


"""simple docstring"""




from __future__ import annotations

def 			lowercase				(						lowerCAmelCase__					:	list[int]       ,   lowerCAmelCase__					:	list[int]       ,   lowerCAmelCase__					:	list[int]       ,   lowerCAmelCase__					:	list[list[str]]       ,   lowerCAmelCase__					:	int       ,   )					-> List[Any]:
		__a	 =     len(snake_case__     )

		# 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(snake_case__     ):
				# 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]       ,   snake_case__       ,   snake_case__       ,   )

def 			lowercase				(						lowerCAmelCase__					:	int     )					-> Tuple:
		__a	 =     []
		depth_first_search([]       ,   []       ,   []       ,   snake_case__       ,   snake_case__     )

		# Print all the boards
		for board in boards:
				for column in board:
						print(snake_case__     )
				print(''''''     )

		print(len(snake_case__     )       ,   '''solutions were found.'''     )


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				n_queens_solution(4)








"""simple docstring"""


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowercase				 =					{
    '''configuration_xlm_roberta_xl''': [
        '''XLM_ROBERTA_XL_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''XLMRobertaXLConfig''',
        '''XLMRobertaXLOnnxConfig''',
    ],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		_lowercase				 =					[
		    '''XLM_ROBERTA_XL_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''XLMRobertaXLForCausalLM''',
		    '''XLMRobertaXLForMaskedLM''',
		    '''XLMRobertaXLForMultipleChoice''',
		    '''XLMRobertaXLForQuestionAnswering''',
		    '''XLMRobertaXLForSequenceClassification''',
		    '''XLMRobertaXLForTokenClassification''',
		    '''XLMRobertaXLModel''',
		    '''XLMRobertaXLPreTrainedModel''',
		]

if TYPE_CHECKING:
		from .configuration_xlm_roberta_xl import (
		    XLM_ROBERTA_XL_PRETRAINED_CONFIG_ARCHIVE_MAP,
		    XLMRobertaXLConfig,
		    XLMRobertaXLOnnxConfig,
		)

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_xlm_roberta_xl import (
				    XLM_ROBERTA_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
				    XLMRobertaXLForCausalLM,
				    XLMRobertaXLForMaskedLM,
				    XLMRobertaXLForMultipleChoice,
				    XLMRobertaXLForQuestionAnswering,
				    XLMRobertaXLForSequenceClassification,
				    XLMRobertaXLForTokenClassification,
				    XLMRobertaXLModel,
				    XLMRobertaXLPreTrainedModel,
				)

else:
		import sys

		_lowercase				 =					_LazyModule(__name__, globals()['''__file__'''], _import_structure)