code: 
  
  
  import math
  from dataclasses import dataclass
  from typing import List, Optional, Tuple, Union
  
  import numpy as np
  import torch
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..utils import BaseOutput, logging, randn_tensor
  from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
  
  
  lowerCAmelCase   :Tuple								=    logging.get_logger(__name__)  # pylint: disable=invalid-name
  @dataclass
  # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
  class _lowerCamelCase (		lowerCAmelCase_							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		A_			:    Tuple   					=       42
  		A_			:    List[Any]   					=       None
  
  
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			Any	,	lowerCAmelCase       :			Tuple=0.999	,	lowerCAmelCase       :			Optional[int]="cosine"	,	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	if alpha_transform_type == "cosine":
  
  		def alpha_bar_fn(lowerCAmelCase       :			List[str]	):
  			return math.cos((t + 0.008) / 1.008 * math.pi / 2	) ** 2
  
  	elif alpha_transform_type == "exp":
  
  		def alpha_bar_fn(lowerCAmelCase       :			Optional[Any]	):
  			return math.exp(t * -12.0	)
  
  	else:
  		raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'	)
  
  	__magic_name__ :					Any  			=  []
  	for i in range(_SCREAMING_SNAKE_CASE	):
  		__magic_name__ :					Optional[int]  			=  i / num_diffusion_timesteps
  		__magic_name__ :					List[str]  			=  (i + 1) / num_diffusion_timesteps
  		betas.append(min(1 - alpha_bar_fn(_SCREAMING_SNAKE_CASE	) / alpha_bar_fn(_SCREAMING_SNAKE_CASE	)	,	_SCREAMING_SNAKE_CASE	)	)
  	return torch.tensor(_SCREAMING_SNAKE_CASE	,	dtype=torch.floataa	)
  
  
  
  
  
  class _lowerCamelCase (		lowerCAmelCase_	,  lowerCAmelCase_							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		A_			:    List[str]   					=       [e.name for e in KarrasDiffusionSchedulers]
  		A_			:    Union[str, Any]   					=       1
  
  
  
  
  
  
  
  		@register_to_config
  		def __init__(      self	:		List[Any]						,  _A	:		str = 1000						,  _A	:		Tuple = 0.0001						,  _A	:		Tuple = 0.02						,  _A	:		Union[str, Any] = "linear"						,  _A	:		str = None						,  _A	:		List[Any] = "epsilon"						,  _A	:		List[Any] = "linear"						,  _A	:		Union[str, Any] = False						,  _A	:		Tuple = "linspace"						,  _A	:		Tuple = 0						,  )						->				str:
  
  
  
  
  
  			if trained_betas is not None:
  				__magic_name__ :					Any  			=  torch.tensor(__a						,  dtype=torch.floataa    )
  			elif beta_schedule == "linear":
  				__magic_name__ :					Dict  			=  torch.linspace(__a						,  __a						,  __a						,  dtype=torch.floataa    )
  			elif beta_schedule == "scaled_linear":
  				# this schedule is very specific to the latent diffusion model.
  				__magic_name__ :					Any  			=  (
  				    torch.linspace(beta_start**0.5						,  beta_end**0.5						,  __a						,  dtype=torch.floataa    ) ** 2
  				)
  			elif beta_schedule == "squaredcos_cap_v2":
  				# Glide cosine schedule
  				__magic_name__ :					int  			=  betas_for_alpha_bar(__a    )
  			else:
  				raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'    )
  
  			__magic_name__ :					List[Any]  			=  1.0 - self.betas
  			__magic_name__ :					int  			=  torch.cumprod(self.alphas						,  dim=0    )
  
  			__magic_name__ :					List[Any]  			=  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
  			__magic_name__ :					List[Any]  			=  np.concatenate([sigmas[::-1], [0.0]]    ).astype(np.floataa    )
  			__magic_name__ :					Union[str, Any]  			=  torch.from_numpy(__a    )
  
