from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

__lowerCamelCase      :			int							       =		TypeVar('''T''')







class __snake_case    (						Generic[T]		):




   def __init__(   self      :    List[Any]	,     _lowercase      :    T				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				data
     SCREAMING_SNAKE_CASE__      							=				None




   def __str__(   self      :    Optional[Any]				):



     """simple docstring"""






     return f"""{self.data}"""







class __snake_case    (						Generic[T]		):




   def __init__(   self      :    List[str]				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				None




   def __iter__(   self      :    int				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				self.top
     while node:
       yield node.data
       SCREAMING_SNAKE_CASE__      							=				node.next




   def __str__(   self      :    str				):



     """simple docstring"""






     return "->".join([str(_lowercase				) for item in self]				)




   def __len__(   self      :    str				):



     """simple docstring"""






     return len(tuple(iter(self				)				)				)




   def      __a						(   self      :    Dict				):



     """simple docstring"""






     return self.top is None




   def      __a						(   self      :    Union[str, Any]	,     _lowercase      :    T				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				Node(_lowercase				)
     if not self.is_empty():
       SCREAMING_SNAKE_CASE__      							=				self.top
     SCREAMING_SNAKE_CASE__      							=				node




   def      __a						(   self      :    Tuple				):



     """simple docstring"""






     if self.is_empty():
       raise IndexError("""pop from empty stack"""				)
     assert isinstance(self.top	,     _lowercase				)
     SCREAMING_SNAKE_CASE__      							=				self.top
     SCREAMING_SNAKE_CASE__      							=				self.top.next
     return pop_node.data




   def      __a						(   self      :    List[Any]				):



     """simple docstring"""






     if self.is_empty():
       raise IndexError("""peek from empty stack"""				)

     assert self.top is not None
     return self.top.data




   def      __a						(   self      :    Any				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				None


if __name__ == "__main__":
   from doctest import testmod

   testmod()

from __future__ import annotations

__lowerCamelCase      :			Tuple							       =		list[list[int]]

# assigning initial values to the grid
__lowerCamelCase      :			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
__lowerCamelCase      :			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  ( __UpperCamelCase   :	Matrix			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	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  ( __UpperCamelCase   :	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  ( __UpperCamelCase   :	Matrix     )							-> Matrix | None:







  """simple docstring"""





  if location := find_empty_location(__UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__							,					SCREAMING_SNAKE_CASE__      							=				location
  else:
    # If the location is ``None``, then the grid is solved.
    return grid

  for digit in range(1			,					10     ):
    if is_safe(__UpperCamelCase			,					__UpperCamelCase			,					__UpperCamelCase			,					__UpperCamelCase     ):
      SCREAMING_SNAKE_CASE__      							=				digit

      if sudoku(__UpperCamelCase     ) is not None:
        return grid

      SCREAMING_SNAKE_CASE__      							=				0

  return None



def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> None:







  """simple docstring"""





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