






"""simple docstring"""



# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin






class 							__SCREAMING_SNAKE_CASE						(				UpperCamelCase       ,		UpperCamelCase		):
							snake_case_     =							1


							@register_to_config
							def __init__(			self      :						Any			,    snake_case      :						Any=2000			,    snake_case      :						Union[str, Any]=0.1			,    snake_case      :						List[Any]=20			,    snake_case      :						int=1e-3							):
													'''simple docstring'''





													A__						:  Any		  =  None
													A__						:  Tuple		  =  None
													A__						:  List[str]		  =  None


							def 						_UpperCamelCase       (			self      :						int			,    snake_case      :						Any			,    snake_case      :						Union[str, torch.device] = None							):
													'''simple docstring'''





													A__						:  Dict		  =  torch.linspace(1			,    self.config.sampling_eps			,    snake_case			,    device=snake_case							)


							def 						_UpperCamelCase       (			self      :						Any			,    snake_case      :						Optional[int]			,    snake_case      :						Tuple			,    snake_case      :						List[Any]			,    snake_case      :						str=None							):
													'''simple docstring'''





													if self.timesteps is None:
																			raise ValueError(
																			    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""							)

													# TODO(Patrick) better comments + non-PyTorch
													# postprocess model score
													A__						:  int		  =  (
													    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
													)
													A__						:  List[str]		  =  torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff							)							)
													A__						:  Tuple		  =  std.flatten()
													while len(std.shape							) < len(score.shape							):
																			A__						:  Optional[int]		  =  std.unsqueeze(-1							)
													A__						:  Tuple		  =  -score / std

													# compute
													A__						:  Optional[int]		  =  -1.0 / len(self.timesteps							)

													A__						:  str		  =  self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
													A__						:  Optional[int]		  =  beta_t.flatten()
													while len(beta_t.shape							) < len(x.shape							):
																			A__						:  Optional[int]		  =  beta_t.unsqueeze(-1							)
													A__						:  int		  =  -0.5 * beta_t * x

													A__						:  Optional[Any]		  =  torch.sqrt(snake_case							)
													A__						:  int		  =  drift - diffusion**2 * score
													A__						:  Tuple		  =  x + drift * dt

													# add noise
													A__						:  List[str]		  =  randn_tensor(x.shape			,    layout=x.layout			,    generator=snake_case			,    device=x.device			,    dtype=x.dtype							)
													A__						:  int		  =  x_mean + diffusion * math.sqrt(-dt							) * noise

													return x, x_mean


							def __len__(			self      :						Dict							):
													'''simple docstring'''





													return self.config.num_train_timesteps














"""simple docstring"""



from __future__ import annotations

A_    =							[]




def      _lowerCAmelCase		(							UpperCAmelCase__       :					list[list[int]],						UpperCAmelCase__       :					int,						UpperCAmelCase__       :					int      )		->bool:
						for i in range(len(UpperCAmelCase__      )      ):
												if board[row][i] == 1:
																		return False
						for i in range(len(UpperCAmelCase__      )      ):
												if board[i][column] == 1:
																		return False
						for i, j in zip(range(UpperCAmelCase__,						-1,						-1      ),						range(UpperCAmelCase__,						-1,						-1      )      ):
												if board[i][j] == 1:
																		return False
						for i, j in zip(range(UpperCAmelCase__,						-1,						-1      ),						range(UpperCAmelCase__,						len(UpperCAmelCase__      )      )      ):
												if board[i][j] == 1:
																		return False
						return True




def      _lowerCAmelCase		(							UpperCAmelCase__       :					list[list[int]],						UpperCAmelCase__       :					int      )		->bool:
						if row >= len(UpperCAmelCase__      ):
												solution.append(UpperCAmelCase__      )
												printboard(UpperCAmelCase__      )
												print()
												return True
						for i in range(len(UpperCAmelCase__      )      ):
												if is_safe(UpperCAmelCase__,						UpperCAmelCase__,						UpperCAmelCase__      ):
																		A__						:  Tuple		  =  1
																		solve(UpperCAmelCase__,						row + 1      )
																		A__						:  Optional[int]		  =  0
						return False




def      _lowerCAmelCase		(							UpperCAmelCase__       :					list[list[int]]      )		->None:
						for i in range(len(UpperCAmelCase__      )      ):
												for j in range(len(UpperCAmelCase__      )      ):
																		if board[i][j] == 1:
																								print("""Q""",						end=""" """      )
																		else:
																								print(""".""",						end=""" """      )
												print()


# n=int(input("The no. of queens"))
A_    =							8
A_    =							[[0 for i in range(n)] for j in range(n)]
solve(board, 0)

print('''The total no. of solutions are :''', len(solution))