  			# setable values
  			__magic_name__ :					List[str]  			=  None
  			__magic_name__ :					List[Any]  			=  np.linspace(0						,  num_train_timesteps - 1						,  __a						,  dtype=__a    )[::-1].copy()
  			__magic_name__ :					Optional[Any]  			=  torch.from_numpy(__a    )
  			__magic_name__ :					Any  			=  False
  			__magic_name__ :					str  			=  use_karras_sigmas
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Tuple    )						->				Tuple:
  
  
  
  
  
  			if self.config.timestep_spacing in ["linspace", "trailing"]:
  				return self.sigmas.max()
  
  			return (self.sigmas.max() ** 2 + 1) ** 0.5
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		List[str]						,  _A	:		Dict						,  _A	:		Optional[Any]    )						->				str:
  
  
  
  
  
  			if isinstance(__a						,  torch.Tensor    ):
  				__magic_name__ :					Optional[int]  			=  timestep.to(self.timesteps.device    )
  			__magic_name__ :					Optional[Any]  			=  (self.timesteps == timestep).nonzero().item()
  			__magic_name__ :					List[str]  			=  self.sigmas[step_index]
  
  			__magic_name__ :					int  			=  sample / ((sigma**2 + 1) ** 0.5)
  
  			__magic_name__ :					Union[str, Any]  			=  True
  			return sample
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		str						,  _A	:		Optional[int]						,  _A	:		Any = None    )						->				Optional[Any]:
  			__magic_name__ :					Dict  			=  num_inference_steps
  
  			# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
  			if self.config.timestep_spacing == "linspace":
  				__magic_name__ :					Optional[Any]  			=  np.linspace(0						,  self.config.num_train_timesteps - 1						,  __a						,  dtype=__a    )[
  				    ::-1
  				].copy()
  			elif self.config.timestep_spacing == "leading":
  				__magic_name__ :					str  			=  self.config.num_train_timesteps // self.num_inference_steps
  				# creates integer timesteps by multiplying by ratio
  				# casting to int to avoid issues when num_inference_step is power of 3
  				__magic_name__ :					int  			=  (np.arange(0						,  __a    ) * step_ratio).round()[::-1].copy().astype(__a    )
  				timesteps += self.config.steps_offset
  			elif self.config.timestep_spacing == "trailing":
  				__magic_name__ :					Optional[int]  			=  self.config.num_train_timesteps / self.num_inference_steps
  				# creates integer timesteps by multiplying by ratio
  				# casting to int to avoid issues when num_inference_step is power of 3
  				__magic_name__ :					str  			=  (np.arange(self.config.num_train_timesteps						,  0						,  -step_ratio    )).round().copy().astype(__a    )
  				timesteps -= 1
  			else:
  				raise ValueError(
  				    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'    )
  
  			__magic_name__ :					Tuple  			=  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5    )
  			__magic_name__ :					Tuple  			=  np.log(__a    )
  
  			if self.config.interpolation_type == "linear":
  				__magic_name__ :					Optional[Any]  			=  np.interp(__a						,  np.arange(0						,  len(__a    )    )						,  __a    )
  			elif self.config.interpolation_type == "log_linear":
  				__magic_name__ :					Optional[Any]  			=  torch.linspace(np.log(sigmas[-1]    )						,  np.log(sigmas[0]    )						,  num_inference_steps + 1    ).exp()
  			else:
  				raise ValueError(
  				    F'{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'
  				    ' \'linear\' or \'log_linear\''    )
  
  			if self.use_karras_sigmas:
  				__magic_name__ :					Any  			=  self._convert_to_karras(in_sigmas=__a						,  num_inference_steps=self.num_inference_steps    )
  				__magic_name__ :					Tuple  			=  np.array([self._sigma_to_t(__a						,  __a    ) for sigma in sigmas]    )
  
