





'''simple docstring'''






from __future__ import annotations

A   : Optional[Any]             =			list[list[int]]

# assigning initial values to the grid
A   : 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
A   : Optional[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       lowercase_      (		lowercase__				,  lowercase__				,  lowercase__				,  lowercase__						)   ->int:
						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       lowercase_      (		lowercase__						)   ->Tuple:
						for i in range(9						):
												for j in range(9						):
																		if grid[i][j] == 0:
																								return i, j
						return None





def       lowercase_      (		lowercase__						)   ->List[str]:
						if location := find_empty_location(lowercase__						):
												_snake_case					,						_snake_case:   Union[str, Any]  					=		location
						else:
												# If the location is ``None``, then the grid is solved.
												return grid

						for digit in range(1				,  10						):
												if is_safe(lowercase__				,  lowercase__				,  lowercase__				,  lowercase__						):
																		_snake_case:   Dict  					=		digit

																		if sudoku(lowercase__						) is not None:
																								return grid

																		_snake_case:   List[Any]  					=		0

						return None





def       lowercase_      (		lowercase__						)   ->Union[str, Any]:
						for row in grid:
												for cell in row:
																		print(lowercase__				,  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   : Any             =			sudoku(example_grid)
				if solution is not None:
						print_solution(solution)
				else:
						print('Cannot find a solution.')












'''simple docstring'''






A   : str             =			{
    'a': 'AAAAA',
    'b': 'AAAAB',
    'c': 'AAABA',
    'd': 'AAABB',
    'e': 'AABAA',
    'f': 'AABAB',
    'g': 'AABBA',
    'h': 'AABBB',
    'i': 'ABAAA',
    'j': 'BBBAA',
    'k': 'ABAAB',
    'l': 'ABABA',
    'm': 'ABABB',
    'n': 'ABBAA',
    'o': 'ABBAB',
    'p': 'ABBBA',
    'q': 'ABBBB',
    'r': 'BAAAA',
    's': 'BAAAB',
    't': 'BAABA',
    'u': 'BAABB',
    'v': 'BBBAB',
    'w': 'BABAA',
    'x': 'BABAB',
    'y': 'BABBA',
    'z': 'BABBB',
    ' ': ' ',
}


A   : Union[str, Any]             =			{value: key for key, value in encode_dict.items()}





def       lowercase_      (		lowercase__						)   ->str:
						_snake_case:   Union[str, Any]  					=		''
						for letter in word.lower():
												if letter.isalpha() or letter == " ":
																		encoded += encode_dict[letter]
												else:
																		raise Exception('encode() accepts only letters of the alphabet and spaces'						)
						return encoded





def       lowercase_      (		lowercase__						)   ->str:
						if set(lowercase__						) - {"A", "B", " "} != set():
												raise Exception('decode() accepts only \'A\', \'B\' and spaces'						)
						_snake_case:   List[Any]  					=		''
						for word in coded.split():
												while len(lowercase__						) != 0:
																		decoded += decode_dict[word[:5]]
																		_snake_case:   Optional[int]  					=		word[5:]
												decoded += " "
						return decoded.strip()


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

		testmod()





