code: 
  
  
  
  '''simple docstring'''
  
  
  
  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
  
  
  a__						:			Union[str, Any]										=			logging.get_logger(__name__)  # pylint: disable=invalid-name
  @dataclass
  # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
  class        UpperCAmelCase__  (    UpperCAmelCase_):
   __SCREAMING_SNAKE_CASE					      =				4_2
   __SCREAMING_SNAKE_CASE					      =				None
  
  
  
  
  
  
  
  def _lowercase   (  __A							,__A=0.999							,__A="cosine"							,):
  
  
  
   '''simple docstring'''
  
  
  
   if alpha_transform_type == "cosine":
  
    def alpha_bar_fn(__A       ):
     return math.cos((t + 0.008) / 1.008 * math.pi / 2       ) ** 2
  
   elif alpha_transform_type == "exp":
  
    def alpha_bar_fn(__A       ):
     return math.exp(t * -12.0       )
  
   else:
    raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}"       )
  
   __UpperCamelCase				      =  []
   for i in range(__A       ):
    __UpperCamelCase				      =  i / num_diffusion_timesteps
    __UpperCamelCase				      =  (i + 1) / num_diffusion_timesteps
    betas.append(min(1 - alpha_bar_fn(__A       ) / alpha_bar_fn(__A       )							,__A       )       )
   return torch.tensor(__A							,dtype=torch.floataa       )
  
  
  
  
  
  
  class        UpperCAmelCase__  (    UpperCAmelCase_							,			UpperCAmelCase_):
   __SCREAMING_SNAKE_CASE					      =				[e.name for e in KarrasDiffusionSchedulers]
   __SCREAMING_SNAKE_CASE					      =				1
  
  
  
   @register_to_config
   def __init__(  self		,	lowercase = 1_0_0_0		,	lowercase = 0.0_001		,	lowercase = 0.02		,	lowercase = "linear"		,	lowercase = None		,	lowercase = "epsilon"		,	lowercase = "linear"		,	lowercase = False		,	lowercase = "linspace"		,	lowercase = 0		,	)  ->							Union[str, Any]:
    if trained_betas is not None:
     __UpperCamelCase				      =  torch.tensor(lowercase		,	dtype=torch.floataa			)
    elif beta_schedule == "linear":
     __UpperCamelCase				      =  torch.linspace(lowercase		,	lowercase		,	lowercase		,	dtype=torch.floataa			)
    elif beta_schedule == "scaled_linear":
     # this schedule is very specific to the latent diffusion model.
     __UpperCamelCase				      =  (
         torch.linspace(beta_start**0.5		,	beta_end**0.5		,	lowercase		,	dtype=torch.floataa			) ** 2
     )
    elif beta_schedule == "squaredcos_cap_v2":
     # Glide cosine schedule
     __UpperCamelCase				      =  betas_for_alpha_bar(lowercase			)
    else:
     raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"			)
  
    __UpperCamelCase				      =  1.0 - self.betas
    __UpperCamelCase				      =  torch.cumprod(self.alphas		,	dim=0			)
  
    __UpperCamelCase				      =  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
    __UpperCamelCase				      =  np.concatenate([sigmas[::-1], [0.0]]			).astype(np.floataa			)
    __UpperCamelCase				      =  torch.from_numpy(lowercase			)
  
    # setable values
    __UpperCamelCase				      =  None
    __UpperCamelCase				      =  np.linspace(0		,	num_train_timesteps - 1		,	lowercase		,	dtype=lowercase			)[::-1].copy()
    __UpperCamelCase				      =  torch.from_numpy(lowercase			)
    __UpperCamelCase				      =  False
    __UpperCamelCase				      =  use_karras_sigmas
  
  
  
   @property
   def    __lowerCamelCase				(  self			)  ->							Dict:
    # standard deviation of the initial noise distribution
    if self.config.timestep_spacing in ["linspace", "trailing"]:
     return self.sigmas.max()
  
    return (self.sigmas.max() ** 2 + 1) ** 0.5
  
  
  
   def    __lowerCamelCase				(  self		,	lowercase		,	lowercase			)  ->							torch.FloatTensor:
    if isinstance(lowercase		,	torch.Tensor			):
     __UpperCamelCase				      =  timestep.to(self.timesteps.device			)
    __UpperCamelCase				      =  (self.timesteps == timestep).nonzero().item()
    __UpperCamelCase				      =  self.sigmas[step_index]
  
    __UpperCamelCase				      =  sample / ((sigma**2 + 1) ** 0.5)
  
    __UpperCamelCase				      =  True
    return sample
  
  
  
   def    __lowerCamelCase				(  self		,	lowercase		,	lowercase = None			)  ->							List[str]:
    __UpperCamelCase				      =  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":
     __UpperCamelCase				      =  np.linspace(0		,	self.config.num_train_timesteps - 1		,	lowercase		,	dtype=lowercase			)[
         ::-1
     ].copy()
    elif self.config.timestep_spacing == "leading":
     __UpperCamelCase				      =  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
     __UpperCamelCase				      =  (np.arange(0		,	lowercase			) * step_ratio).round()[::-1].copy().astype(lowercase			)
     timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
     __UpperCamelCase				      =  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
     __UpperCamelCase				      =  (np.arange(self.config.num_train_timesteps		,	0		,	-step_ratio			)).round().copy().astype(lowercase			)
     timesteps -= 1
    else:
     raise ValueError(
         f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."			)
  
