






from __future__ import annotations

def      lowerCAmelCase__	(    _a       :			List[str]  ,      _a       :			str  ,      _a       :			int  ,      _a       :			int  ,      _a       :			Optional[Any]  ,      ):
		snake_case_				:							Optional[Any]						 =       len(__UpperCamelCase    )

		# 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(__UpperCamelCase    ):
				# 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]  ,      __UpperCamelCase  ,      __UpperCamelCase  ,      )

def      lowerCAmelCase__	(    _a       :			Tuple    ):
		snake_case_				:							Optional[int]						 =       []
		depth_first_search([]  ,      []  ,      []  ,      __UpperCamelCase  ,      __UpperCamelCase    )

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

		print(len(__UpperCamelCase    )  ,      "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_speech_available, is_torch_available


lowercase  :							int			  =    {
    '''configuration_audio_spectrogram_transformer''': [
        '''AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''ASTConfig''',
    ]
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							lowercase  :							Optional[Any]			  =    [
							    '''AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''ASTForAudioClassification''',
							    '''ASTModel''',
							    '''ASTPreTrainedModel''',
							]

try:
							if not is_speech_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							lowercase  :							Optional[int]			  =    ['''ASTFeatureExtractor''']

if TYPE_CHECKING:
							from .configuration_audio_spectrogram_transformer import (
							    AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    ASTConfig,
							)

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_audio_spectrogram_transformer import (
														    AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
														    ASTForAudioClassification,
														    ASTModel,
														    ASTPreTrainedModel,
														)

							try:
														if not is_speech_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .feature_extraction_audio_spectrogram_transformer import ASTFeatureExtractor


else:
							import sys

							lowercase  :							Optional[int]			  =    _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
