



from __future__ import annotations


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__					,			):

				"""simple docstring"""


				lowercase__					:   Union[str, Any]													=					len(lowerCamelCase__						)

				# If row is equal to the size of the board it means there are a queen in each row in
				# the current board (possible_board)
				if row == n:
								# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
								# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
								boards.append([". " * i + "Q " + ". " * (n - 1 - i) for i in possible_board]						)
								return

				# We iterate each column in the row to find all possible results in each row
				for col in range(lowerCamelCase__						):
								# We apply that we learned previously. First we check that in the current board
								# (possible_board) there are not other same value because if there is it means
								# that there are a collision in vertical. Then we apply the two formulas we
								# learned before:
								#
								# 45º: y - x = b or 45: row - col = b
								# 135º: y + x = b or row + col = b.
								#
								# And we verify if the results of this two formulas not exist in their variables
								# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
								#
								# If any or these are True it means there is a collision so we continue to the
								# next value in the for loop.
								if (
								    col in possible_board
								    or row - col in diagonal_right_collisions
								    or row + col in diagonal_left_collisions
								):
												continue

								# If it is False we call dfs function again and we update the inputs
								depth_first_search(
								    [*possible_board, col]					,			[*diagonal_right_collisions, row - col]					,			[*diagonal_left_collisions, row + col]					,			lowerCamelCase__					,			lowerCamelCase__					,			)


def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				lowercase__					:   list[list[str]]													=					[]
				depth_first_search([]					,			[]					,			[]					,			lowerCamelCase__					,			lowerCamelCase__						)

				# Print all the boards
				for board in boards:
								for column in board:
												print(lowerCamelCase__						)
								print(""						)

				print(len(lowerCamelCase__						)					,			"solutions were found."						)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				n_queens_solution(4)









from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase__					  =  {}

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

try:
				if not is_tokenizers_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				lowerCAmelCase__					  =  ['''NllbTokenizerFast''']


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

				try:
								if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_nllb_fast import NllbTokenizerFast

else:
				import sys

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




