

'''simple docstring'''
from __future__ import annotations


def  a__       (    _SCREAMING_SNAKE_CASE   :       list[int]	,				_SCREAMING_SNAKE_CASE   :       list[int]	,				_SCREAMING_SNAKE_CASE   :       list[int]	,				_SCREAMING_SNAKE_CASE   :       list[list[str]]	,				_SCREAMING_SNAKE_CASE   :       int	,				)     ->					None:


	"""simple docstring"""





	UpperCAmelCase_     :      Optional[int]						=  len(_SCREAMING_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(_SCREAMING_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]	,				_SCREAMING_SNAKE_CASE	,				_SCREAMING_SNAKE_CASE	,				)


def  a__       (    _SCREAMING_SNAKE_CASE   :       int				)     ->					None:


	"""simple docstring"""





	UpperCAmelCase_     :      list[list[str]]						=  []
	depth_first_search([]	,				[]	,				[]	,				_SCREAMING_SNAKE_CASE	,				_SCREAMING_SNAKE_CASE				)

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

	print(len(_SCREAMING_SNAKE_CASE				)	,				"solutions were found."				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)






"""simple docstring"""





import torch

from diffusers import DPMSolverSDEScheduler
from diffusers.utils import torch_device
from diffusers.utils.testing_utils import require_torchsde

from .test_schedulers import SchedulerCommonTest






@require_torchsde
class        _UpperCAmelCase(       lowerCamelCase      ):
		lowercase__         = (DPMSolverSDEScheduler,)
		lowercase__         = 10



		def 		UpperCAmelCase				(   self							,						**__a)			->			int:






							'''simple docstring'''
							_UpperCamelCase									=    {
							    '''num_train_timesteps''': 11_00,
							    '''beta_start''': 0.0001,
							    '''beta_end''': 0.02,
							    '''beta_schedule''': '''linear''',
							    '''noise_sampler_seed''': 0,
							}

							config.update(**__a)
							return config



		def 		UpperCAmelCase				(   self)			->			Union[str, Any]:






							'''simple docstring'''
							for timesteps in [10, 50, 1_00, 10_00]:
												self.check_over_configs(num_train_timesteps=__a)



		def 		UpperCAmelCase				(   self)			->			Dict:






							'''simple docstring'''
							for beta_start, beta_end in zip([0.0_0001, 0.0001, 0.001]							,						[0.0002, 0.002, 0.02]):
												self.check_over_configs(beta_start=__a							,						beta_end=__a)



		def 		UpperCAmelCase				(   self)			->			Optional[int]:






							'''simple docstring'''
							for schedule in ["linear", "scaled_linear"]:
												self.check_over_configs(beta_schedule=__a)



		def 		UpperCAmelCase				(   self)			->			str:






							'''simple docstring'''
							for prediction_type in ["epsilon", "v_prediction"]:
												self.check_over_configs(prediction_type=__a)



		def 		UpperCAmelCase				(   self)			->			Union[str, Any]:






							'''simple docstring'''
							_UpperCamelCase									=    self.scheduler_classes[0]
							_UpperCamelCase									=    self.get_scheduler_config()
							_UpperCamelCase									=    scheduler_class(**__a)

							scheduler.set_timesteps(self.num_inference_steps)

							_UpperCamelCase									=    self.dummy_model()
							_UpperCamelCase									=    self.dummy_sample_deter * scheduler.init_noise_sigma
							_UpperCamelCase									=    sample.to(__a)

							for i, t in enumerate(scheduler.timesteps):
												_UpperCamelCase									=    scheduler.scale_model_input(__a							,						__a)

												_UpperCamelCase									=    model(__a							,						__a)

												_UpperCamelCase									=    scheduler.step(__a							,						__a							,						__a)
												_UpperCamelCase									=    output.prev_sample

							_UpperCamelCase									=    torch.sum(torch.abs(__a))
							_UpperCamelCase									=    torch.mean(torch.abs(__a))

							if torch_device in ["mps"]:
												assert abs(result_sum.item() - 167.47_8210_4492_1875) < 1e-2
												assert abs(result_mean.item() - 0.2178_7059_6456_5277) < 1e-3
							elif torch_device in ["cuda"]:
												assert abs(result_sum.item() - 171.59_3521_1181_6406) < 1e-2
												assert abs(result_mean.item() - 0.2_2342_9068_9229_9652) < 1e-3
							else:
												assert abs(result_sum.item() - 162.52_3834_2285_1562) < 1e-2
												assert abs(result_mean.item() - 0.211_6195_7085_1326) < 1e-3



		def 		UpperCAmelCase				(   self)			->			List[str]:






							'''simple docstring'''
							_UpperCamelCase									=    self.scheduler_classes[0]
							_UpperCamelCase									=    self.get_scheduler_config(prediction_type='''v_prediction''')
							_UpperCamelCase									=    scheduler_class(**__a)

							scheduler.set_timesteps(self.num_inference_steps)