  			__magic_name__ :					str  			=  np.concatenate([sigmas, [0.0]]    ).astype(np.floataa    )
  			__magic_name__ :					List[Any]  			=  torch.from_numpy(__a    ).to(device=__a    )
  			if str(__a    ).startswith('mps'    ):
  				# mps does not support float64
  				__magic_name__ :					int  			=  torch.from_numpy(__a    ).to(__a						,  dtype=torch.floataa    )
  			else:
  				__magic_name__ :					int  			=  torch.from_numpy(__a    ).to(device=__a    )
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		int						,  _A	:		str						,  _A	:		str    )						->				Union[str, Any]:
  			__magic_name__ :					Any  			=  np.log(__a    )
  
  			# get distribution
  			__magic_name__ :					Dict  			=  log_sigma - log_sigmas[:, np.newaxis]
  
  			# get sigmas range
  			__magic_name__ :					Optional[Any]  			=  np.cumsum((dists >= 0)						,  axis=0    ).argmax(axis=0    ).clip(max=log_sigmas.shape[0] - 2    )
  			__magic_name__ :					int  			=  low_idx + 1
  
  			__magic_name__ :					Tuple  			=  log_sigmas[low_idx]
  			__magic_name__ :					Any  			=  log_sigmas[high_idx]
  
  			# interpolate sigmas
  			__magic_name__ :					Dict  			=  (low - log_sigma) / (low - high)
  			__magic_name__ :					List[Any]  			=  np.clip(__a						,  0						,  1    )
  
  			# transform interpolation to time range
  			__magic_name__ :					Union[str, Any]  			=  (1 - w) * low_idx + w * high_idx
  			__magic_name__ :					Optional[Any]  			=  t.reshape(sigma.shape    )
  			return t
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		str						,  _A	:		Any						,  _A	:		Dict    )						->				Dict:
  			__magic_name__ :					float  			=  in_sigmas[-1].item()
  			__magic_name__ :					float  			=  in_sigmas[0].item()
  
  			__magic_name__ :					Union[str, Any]  			=  7.0  # 7.0 is the value used in the paper
  			__magic_name__ :					int  			=  np.linspace(0						,  1						,  __a    )
  			__magic_name__ :					int  			=  sigma_min ** (1 / rho)
  			__magic_name__ :					Optional[Any]  			=  sigma_max ** (1 / rho)
  			__magic_name__ :					Optional[Any]  			=  (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
  			return sigmas
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Tuple						,  _A	:		Optional[int]						,  _A	:		List[Any]						,  _A	:		Dict						,  _A	:		Tuple = 0.0						,  _A	:		Union[str, Any] = 0.0						,  _A	:		int = float('inf'    )						,  _A	:		Dict = 1.0						,  _A	:		str = None						,  _A	:		Tuple = True						,  )						->				Tuple:
  
  
  
  
  
  			if (
  			    isinstance(__a						,  __a    )
  			    or isinstance(__a						,  torch.IntTensor    )
  			    or isinstance(__a						,  torch.LongTensor    )
  			):
  				raise ValueError(
  				    (
  				        'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
  				        ' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'
  				        ' one of the `scheduler.timesteps` as a timestep.'
  				    )						,  )
  
  			if not self.is_scale_input_called:
  				logger.warning(
  				    'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
  				    'See `StableDiffusionPipeline` for a usage example.'    )
  
  			if isinstance(__a						,  torch.Tensor    ):
  				__magic_name__ :					Optional[int]  			=  timestep.to(self.timesteps.device    )
  
  			__magic_name__ :					str  			=  (self.timesteps == timestep).nonzero().item()
  			__magic_name__ :					List[Any]  			=  self.sigmas[step_index]
  
  			__magic_name__ :					List[Any]  			=  min(s_churn / (len(self.sigmas    ) - 1)						,  2**0.5 - 1    ) if s_tmin <= sigma <= s_tmax else 0.0
  
  			__magic_name__ :					Optional[Any]  			=  randn_tensor(
  			    model_output.shape						,  dtype=model_output.dtype						,  device=model_output.device						,  generator=__a    )
  
