
from __future__ import annotations


def 							__A(lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase						,  )		->				None:

		"""simple docstring"""






		_UpperCamelCase						    =	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 							__A(lowerCAmelCase )		->				None:

		"""simple docstring"""






		_UpperCamelCase						    =	[]
		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 List, Optional, Tuple, Union

import torch

from ...utils import logging, randn_tensor
from ..pipeline_utils import AudioPipelineOutput, DiffusionPipeline


lowerCamelCase__	=							logging.get_logger(__name__)  # pylint: disable=invalid-name







class        lowerCAmelCase__      (   __lowercase	):

						def __init__(			self       ,							a       ,							a				)					->      Any:


								'''simple docstring'''

								super().__init__()
								self.register_modules(unet=a       ,							scheduler=a				)







						@torch.no_grad()
						def __call__(			self       ,							a = 1       ,							a = 1_00       ,							a = None       ,							a = None       ,							a = True       ,							)					->      Union[AudioPipelineOutput, Tuple]:


								'''simple docstring'''

								if audio_length_in_s is None:
										_UpperCamelCase						    =	self.unet.config.sample_size / self.unet.config.sample_rate

								_UpperCamelCase						    =	audio_length_in_s * self.unet.config.sample_rate

								_UpperCamelCase						    =	2 ** len(self.unet.up_blocks				)
								if sample_size < 3 * down_scale_factor:
										raise ValueError(
										    F'{audio_length_in_s} is too small. Make sure it\'s bigger or equal to'
										    F' {3 * down_scale_factor / self.unet.config.sample_rate}.'				)

								_UpperCamelCase						    =	int(a				)
								if sample_size % down_scale_factor != 0:
										_UpperCamelCase						    =	(
										    (audio_length_in_s * self.unet.config.sample_rate) // down_scale_factor + 1
										) * down_scale_factor
										logger.info(
										    F'{audio_length_in_s} is increased to {sample_size / self.unet.config.sample_rate} so that it can be handled'
										    F' by the model. It will be cut to {original_sample_size / self.unet.config.sample_rate} after the denoising'
										    """ process."""				)
								_UpperCamelCase						    =	int(a				)

								_UpperCamelCase						    =	next(iter(self.unet.parameters()				)				).dtype
								_UpperCamelCase						    =	(batch_size, self.unet.config.in_channels, sample_size)
								if isinstance(a       ,							a				) and len(a				) != batch_size:
										raise ValueError(
										    F'You have passed a list of generators of length {len(a				)}, but requested an effective batch'
										    F' size of {batch_size}. Make sure the batch size matches the length of the generators.'				)

								_UpperCamelCase						    =	randn_tensor(a       ,							generator=a       ,							device=self.device       ,							dtype=a				)

								# set step values
								self.scheduler.set_timesteps(a       ,							device=audio.device				)
								_UpperCamelCase						    =	self.scheduler.timesteps.to(a				)

								for t in self.progress_bar(self.scheduler.timesteps				):
										# 1. predict noise model_output
										_UpperCamelCase						    =	self.unet(a       ,							a				).sample

										# 2. compute previous image: x_t -> t_t-1
										_UpperCamelCase						    =	self.scheduler.step(a       ,							a       ,							a				).prev_sample

								_UpperCamelCase						    =	audio.clamp(-1       ,							1				).float().cpu().numpy()

								_UpperCamelCase						    =	audio[:, :, :original_sample_size]

								if not return_dict:
										return (audio,)

								return AudioPipelineOutput(audios=a				)



