

import warnings
from typing import Any, Dict, List, Optional, Union

import numpy as np

from ...audio_utils import mel_filter_bank, optimal_fft_length, spectrogram, window_function
from ...feature_extraction_sequence_utils import SequenceFeatureExtractor
from ...feature_extraction_utils import BatchFeature
from ...utils import PaddingStrategy, TensorType, logging


a		=logging.get_logger(__name__)






class 	A_		(	SCREAMING_SNAKE_CASE    ):
							_UpperCAmelCase   :  Any										=				['''input_values''', '''attention_mask''']
							def __init__(		self		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      int = 1       ,SCREAMING_SNAKE_CASE__		:      int = 1_6_0_0_0       ,SCREAMING_SNAKE_CASE__		:      float = 0.0       ,SCREAMING_SNAKE_CASE__		:      bool = False       ,SCREAMING_SNAKE_CASE__		:      int = 8_0       ,SCREAMING_SNAKE_CASE__		:      int = 1_6       ,SCREAMING_SNAKE_CASE__		:      int = 6_4       ,SCREAMING_SNAKE_CASE__		:      str = "hann_window"       ,SCREAMING_SNAKE_CASE__		:      float = 1.0       ,SCREAMING_SNAKE_CASE__		:      float = 8_0       ,SCREAMING_SNAKE_CASE__		:      float = 7_6_0_0       ,SCREAMING_SNAKE_CASE__		:      float = 1E-10       ,SCREAMING_SNAKE_CASE__		:      int = 2       ,SCREAMING_SNAKE_CASE__		:      bool = True       ,**SCREAMING_SNAKE_CASE__		:      Optional[int]       ,):
								super().__init__(feature_size=SCREAMING_SNAKE_CASE__       ,sampling_rate=SCREAMING_SNAKE_CASE__       ,padding_value=SCREAMING_SNAKE_CASE__       ,**SCREAMING_SNAKE_CASE__)
								__lowerCamelCase    :    List[Any] 	=			do_normalize
								__lowerCamelCase    :    Any 	=			return_attention_mask

								__lowerCamelCase    :    List[str] 	=			num_mel_bins
								__lowerCamelCase    :    str 	=			hop_length
								__lowerCamelCase    :    Optional[Any] 	=			win_length
								__lowerCamelCase    :    str 	=			win_function
								__lowerCamelCase    :    Union[str, Any] 	=			frame_signal_scale
								__lowerCamelCase    :    Dict 	=			fmin
								__lowerCamelCase    :    Optional[int] 	=			fmax
								__lowerCamelCase    :    Dict 	=			mel_floor
								__lowerCamelCase    :    Optional[Any] 	=			reduction_factor

								__lowerCamelCase    :    str 	=			win_length * sampling_rate // 1_0_0_0
								__lowerCamelCase    :    Optional[int] 	=			hop_length * sampling_rate // 1_0_0_0
								__lowerCamelCase    :    Union[str, Any] 	=			optimal_fft_length(self.sample_size)
								__lowerCamelCase    :    List[str] 	=			(self.n_fft // 2) + 1

								__lowerCamelCase    :    Optional[Any] 	=			window_function(window_length=self.sample_size       ,name=self.win_function       ,periodic=SCREAMING_SNAKE_CASE__)

								__lowerCamelCase    :    Dict 	=			mel_filter_bank(
								    num_frequency_bins=self.n_freqs       ,num_mel_filters=self.num_mel_bins       ,min_frequency=self.fmin       ,max_frequency=self.fmax       ,sampling_rate=self.sampling_rate       ,norm='slaney'       ,mel_scale='slaney'       ,)

								if frame_signal_scale != 1.0:
									warnings.warn(
									    'The argument `frame_signal_scale` is deprecated and will be removed in version 4.30.0 of Transformers'       ,SCREAMING_SNAKE_CASE__       ,)
								if reduction_factor != 2.0:
									warnings.warn(
									    'The argument `reduction_factor` is deprecated and will be removed in version 4.30.0 of Transformers'       ,SCREAMING_SNAKE_CASE__       ,)
							@staticmethod
							# Copied from transformers.models.wav2vec2.feature_extraction_wav2vec2.Wav2Vec2FeatureExtractor.zero_mean_unit_var_norm
							def    lowerCAmelCase					(		SCREAMING_SNAKE_CASE__		:      List[np.ndarray]       ,SCREAMING_SNAKE_CASE__		:      List[np.ndarray]       ,SCREAMING_SNAKE_CASE__		:      float = 0.0):
								if attention_mask is not None:
									__lowerCamelCase    :    List[Any] 	=			np.array(SCREAMING_SNAKE_CASE__       ,np.intaa)
									__lowerCamelCase    :    Optional[int] 	=			[]

