




import re

from filelock import FileLock


try:
 import nltk

 _lowerCamelCase      			=						True
except (ImportError, ModuleNotFoundError):
 _lowerCamelCase      			=						False

if NLTK_AVAILABLE:
 with FileLock('.lock') as lock:
  nltk.download('punkt', quiet=True)




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						str				)  ->							str:
    re.sub('''<n>'''	,					''''''	,					__UpperCamelCase				)  # remove pegasus newline char
    assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
    return "\n".join(nltk.sent_tokenize(__UpperCamelCase				)				)











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  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						int	,					__UpperCamelCase      :						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  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						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  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							Matrix | None:
    if location := find_empty_location(__UpperCamelCase				):
        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(__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase	,					__UpperCamelCase				):
            UpperCAmelCase_										=					digit

            if sudoku(__UpperCamelCase				) is not None:
                return grid

            UpperCAmelCase_										=					0

    return None




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Matrix				)  ->							None:
    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      			=						sudoku(example_grid)
  if solution is not None:
   print_solution(solution)
  else:
   print('Cannot find a solution.')





