





'''simple docstring'''




from __future__ import annotations



def 		__A		(  lowerCamelCase_			,			lowerCamelCase_			,			lowerCamelCase_			,			lowerCamelCase_			,			lowerCamelCase_			,			):


		"""simple docstring"""



		SCREAMING_SNAKE_CASE :				str		=			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_	):


		"""simple docstring"""



		SCREAMING_SNAKE_CASE :				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)










'''simple docstring'''




import unittest
from typing import Tuple

import torch

from diffusers.utils import floats_tensor, randn_tensor, torch_all_close, torch_device
from diffusers.utils.testing_utils import require_torch




@require_torch
class      UpperCamelCase__					:




					"""simple docstring"""


					@property
					def lowerCamelCase_			(						self				:			Union[str, Any]						):

							'''simple docstring'''



							return self.get_dummy_input()


					@property
					def lowerCamelCase_			(						self				:			List[Any]						):

							'''simple docstring'''



							if self.block_type == "down":
									return (4, 32, 16, 16)
							elif self.block_type == "mid":
									return (4, 32, 32, 32)
							elif self.block_type == "up":
									return (4, 32, 64, 64)

							raise ValueError(f'''\'{self.block_type}\' is not a supported block_type. Set it to \'up\', \'mid\', or \'down\'.'''						)


					def lowerCamelCase_			(						self				:			Union[str, Any]      ,						lowerCamelCase_				:			Dict=True      ,						lowerCamelCase_				:			List[Any]=False      ,						lowerCamelCase_				:			str=False      ,						lowerCamelCase_				:			Optional[int]=False      ,						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE :				Dict		=			4
							SCREAMING_SNAKE_CASE :				Any		=			32
							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			(32, 32)

							SCREAMING_SNAKE_CASE :				int		=			torch.manual_seed(0						)
							SCREAMING_SNAKE_CASE :				Optional[Any]		=			torch.device(lowerCamelCase_						)
							SCREAMING_SNAKE_CASE :				Tuple		=			(batch_size, num_channels) + sizes
							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			randn_tensor(lowerCamelCase_      ,						generator=lowerCamelCase_      ,						device=lowerCamelCase_						)
							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			{"""hidden_states""": hidden_states}

							if include_temb:
									SCREAMING_SNAKE_CASE :				Union[str, Any]		=			1_28
									SCREAMING_SNAKE_CASE :				Optional[Any]		=			randn_tensor((batch_size, temb_channels)      ,						generator=lowerCamelCase_      ,						device=lowerCamelCase_						)

							if include_res_hidden_states_tuple:
									SCREAMING_SNAKE_CASE :				str		=			torch.manual_seed(1						)
									SCREAMING_SNAKE_CASE :				int		=			(randn_tensor(lowerCamelCase_      ,						generator=lowerCamelCase_      ,						device=lowerCamelCase_						),)

							if include_encoder_hidden_states:
									SCREAMING_SNAKE_CASE :				Optional[int]		=			floats_tensor((batch_size, 32, 32)						).to(lowerCamelCase_						)

							if include_skip_sample:
									SCREAMING_SNAKE_CASE :				str		=			randn_tensor(((batch_size, 3) + sizes)      ,						generator=lowerCamelCase_      ,						device=lowerCamelCase_						)

							return dummy_input


					def lowerCamelCase_			(						self				:			Optional[Any]						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE :				Dict		=			{
							    """in_channels""": 32,
							    """out_channels""": 32,
							    """temb_channels""": 1_28,
							}
							if self.block_type == "up":
									SCREAMING_SNAKE_CASE :				List[str]		=			32

							if self.block_type == "mid":
									init_dict.pop("""out_channels"""						)

							SCREAMING_SNAKE_CASE :				Tuple		=			self.dummy_input
							return init_dict, inputs_dict


					def lowerCamelCase_			(						self				:			Any      ,						lowerCamelCase_				:			Any						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE,							SCREAMING_SNAKE_CASE :				Optional[Any]		=			self.prepare_init_args_and_inputs_for_common()
							SCREAMING_SNAKE_CASE :				Tuple		=			self.block_class(**lowerCamelCase_						)
							unet_block.to(lowerCamelCase_						)
							unet_block.eval()

							with torch.no_grad():
									SCREAMING_SNAKE_CASE :				List[str]		=			unet_block(**lowerCamelCase_						)

							if isinstance(lowerCamelCase_      ,						lowerCamelCase_						):
									SCREAMING_SNAKE_CASE :				Dict		=			output[0]

							self.assertEqual(output.shape      ,						self.output_shape						)

							SCREAMING_SNAKE_CASE :				Dict		=			output[0, -1, -3:, -3:]
							SCREAMING_SNAKE_CASE :				List[Any]		=			torch.tensor(lowerCamelCase_						).to(lowerCamelCase_						)
							assert torch_all_close(output_slice.flatten()      ,						lowerCamelCase_      ,						atol=5e-3						)



					@unittest.skipIf(torch_device == """mps"""      ,						"""Training is not supported in mps"""						)
					def lowerCamelCase_			(						self				:			int						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE,							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			self.prepare_init_args_and_inputs_for_common()
							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			self.block_class(**lowerCamelCase_						)
							model.to(lowerCamelCase_						)
							model.train()
							SCREAMING_SNAKE_CASE :				Tuple		=			model(**lowerCamelCase_						)

							if isinstance(lowerCamelCase_      ,						lowerCamelCase_						):
									SCREAMING_SNAKE_CASE :				Optional[Any]		=			output[0]

							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			torch.device(lowerCamelCase_						)
							SCREAMING_SNAKE_CASE :				Optional[int]		=			randn_tensor(output.shape      ,						device=lowerCamelCase_						)
							SCREAMING_SNAKE_CASE :				str		=			torch.nn.functional.mse_loss(lowerCamelCase_      ,						lowerCamelCase_						)
							loss.backward()



