


from __future__ import annotations

A      :    Optional[int]		=					list[list[int]]

# assigning initial values to the grid
A      :    int		=					[
    [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
A      :    Dict		=					[
    [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       lowercase_		(		_A			:    Union[str, Any]    ,					_A			:    Optional[Any]    ,					_A			:    Tuple    ,					_A			:    List[str]						):

      """simple docstring"""




      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       lowercase_		(		_A			:    int						):

      """simple docstring"""




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

def       lowercase_		(		_A			:    Optional[Any]						):

      """simple docstring"""




      if location := find_empty_location(_lowerCAmelCase						):
            lowerCamelCase__		:				str    =  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						):
                  lowerCamelCase__		:				Optional[Any]    =  digit

                  if sudoku(_lowerCAmelCase						) is not None:
                        return grid

                  lowerCamelCase__		:				Any    =  0

      return None

def       lowercase_		(		_A			:    int						):

      """simple docstring"""




      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:")
        A      :    int		=					sudoku(example_grid)
        if solution is not None:
            print_solution(solution)
        else:
            print("Cannot find a solution.")







'''simple docstring'''





def 						__snake_case(				_lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase		)		-> float:
      snake_case__  :    str    						=      (num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
      # formula for sum of series
      return total





def 						__snake_case(				)		-> List[str]:
      print(sum_of_series(1     ,   1     ,   10		)		)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
