




'''simple docstring'''



from __future__ import annotations

UpperCAmelCase_							:	List[Any]	     =		list[list[int]]

# assigning initial values to the grid
UpperCAmelCase_							:	int	     =		[
    [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_							:	int	     =		[
    [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			(_lowerCamelCase				:  Any ,						_lowerCamelCase				:  Union[str, Any] ,						_lowerCamelCase				:  List[Any] ,						_lowerCamelCase				:  str						)-> int:




     '''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			(_lowerCamelCase				:  Union[str, Any]						)-> int:




     '''simple docstring'''





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







def       _UpperCamelCase			(_lowerCamelCase				:  Optional[int]						)-> List[str]:




     '''simple docstring'''





     if location := find_empty_location(lowerCAmelCase__						):
          __snake_case       ,     __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(lowerCAmelCase__ ,						lowerCAmelCase__ ,						lowerCAmelCase__ ,						lowerCAmelCase__						):
               __snake_case            =	digit

               if sudoku(lowerCAmelCase__						) is not None:
                    return grid

               __snake_case            =	0

     return None







def       _UpperCamelCase			(_lowerCamelCase				:  Tuple						)-> str:




     '''simple docstring'''





     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''' + '''=''' * 2_0)
          print_solution(example_grid)
          print('''\nExample grid solution:''')
          UpperCAmelCase_							:	Dict	     =		sudoku(example_grid)
          if solution is not None:
               print_solution(solution)
          else:
               print('''Cannot find a solution.''')










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


SCREAMING_SNAKE_CASE							    =							{}


try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  SCREAMING_SNAKE_CASE							    =							['MLukeTokenizer']

if TYPE_CHECKING:
  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_mluke import MLukeTokenizer


else:
  import sys

  SCREAMING_SNAKE_CASE							    =							_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



