


from __future__ import annotations

UpperCAmelCase_				:			Optional[int]   =	list[list[int]]

# assigning initial values to the grid
UpperCAmelCase_				:			Matrix   =	[
    [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
UpperCAmelCase_				:			Matrix   =	[
    [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 	SCREAMING_SNAKE_CASE_						(      __A			:      Matrix  ,   __A			:      int  ,   __A			:      int  ,   __A			:      int    )     ->		bool:

       """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 	SCREAMING_SNAKE_CASE_						(      __A			:      Matrix    )     ->		tuple[int, int] | None:

       """simple docstring"""

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







def 	SCREAMING_SNAKE_CASE_						(      __A			:      Matrix    )     ->		Matrix | None:

       """simple docstring"""

       if location := find_empty_location(__A    ):
              a_ :		List[Any]							=  location
       else:
              # If the location is ``None``, then the grid is solved.
              return grid

       for digit in range(1  ,   10    ):
              if is_safe(__A  ,   __A  ,   __A  ,   __A    ):
                     a_ :		Any							=  digit

                     if sudoku(__A    ) is not None:
                            return grid

                     a_ :		Optional[int]							=  0

       return None







def 	SCREAMING_SNAKE_CASE_						(      __A			:      Matrix    )     ->		None:

       """simple docstring"""

       for row in grid:
              for cell in row:
                     print(__A  ,   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:')
        UpperCAmelCase_				:			int   =	sudoku(example_grid)
        if solution is not None:
            print_solution(solution)
        else:
            print('Cannot find a solution.')






def 	SCREAMING_SNAKE_CASE_						(      __A			:      list    )     ->		list:

       """simple docstring"""

       a_ :		int							=  len(__A    )
       for _ in range(__A    ):
              for i in range(_ % 2  ,   arr_size - 1  ,   2    ):
                     if arr[i + 1] < arr[i]:
                            a_							,		a_ :		int							=  arr[i + 1], arr[i]

       return arr


if __name__ == "__main__":
   UpperCAmelCase_				:			int   =	list(range(10, 0, -1))
   print(F'Original: {arr}. Sorted: {odd_even_transposition(arr)}')