									for vector, length in zip(SCREAMING_SNAKE_CASE__       ,attention_mask.sum(-1)):
										__lowerCamelCase    :    Tuple 	=			(vector - vector[:length].mean()) / np.sqrt(vector[:length].var() + 1E-7)
										if length < normed_slice.shape[0]:
											__lowerCamelCase    :    Optional[int] 	=			padding_value

										normed_input_values.append(SCREAMING_SNAKE_CASE__)
								else:
									__lowerCamelCase    :    Optional[int] 	=			[(x - x.mean()) / np.sqrt(x.var() + 1E-7) for x in input_values]

								return normed_input_values
							def    lowerCAmelCase					(		self		:      int       ,SCREAMING_SNAKE_CASE__		:      np.ndarray       ,):
								__lowerCamelCase    :    Any 	=			spectrogram(
								    SCREAMING_SNAKE_CASE__       ,window=self.window       ,frame_length=self.sample_size       ,hop_length=self.sample_stride       ,fft_length=self.n_fft       ,mel_filters=self.mel_filters       ,mel_floor=self.mel_floor       ,log_mel='log10'       ,)
								return log_mel_spec.T
							def __call__(		self		:      int       ,SCREAMING_SNAKE_CASE__		:      Optional[Union[np.ndarray, List[float], List[np.ndarray], List[List[float]]]] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[Union[np.ndarray, List[float], List[np.ndarray], List[List[float]]]] = None       ,SCREAMING_SNAKE_CASE__		:      Union[bool, str, PaddingStrategy] = False       ,SCREAMING_SNAKE_CASE__		:      Optional[int] = None       ,SCREAMING_SNAKE_CASE__		:      bool = False       ,SCREAMING_SNAKE_CASE__		:      Optional[int] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[bool] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[Union[str, TensorType]] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[int] = None       ,**SCREAMING_SNAKE_CASE__		:      Optional[Any]       ,):
								if audio is None and audio_target is None:
									raise ValueError('You must provide either `audio` or `audio_target` values.')

								if sampling_rate is not None:
									if sampling_rate != self.sampling_rate:
										raise ValueError(
										    F"The model corresponding to this feature extractor: {self} was trained using a sampling rate of"
										    F" {self.sampling_rate}. Please make sure that the provided audio input was sampled with"
										    F" {self.sampling_rate} and not {sampling_rate}.")
								else:
									logger.warning(
									    'It is strongly recommended to pass the ``sampling_rate`` argument to this function. '
									    'Failing to do so can result in silent errors that might be hard to debug.')

								if audio is not None:
									__lowerCamelCase    :    Dict 	=			self._process_audio(
									    SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,**SCREAMING_SNAKE_CASE__       ,)
								else:
									__lowerCamelCase    :    List[str] 	=			None

								if audio_target is not None:
									__lowerCamelCase    :    Optional[Any] 	=			self._process_audio(
									    SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,**SCREAMING_SNAKE_CASE__       ,)

									if inputs is None:
										return inputs_target
									else:
										__lowerCamelCase    :    str 	=			inputs_target['input_values']
										__lowerCamelCase    :    Any 	=			inputs_target.get('attention_mask')
										if decoder_attention_mask is not None:
											__lowerCamelCase    :    Union[str, Any] 	=			decoder_attention_mask

								return inputs
							def    lowerCAmelCase					(		self		:      Optional[int]       ,SCREAMING_SNAKE_CASE__		:      Union[np.ndarray, List[float], List[np.ndarray], List[List[float]]]       ,SCREAMING_SNAKE_CASE__		:      bool = False       ,SCREAMING_SNAKE_CASE__		:      Union[bool, str, PaddingStrategy] = False       ,SCREAMING_SNAKE_CASE__		:      Optional[int] = None       ,SCREAMING_SNAKE_CASE__		:      bool = False       ,SCREAMING_SNAKE_CASE__		:      Optional[int] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[bool] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[Union[str, TensorType]] = None       ,**SCREAMING_SNAKE_CASE__		:      List[str]       ,):
								__lowerCamelCase    :    List[Any] 	=			isinstance(SCREAMING_SNAKE_CASE__       ,np.ndarray) and len(speech.shape) > 1
								if is_batched_numpy and len(speech.shape) > 2:
									raise ValueError(F"Only mono-channel audio is supported for input to {self}")
								__lowerCamelCase    :    Union[str, Any] 	=			is_batched_numpy or (
								    isinstance(SCREAMING_SNAKE_CASE__       ,(list, tuple)) and (isinstance(speech[0]       ,(np.ndarray, tuple, list)))
								)

