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       __lowerCAmelCase      (						A_   : Matrix						,	A_   : int						,	A_   : int						,	A_   : int					)    ->  bool:
  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       __lowerCAmelCase      (						A_   : Matrix					)    ->  tuple[int, int] | None:
  for i in range(9					):
    for j in range(9					):
      if grid[i][j] == 0:
        return i, j
  return None




def       __lowerCAmelCase      (						A_   : Matrix					)    ->  Matrix | None:
  if location := find_empty_location(A_					):
    __UpperCAmelCase    ,		__UpperCAmelCase						    =       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_					):
      __UpperCAmelCase						    =       digit

      if sudoku(A_					) is not None:
        return grid

      __UpperCAmelCase						    =       0

  return None




def       __lowerCAmelCase      (						A_   : Matrix					)    ->  None:
  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.""")




from abc import ABC, abstractmethod
from argparse import ArgumentParser


class 			UpperCAmelCase__    (		snake_case					):



  """simple docstring"""






  @staticmethod
  @abstractmethod
  def 	_UpperCAmelCase				(				__lowerCAmelCase:			ArgumentParser   ) -> Tuple:




    '''simple docstring'''




    raise NotImplementedError()






  @abstractmethod
  def 	_UpperCAmelCase				(				self:			List[str]   ) -> List[Any]:




    '''simple docstring'''




    raise NotImplementedError()



