000000000000000000000022222222222222222222", "0000000000000000000000000222222222222222222222", "0000000000000000000000002222222222222222222222", "0000000000000000000000122222222222222222222222", "0000000000000000000001222222222222222222222222", "0000000000000000000012222222222222222222222222", "0000000000000000000122222222222222222222222222", "0000000000000000001222222222222222222222222222", "0000000000000000012222222222222222222222222222", "0000000000000000122222222222222222222222222222", "0000000000000001222222222222222222222222222222", "0000000000000012222222222222222222222222222222", "0000000000000122222222222222222222222222222222", "0000000000001222222222222222222222222222222222", "0000000000012222222222222222222222222222222222", "0000000000122222222222222222222222222222222222", "0000000001222222222222222222222222222222222222", "0000000012222222222222222222222222222222222222", "0000000122222222222222222222222222222222222222", "0000001222222222222222222222222222222222222222", "0000012222222222222222222222222222222222222222", "0000122222222222222222222222222222222222222222", "0001222222222222222222222222222222222222222222", "0012222222222222222222222222222222222222222222", "0122222222222222222222222222222222222222222222", "1222222222222222222222222222222222222222222222" }

  47. 47

    Returns: {"00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000002", "00000000000000000000000000000000000000000000022", "00000000000000000000000000000000000000000000222", "00000000000000000000000000000000000000000002222", "00000000000000000000000000000000000000000022222", "00000000000000000000000000000000000000000222222", "00000000000000000000000000000000000000002222222", "00000000000000000000000000000000000000022222222", "00000000000000000000000000000000000000222222222", "00000000000000000000000000000000000002222222222", "00000000000000000000000000000000000022222222222", "00000000000000000000000000000000000222222222222", "00000000000000000000000000000000002222222222222", "00000000000000000000000000000000022222222222222", "00000000000000000000000000000000222222222222222", "00000000000000000000000000000002222222222222222", "00000000000000000000000000000022222222222222222", "00000000000000000000000000000222222222222222222", "00000000000000000000000000002222222222222222222", "00000000000000000000000000022222222222222222222", "00000000000000000000000000222222222222222222222", "00000000000000000000000002222222222222222222222", "00000000000000000000000122222222222222222222222", "00000000000000000000001222222222222222222222222", "00000000000000000000012222222222222222222222222", "00000000000000000000122222222222222222222222222", "00000000000000000001222222222222222222222222222", "00000000000000000012222222222222222222222222222", "00000000000000000122222222222222222222222222222", "00000000000000001222222222222222222222222222222", "00000000000000012222222222222222222222222222222", "00000000000000122222222222222222222222222222222", "00000000000001222222222222222222222222222222222", "00000000000012222222222222222222222222222222222", "00000000000122222222222222222222222222222222222", "00000000001222222222222222222222222222222222222", "00000000012222222222222222222222222222222222222", "00000000122222222222222222222222222222222222222", "00000001222222222222222222222222222222222222222", "00000012222222222222222222222222222222222222222", "00000122222222222222222222222222222222222222222", "00001222222222222222222222222222222222222222222", "00012222222222222222222222222222222222222222222", "00122222222222222222222222222222222222222222222", "01222222222222222222222222222222222222222222222", "12222222222222222222222222222222222222222222222" }

  48. 48

    Returns: {"000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000002", "000000000000000000000000000000000000000000000022", "000000000000000000000000000000000000000000000222", "000000000000000000000000000000000000000000002222", "000000000000000000000000000000000000000000022222", "000000000000000000000000000000000000000000222222", "000000000000000000000000000000000000000002222222", "000000000000000000000000000000000000000022222222", "000000000000000000000000000000000000000222222222", "000000000000000000000000000000000000002222222222", "000000000000000000000000000000000000022222222222", "000000000000000000000000000000000000222222222222", "000000000000000000000000000000000002222222222222", "000000000000000000000000000000000022222222222222", "000000000000000000000000000000000222222222222222", "000000000000000000000000000000002222222222222222", "000000000000000000000000000000022222222222222222", "000000000000000000000000000000222222222222222222", "000000000000000000000000000002222222222222222222", "000000000000000000000000000022222222222222222222", "000000000000000000000000000222222222222222222222", "000000000000000000000000002222222222222222222222", "000000000000000000000000022222222222222222222222", "000000000000000000000001222222222222222222222222", "000000000000000000000012222222222222222222222222", "000000000000000000000122222222222222222222222222", "000000000000000000001222222222222222222222222222", "000000000000000000012222222222222222222222222222", "000000000000000000122222222222222222222222222222", "000000000000000001222222222222222222222222222222", "000000000000000012222222222222222222222222222222", "000000000000000122222222222222222222222222222222", "000000000000001222222222222222222222222222222222", "000000000000012222222222222222222222222222222222", "000000000000122222222222222222222222222222222222", "000000000001222222222222222222222222222222222222", "000000000012222222222222222222222222222222222222", "000000000122222222222222222222222222222222222222", "000000001222222222222222222222222222222222222222", "000000012222222222222222222222222222222222222222", "000000122222222222222222222222222222222222222222", "000001222222222222222222222222222222222222222222", "000012222222222222222222222222222222222222222222", "000122222222222222222222222222222222222222222222", "001222222222222222222222222222222222222222222222", "012222222222222222222222222222222222222222222222", "122222222222222222222222222222222222222222222222" }

