



"""simple docstring"""





from __future__ import annotations

lowerCamelCase       	=						list[list[int]]

# assigning initial values to the grid
lowerCamelCase       	=						[
    [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       	=						[
    [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        a__     (				lowerCAmelCase__     ,      lowerCAmelCase__     ,      lowerCAmelCase__     ,      lowerCAmelCase__				):
      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        a__     (				lowerCAmelCase__				):
      for i in range(9				):
            for j in range(9				):
                  if grid[i][j] == 0:
                        return i, j
      return None
def        a__     (				lowerCAmelCase__				):
      if location := find_empty_location(lowerCAmelCase__				):
            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(lowerCAmelCase__     ,      lowerCAmelCase__     ,      lowerCAmelCase__     ,      lowerCAmelCase__				):
                  UpperCAmelCase_      			=							digit

                  if sudoku(lowerCAmelCase__				) is not None:
                        return grid

                  UpperCAmelCase_      			=							0

      return None
def        a__     (				lowerCAmelCase__				):
      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:""")
    lowerCamelCase       	=						sudoku(example_grid)
    if solution is not None:
      print_solution(solution)
    else:
      print("""Cannot find a solution.""")









"""simple docstring"""





from ..utils import DummyObject, requires_backends
class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Tuple		,    *_UpperCAmelCase      :  str		,    **_UpperCAmelCase      :  Any   )			->						List[str]:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  Tuple   )			->						List[Any]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  List[Any]		,    **_UpperCAmelCase      :  str   )			->						int:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Union[str, Any]		,    *_UpperCAmelCase      :  Any		,    **_UpperCAmelCase      :  Tuple   )			->						str:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  str		,    *_UpperCAmelCase      :  Optional[int]		,    **_UpperCAmelCase      :  int   )			->						Any:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[str]		,    *_UpperCAmelCase      :  Optional[Any]		,    **_UpperCAmelCase      :  Optional[int]   )			->						Dict:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Union[str, Any]		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  Dict   )			->						str:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Optional[int]		,    *_UpperCAmelCase      :  int		,    **_UpperCAmelCase      :  List[Any]   )			->						List[str]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  Dict		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  Union[str, Any]   )			->						int:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Any		,    *_UpperCAmelCase      :  str		,    **_UpperCAmelCase      :  Tuple   )			->						Optional[int]:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  str		,    *_UpperCAmelCase      :  Optional[Any]		,    **_UpperCAmelCase      :  List[str]   )			->						str:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  int		,    *_UpperCAmelCase      :  Any		,    **_UpperCAmelCase      :  int   )			->						Dict:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  str		,    *_UpperCAmelCase      :  int		,    **_UpperCAmelCase      :  Dict   )			->						Tuple:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Optional[Any]		,    *_UpperCAmelCase      :  List[str]		,    **_UpperCAmelCase      :  List[Any]   )			->						List[Any]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  int		,    **_UpperCAmelCase      :  int   )			->						Optional[Any]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Dict		,    *_UpperCAmelCase      :  Any		,    **_UpperCAmelCase      :  Optional[Any]   )			->						int:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  str		,    **_UpperCAmelCase      :  List[str]   )			->						Any:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[str]		,    *_UpperCAmelCase      :  str		,    **_UpperCAmelCase      :  Optional[Any]   )			->						Tuple:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Union[str, Any]		,    *_UpperCAmelCase      :  Optional[int]		,    **_UpperCAmelCase      :  Tuple   )			->						str:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  str		,    *_UpperCAmelCase      :  Union[str, Any]		,    **_UpperCAmelCase      :  Union[str, Any]   )			->						List[str]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  Optional[int]		,    **_UpperCAmelCase      :  Optional[Any]   )			->						str:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Optional[Any]		,    *_UpperCAmelCase      :  str		,    **_UpperCAmelCase      :  int   )			->						Union[str, Any]:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Union[str, Any]		,    *_UpperCAmelCase      :  Optional[Any]		,    **_UpperCAmelCase      :  List[Any]   )			->						str:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  str   )			->						List[str]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  List[str]		,    *_UpperCAmelCase      :  Optional[int]		,    **_UpperCAmelCase      :  Optional[int]   )			->						Tuple:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Union[str, Any]		,    *_UpperCAmelCase      :  Optional[int]		,    **_UpperCAmelCase      :  str   )			->						Union[str, Any]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  Optional[int]		,    *_UpperCAmelCase      :  Any		,    **_UpperCAmelCase      :  List[str]   )			->						Optional[int]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Optional[Any]		,    *_UpperCAmelCase      :  Union[str, Any]		,    **_UpperCAmelCase      :  Optional[Any]   )			->						Tuple:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Optional[int]		,    *_UpperCAmelCase      :  Union[str, Any]		,    **_UpperCAmelCase      :  Dict   )			->						Any:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[str]		,    *_UpperCAmelCase      :  List[str]		,    **_UpperCAmelCase      :  Optional[Any]   )			->						List[str]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Tuple		,    *_UpperCAmelCase      :  List[str]		,    **_UpperCAmelCase      :  Optional[int]   )			->						Tuple:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Any		,    *_UpperCAmelCase      :  Tuple		,    **_UpperCAmelCase      :  Optional[int]   )			->						Any:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  List[Any]		,    *_UpperCAmelCase      :  int		,    **_UpperCAmelCase      :  int   )			->						int:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  Tuple		,    *_UpperCAmelCase      :  int		,    **_UpperCAmelCase      :  Any   )			->						List[Any]:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  str		,    *_UpperCAmelCase      :  int		,    **_UpperCAmelCase      :  str   )			->						Any:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  int		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  List[Any]   )			->						Dict:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )



class 				lowercase__       (   metaclass=SCREAMING_SNAKE_CASE				):







       '''simple docstring'''


       UpperCamelCase						=					['''flax''']



       def __init__(							self      :  int		,    *_UpperCAmelCase      :  Any		,    **_UpperCAmelCase      :  int   )			->						Union[str, Any]:


             '''simple docstring'''




             requires_backends(self		,    ["flax"]   )



       @classmethod
       def 					lowercase__    (							cls      :  Optional[int]		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  Dict   )			->						Dict:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )







       @classmethod
       def 					lowercase__    (							cls      :  str		,    *_UpperCAmelCase      :  Dict		,    **_UpperCAmelCase      :  Any   )			->						List[str]:


             '''simple docstring'''




             requires_backends(cls		,    ["flax"]   )