							_UpperCamelCase									=    self.dummy_model()
							_UpperCamelCase									=    self.dummy_sample_deter * scheduler.init_noise_sigma
							_UpperCamelCase									=    sample.to(__a)

							for i, t in enumerate(scheduler.timesteps):
												_UpperCamelCase									=    scheduler.scale_model_input(__a							,						__a)

												_UpperCamelCase									=    model(__a							,						__a)

												_UpperCamelCase									=    scheduler.step(__a							,						__a							,						__a)
												_UpperCamelCase									=    output.prev_sample

							_UpperCamelCase									=    torch.sum(torch.abs(__a))
							_UpperCamelCase									=    torch.mean(torch.abs(__a))

							if torch_device in ["mps"]:
												assert abs(result_sum.item() - 124.77_1492_0043_9453) < 1e-2
												assert abs(result_mean.item() - 0.1_6226_2890_1481_6284) < 1e-3
							elif torch_device in ["cuda"]:
												assert abs(result_sum.item() - 128.1_6633_6059_5703) < 1e-2
												assert abs(result_mean.item() - 0.1_6688_3260_0116_7297) < 1e-3
							else:
												assert abs(result_sum.item() - 119.8_4875_4882_8125) < 1e-2
												assert abs(result_mean.item() - 0.1560_5306_6253_6621) < 1e-3



		def 		UpperCAmelCase				(   self)			->			Any:






							'''simple docstring'''
							_UpperCamelCase									=    self.scheduler_classes[0]
							_UpperCamelCase									=    self.get_scheduler_config()
							_UpperCamelCase									=    scheduler_class(**__a)

							scheduler.set_timesteps(self.num_inference_steps							,						device=__a)

							_UpperCamelCase									=    self.dummy_model()
							_UpperCamelCase									=    self.dummy_sample_deter.to(__a) * scheduler.init_noise_sigma

							for t in scheduler.timesteps:
												_UpperCamelCase									=    scheduler.scale_model_input(__a							,						__a)

												_UpperCamelCase									=    model(__a							,						__a)

												_UpperCamelCase									=    scheduler.step(__a							,						__a							,						__a)
												_UpperCamelCase									=    output.prev_sample

							_UpperCamelCase									=    torch.sum(torch.abs(__a))
							_UpperCamelCase									=    torch.mean(torch.abs(__a))

							if torch_device in ["mps"]:
												assert abs(result_sum.item() - 167.46_9573_9746_0938) < 1e-2
												assert abs(result_mean.item() - 0.2_1805_9346_0798_2635) < 1e-3
							elif torch_device in ["cuda"]:
												assert abs(result_sum.item() - 171.59_3536_3769_5312) < 1e-2
												assert abs(result_mean.item() - 0.2_2342_9083_8241_5771) < 1e-3
							else:
												assert abs(result_sum.item() - 162.52_3834_2285_1562) < 1e-2
												assert abs(result_mean.item() - 0.211_6195_7085_1326) < 1e-3




		def 		UpperCAmelCase				(   self)			->			Any:






							'''simple docstring'''
							_UpperCamelCase									=    self.scheduler_classes[0]
							_UpperCamelCase									=    self.get_scheduler_config()
							_UpperCamelCase									=    scheduler_class(**__a							,						use_karras_sigmas=__a)

							scheduler.set_timesteps(self.num_inference_steps							,						device=__a)

							_UpperCamelCase									=    self.dummy_model()
							_UpperCamelCase									=    self.dummy_sample_deter.to(__a) * scheduler.init_noise_sigma
							_UpperCamelCase									=    sample.to(__a)

							for t in scheduler.timesteps:
												_UpperCamelCase									=    scheduler.scale_model_input(__a							,						__a)

												_UpperCamelCase									=    model(__a							,						__a)

												_UpperCamelCase									=    scheduler.step(__a							,						__a							,						__a)
												_UpperCamelCase									=    output.prev_sample

							_UpperCamelCase									=    torch.sum(torch.abs(__a))
							_UpperCamelCase									=    torch.mean(torch.abs(__a))

							if torch_device in ["mps"]:
												assert abs(result_sum.item() - 176.66_9741_3574_2188) < 1e-2
												assert abs(result_mean.item() - 0.2_3003_8727_3098_1811) < 1e-2
							elif torch_device in ["cuda"]:
												assert abs(result_sum.item() - 177.63_6535_6445_3125) < 1e-2
												assert abs(result_mean.item() - 0.2_3003_8727_3098_1811) < 1e-2
							else:
												assert abs(result_sum.item() - 170.3_1352_2338_8672) < 1e-2
												assert abs(result_mean.item() - 0.2_3003_8727_3098_1811) < 1e-2