  			__magic_name__ :					Optional[Any]  			=  noise * s_noise
  			__magic_name__ :					int  			=  sigma * (gamma + 1)
  
  			if gamma > 0:
  				__magic_name__ :					Optional[Any]  			=  sample + eps * (sigma_hat**2 - sigma**2) ** 0.5
  
  			# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
  			# NOTE: "original_sample" should not be an expected prediction_type but is left in for
  			# backwards compatibility
  			if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
  				__magic_name__ :					Optional[Any]  			=  model_output
  			elif self.config.prediction_type == "epsilon":
  				__magic_name__ :					Tuple  			=  sample - sigma_hat * model_output
  			elif self.config.prediction_type == "v_prediction":
  				# * c_out + input * c_skip
  				__magic_name__ :					List[Any]  			=  model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
  			else:
  				raise ValueError(
  				    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'    )
  
  			# 2. Convert to an ODE derivative
  			__magic_name__ :					List[Any]  			=  (sample - pred_original_sample) / sigma_hat
  
  			__magic_name__ :					Union[str, Any]  			=  self.sigmas[step_index + 1] - sigma_hat
  
  			__magic_name__ :					Tuple  			=  sample + derivative * dt
  
  			if not return_dict:
  				return (prev_sample,)
  
  			return EulerDiscreteSchedulerOutput(prev_sample=__a						,  pred_original_sample=__a    )
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Tuple						,  _A	:		Optional[int]						,  _A	:		Optional[Any]						,  _A	:		Optional[int]						,  )						->				Tuple:
  			__magic_name__ :					Optional[int]  			=  self.sigmas.to(device=original_samples.device						,  dtype=original_samples.dtype    )
  			if original_samples.device.type == "mps" and torch.is_floating_point(__a    ):
  				# mps does not support float64
  				__magic_name__ :					int  			=  self.timesteps.to(original_samples.device						,  dtype=torch.floataa    )
  				__magic_name__ :					int  			=  timesteps.to(original_samples.device						,  dtype=torch.floataa    )
  			else:
  				__magic_name__ :					Optional[Any]  			=  self.timesteps.to(original_samples.device    )
  				__magic_name__ :					Any  			=  timesteps.to(original_samples.device    )
  
  			__magic_name__ :					Tuple  			=  [(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
  			__magic_name__ :					str  			=  sigmas[step_indices].flatten()
  			while len(sigma.shape    ) < len(original_samples.shape    ):
  				__magic_name__ :					str  			=  sigma.unsqueeze(-1    )
  
  			__magic_name__ :					Optional[Any]  			=  original_samples + noise * sigma
  			return noisy_samples
  
  
  
  
  
  
  
  		def __len__(      self	:		Optional[Any]    )						->				Tuple:
  			return self.config.num_train_timesteps
style_context: 
  
  
  '''simple docstring'''
  
  import itertools
  from pathlib import Path
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			list[str]	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					str  			=  [tuple(lowerCAmelCase	) for login in logins]
  
  	__magic_name__ :					int  			=  {char for login in split_logins for char in login}
  
  	for permutation in itertools.permutations(lowerCAmelCase	):
  		__magic_name__ :					List[Any]  			=  True
  		for login in logins:
  			if not (
  			    permutation.index(login[0]	)
  			    < permutation.index(login[1]	)
  			    < permutation.index(login[2]	)
  			):
  				__magic_name__ :					Tuple  			=  False
  				break
  
  		if satisfied:
  			return int(''.join(lowerCAmelCase	)	)
  
  	raise Exception('Unable to find the secret passcode'	)
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			str = "keylog.txt"	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					List[Any]  			=  Path(lowerCAmelCase	).parent.joinpath(lowerCAmelCase	).read_text().splitlines()
  
  	return find_secret_passcode(lowerCAmelCase	)
  
  
  if __name__ == "__main__":
  							print(F'{solution() = }')