  49. 49

    Returns: {"0000000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000002", "0000000000000000000000000000000000000000000000022", "0000000000000000000000000000000000000000000000222", "0000000000000000000000000000000000000000000002222", "0000000000000000000000000000000000000000000022222", "0000000000000000000000000000000000000000000222222", "0000000000000000000000000000000000000000002222222", "0000000000000000000000000000000000000000022222222", "0000000000000000000000000000000000000000222222222", "0000000000000000000000000000000000000002222222222", "0000000000000000000000000000000000000022222222222", "0000000000000000000000000000000000000222222222222", "0000000000000000000000000000000000002222222222222", "0000000000000000000000000000000000022222222222222", "0000000000000000000000000000000000222222222222222", "0000000000000000000000000000000002222222222222222", "0000000000000000000000000000000022222222222222222", "0000000000000000000000000000000222222222222222222", "0000000000000000000000000000002222222222222222222", "0000000000000000000000000000022222222222222222222", "0000000000000000000000000000222222222222222222222", "0000000000000000000000000002222222222222222222222", "0000000000000000000000000022222222222222222222222", "0000000000000000000000001222222222222222222222222", "0000000000000000000000012222222222222222222222222", "0000000000000000000000122222222222222222222222222", "0000000000000000000001222222222222222222222222222", "0000000000000000000012222222222222222222222222222", "0000000000000000000122222222222222222222222222222", "0000000000000000001222222222222222222222222222222", "0000000000000000012222222222222222222222222222222", "0000000000000000122222222222222222222222222222222", "0000000000000001222222222222222222222222222222222", "0000000000000012222222222222222222222222222222222", "0000000000000122222222222222222222222222222222222", "0000000000001222222222222222222222222222222222222", "0000000000012222222222222222222222222222222222222", "0000000000122222222222222222222222222222222222222", "0000000001222222222222222222222222222222222222222", "0000000012222222222222222222222222222222222222222", "0000000122222222222222222222222222222222222222222", "0000001222222222222222222222222222222222222222222", "0000012222222222222222222222222222222222222222222", "0000122222222222222222222222222222222222222222222", "0001222222222222222222222222222222222222222222222", "0012222222222222222222222222222222222222222222222", "0122222222222222222222222222222222222222222222222", "1222222222222222222222222222222222222222222222222" }

  50. 50

    Returns: {"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000002", "00000000000000000000000000000000000000000000000022", "00000000000000000000000000000000000000000000000222", "00000000000000000000000000000000000000000000002222", "00000000000000000000000000000000000000000000022222", "00000000000000000000000000000000000000000000222222", "00000000000000000000000000000000000000000002222222", "00000000000000000000000000000000000000000022222222", "00000000000000000000000000000000000000000222222222", "00000000000000000000000000000000000000002222222222", "00000000000000000000000000000000000000022222222222", "00000000000000000000000000000000000000222222222222", "00000000000000000000000000000000000002222222222222", "00000000000000000000000000000000000022222222222222", "00000000000000000000000000000000000222222222222222", "00000000000000000000000000000000002222222222222222", "00000000000000000000000000000000022222222222222222", "00000000000000000000000000000000222222222222222222", "00000000000000000000000000000002222222222222222222", "00000000000000000000000000000022222222222222222222", "00000000000000000000000000000222222222222222222222", "00000000000000000000000000002222222222222222222222", "00000000000000000000000000022222222222222222222222", "00000000000000000000000000222222222222222222222222", "00000000000000000000000012222222222222222222222222", "00000000000000000000000122222222222222222222222222", "00000000000000000000001222222222222222222222222222", "00000000000000000000012222222222222222222222222222", "00000000000000000000122222222222222222222222222222", "00000000000000000001222222222222222222222222222222", "00000000000000000012222222222222222222222222222222", "00000000000000000122222222222222222222222222222222", "00000000000000001222222222222222222222222222222222", "00000000000000012222222222222222222222222222222222", "00000000000000122222222222222222222222222222222222", "00000000000001222222222222222222222222222222222222", "00000000000012222222222222222222222222222222222222", "00000000000122222222222222222222222222222222222222", "00000000001222222222222222222222222222222222222222", "00000000012222222222222222222222222222222222222222", "00000000122222222222222222222222222222222222222222", "00000001222222222222222222222222222222222222222222", "00000012222222222222222222222222222222222222222222", "00000122222222222222222222222222222222222222222222", "00001222222222222222222222222222222222222222222222", "00012222222222222222222222222222222222222222222222", "00122222222222222222222222222222222222222222222222", "01222222222222222222222222222222222222222222222222", "12222222222222222222222222222222222222222222222222" }

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