								if is_batched:
									__lowerCamelCase    :    Optional[int] 	=			[np.asarray(SCREAMING_SNAKE_CASE__       ,dtype=np.floataa) for speech in speech]
								elif not is_batched and not isinstance(SCREAMING_SNAKE_CASE__       ,np.ndarray):
									__lowerCamelCase    :    Dict 	=			np.asarray(SCREAMING_SNAKE_CASE__       ,dtype=np.floataa)
								elif isinstance(SCREAMING_SNAKE_CASE__       ,np.ndarray) and speech.dtype is np.dtype(np.floataa):
									__lowerCamelCase    :    str 	=			speech.astype(np.floataa)

								# always return batch
								if not is_batched:
									__lowerCamelCase    :    List[str] 	=			[speech]

								# needed to make pad() work on spectrogram inputs
								__lowerCamelCase    :    str 	=			self.feature_size

								# convert into correct format for padding
								if is_target:
									__lowerCamelCase    :    Union[str, Any] 	=			[self._extract_mel_features(SCREAMING_SNAKE_CASE__) for waveform in speech]
									__lowerCamelCase    :    int 	=			BatchFeature({'input_values': features})
									__lowerCamelCase    :    Optional[Any] 	=			self.num_mel_bins
								else:
									__lowerCamelCase    :    Optional[Any] 	=			BatchFeature({'input_values': speech})

								__lowerCamelCase    :    List[str] 	=			self.pad(
								    SCREAMING_SNAKE_CASE__       ,padding=SCREAMING_SNAKE_CASE__       ,max_length=SCREAMING_SNAKE_CASE__       ,truncation=SCREAMING_SNAKE_CASE__       ,pad_to_multiple_of=SCREAMING_SNAKE_CASE__       ,return_attention_mask=SCREAMING_SNAKE_CASE__       ,**SCREAMING_SNAKE_CASE__       ,)

								__lowerCamelCase    :    Optional[int] 	=			feature_size_hack

								# convert input values to correct format
								__lowerCamelCase    :    Tuple 	=			padded_inputs['input_values']
								if not isinstance(input_values[0]       ,np.ndarray):
									__lowerCamelCase    :    List[Any] 	=			[np.asarray(SCREAMING_SNAKE_CASE__       ,dtype=np.floataa) for array in input_values]
								elif (
								    not isinstance(SCREAMING_SNAKE_CASE__       ,np.ndarray)
								    and isinstance(input_values[0]       ,np.ndarray)
								    and input_values[0].dtype is np.dtype(np.floataa)
								):
									__lowerCamelCase    :    str 	=			[array.astype(np.floataa) for array in input_values]
								elif isinstance(SCREAMING_SNAKE_CASE__       ,np.ndarray) and input_values.dtype is np.dtype(np.floataa):
									__lowerCamelCase    :    List[str] 	=			input_values.astype(np.floataa)

								# convert attention_mask to correct format
								__lowerCamelCase    :    Tuple 	=			padded_inputs.get('attention_mask')
								if attention_mask is not None:
									__lowerCamelCase    :    Dict 	=			[np.asarray(SCREAMING_SNAKE_CASE__       ,dtype=np.intaa) for array in attention_mask]

								# zero-mean and unit-variance normalization
								if not is_target and self.do_normalize:
									__lowerCamelCase    :    Optional[int] 	=			(
									    attention_mask
									    if self._get_padding_strategies(SCREAMING_SNAKE_CASE__       ,max_length=SCREAMING_SNAKE_CASE__) is not PaddingStrategy.DO_NOT_PAD
									    else None
									)
									__lowerCamelCase    :    List[str] 	=			self.zero_mean_unit_var_norm(
									    padded_inputs['input_values']       ,attention_mask=SCREAMING_SNAKE_CASE__       ,padding_value=self.padding_value)

								if return_tensors is not None:
									__lowerCamelCase    :    int 	=			padded_inputs.convert_to_tensors(SCREAMING_SNAKE_CASE__)

								return padded_inputs


							def    lowerCAmelCase					(		self		:      Dict):
								__lowerCamelCase    :    Any 	=			super().to_dict()

								# Don't serialize these as they are derived from the other properties.
								__lowerCamelCase    :    List[Any] 	=			['window', 'mel_filters', 'sample_size', 'sample_stride', 'n_fft', 'n_freqs']
								for name in names:
									if name in output:
										del output[name]

								return output







from __future__ import annotations






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)  ->					None:
	__lowerCamelCase    :    int 	=			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        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					None:
	__lowerCamelCase    :    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)




