

from __future__ import annotations

a__												=						list[list[int]]

# assigning initial values to the grid
a__												=						[
    [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__												=						[
    [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					(      __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   __UpperCAmelCase					(      __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   __UpperCAmelCase					(      __a :     Matrix      )     ->	Matrix | None:

					"""simple docstring"""

					if location := find_empty_location(__a      ):
										_a ,   _a      :       Optional[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      :       List[str]   =						digit

															if sudoku(__a      ) is not None:
																				return grid

															_a      :       Optional[int]   =						0

					return None



def   __UpperCAmelCase					(      __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:''')
						a__												=						sudoku(example_grid)
						if solution is not None:
									print_solution(solution)
						else:
									print('''Cannot find a solution.''')





def  __lowerCamelCase					( _lowercase			)       ->      list:
     UpperCamelCase						    =					len(_lowercase			)
     for _ in range(_lowercase			):
          for i in range(_ % 2						,     arr_size - 1						,     2			):
               if arr[i + 1] < arr[i]:
                    UpperCamelCase    ,		UpperCamelCase						    =					arr[i + 1], arr[i]

     return arr


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


