
from __future__ import annotations


def 			UpperCamelCase					(    __lowerCamelCase     : list[int]    ):
       return len(set(__lowerCamelCase    )    ) == len(__lowerCamelCase    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()







from __future__ import annotations

__lowerCamelCase							=       list[list[int]]

# assigning initial values to the grid
__lowerCamelCase							=       [
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
__lowerCamelCase							=       [
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]


def 			UpperCamelCase					(    __lowerCamelCase     : Matrix				,					__lowerCamelCase     : int				,					__lowerCamelCase     : int				,					__lowerCamelCase     : int    ):
       for i in range(9    ):
              if grid[row][i] == n or grid[i][column] == n:
                     return False

       for i in range(3    ):
              for j in range(3    ):
                     if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
                            return False

       return True


def 			UpperCamelCase					(    __lowerCamelCase     : Matrix    ):
       for i in range(9    ):
              for j in range(9    ):
                     if grid[i][j] == 0:
                            return i, j
       return None


def 			UpperCamelCase					(    __lowerCamelCase     : Matrix    ):
       if location := find_empty_location(__lowerCamelCase    ):
              snake_case				,					snake_case       :   Union[str, Any]							=      location
       else:
              # If the location is ``None``, then the grid is solved.
              return grid

       for digit in range(1				,					10    ):
              if is_safe(__lowerCamelCase				,					__lowerCamelCase				,					__lowerCamelCase				,					__lowerCamelCase    ):
                     snake_case       :   List[Any]							=      digit

                     if sudoku(__lowerCamelCase    ) is not None:
                            return grid

                     snake_case       :   Union[str, Any]							=      0

       return None


def 			UpperCamelCase					(    __lowerCamelCase     : Matrix    ):
       for row in grid:
              for cell in row:
                     print(__lowerCamelCase				,					end=" "    )
              print()


if __name__ == "__main__":
   # make a copy of grid so that you can compare with the unmodified grid
   for example_grid in (initial_grid, no_solution):
      print("""\nExample grid:\n""" + """=""" * 20)
      print_solution(example_grid)
      print("""\nExample grid solution:""")
      __lowerCamelCase							=       sudoku(example_grid)
      if solution is not None:
         print_solution(solution)
      else:
         print("""Cannot find a solution.""")