    __UpperCamelCase				      =  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
    __UpperCamelCase				      =  np.log(lowercase			)
  
    if self.config.interpolation_type == "linear":
     __UpperCamelCase				      =  np.interp(lowercase		,	np.arange(0		,	len(lowercase			)			)		,	lowercase			)
    elif self.config.interpolation_type == "log_linear":
     __UpperCamelCase				      =  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:
     __UpperCamelCase				      =  self._convert_to_karras(in_sigmas=lowercase		,	num_inference_steps=self.num_inference_steps			)
     __UpperCamelCase				      =  np.array([self._sigma_to_t(lowercase		,	lowercase			) for sigma in sigmas]			)
  
    __UpperCamelCase				      =  np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
    __UpperCamelCase				      =  torch.from_numpy(lowercase			).to(device=lowercase			)
    if str(lowercase			).startswith("""mps"""			):
     # mps does not support float64
     __UpperCamelCase				      =  torch.from_numpy(lowercase			).to(lowercase		,	dtype=torch.floataa			)
    else:
     __UpperCamelCase				      =  torch.from_numpy(lowercase			).to(device=lowercase			)
  
  
  
   def    __lowerCamelCase				(  self		,	lowercase		,	lowercase			)  ->							Any:
    # get log sigma
    __UpperCamelCase				      =  np.log(lowercase			)
  
    # get distribution
    __UpperCamelCase				      =  log_sigma - log_sigmas[:, np.newaxis]
  
    # get sigmas range
    __UpperCamelCase				      =  np.cumsum((dists >= 0)		,	axis=0			).argmax(axis=0			).clip(max=log_sigmas.shape[0] - 2			)
    __UpperCamelCase				      =  low_idx + 1
  
    __UpperCamelCase				      =  log_sigmas[low_idx]
    __UpperCamelCase				      =  log_sigmas[high_idx]
  
    # interpolate sigmas
    __UpperCamelCase				      =  (low - log_sigma) / (low - high)
    __UpperCamelCase				      =  np.clip(lowercase		,	0		,	1			)
  
    # transform interpolation to time range
    __UpperCamelCase				      =  (1 - w) * low_idx + w * high_idx
    __UpperCamelCase				      =  t.reshape(sigma.shape			)
    return t
  
  
  
   def    __lowerCamelCase				(  self		,	lowercase		,	lowercase			)  ->							torch.FloatTensor:
    __UpperCamelCase				      =  in_sigmas[-1].item()
    __UpperCamelCase				      =  in_sigmas[0].item()
  
    __UpperCamelCase				      =  7.0  # 7.0 is the value used in the paper
    __UpperCamelCase				      =  np.linspace(0		,	1		,	lowercase			)
    __UpperCamelCase				      =  sigma_min ** (1 / rho)
    __UpperCamelCase				      =  sigma_max ** (1 / rho)
    __UpperCamelCase				      =  (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
    return sigmas
  
  
  
   def    __lowerCamelCase				(  self		,	lowercase		,	lowercase		,	lowercase		,	lowercase = 0.0		,	lowercase = 0.0		,	lowercase = float("""inf"""			)		,	lowercase = 1.0		,	lowercase = None		,	lowercase = True		,	)  ->							Union[EulerDiscreteSchedulerOutput, Tuple]:
  
    if (
        isinstance(lowercase		,	lowercase			)
        or isinstance(lowercase		,	torch.IntTensor			)
        or isinstance(lowercase		,	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(lowercase		,	torch.Tensor			):
     __UpperCamelCase				      =  timestep.to(self.timesteps.device			)
  
    __UpperCamelCase				      =  (self.timesteps == timestep).nonzero().item()
    __UpperCamelCase				      =  self.sigmas[step_index]
  
    __UpperCamelCase				      =  min(s_churn / (len(self.sigmas			) - 1)		,	2**0.5 - 1			) if s_tmin <= sigma <= s_tmax else 0.0
  
    __UpperCamelCase				      =  randn_tensor(
        model_output.shape		,	dtype=model_output.dtype		,	device=model_output.device		,	generator=lowercase			)
  
    __UpperCamelCase				      =  noise * s_noise
    __UpperCamelCase				      =  sigma * (gamma + 1)
  
    if gamma > 0:
     __UpperCamelCase				      =  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":
     __UpperCamelCase				      =  model_output
    elif self.config.prediction_type == "epsilon":
     __UpperCamelCase				      =  sample - sigma_hat * model_output
    elif self.config.prediction_type == "v_prediction":
     # * c_out + input * c_skip
     __UpperCamelCase				      =  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
    __UpperCamelCase				      =  (sample - pred_original_sample) / sigma_hat
  
    __UpperCamelCase				      =  self.sigmas[step_index + 1] - sigma_hat
  
    __UpperCamelCase				      =  sample + derivative * dt
  
    if not return_dict:
     return (prev_sample,)
  
    return EulerDiscreteSchedulerOutput(prev_sample=lowercase		,	pred_original_sample=lowercase			)
  
  
  
   def    __lowerCamelCase				(  self		,	lowercase		,	lowercase		,	lowercase		,	)  ->							torch.FloatTensor:
    # Make sure sigmas and timesteps have the same device and dtype as original_samples
    __UpperCamelCase				      =  self.sigmas.to(device=original_samples.device		,	dtype=original_samples.dtype			)
    if original_samples.device.type == "mps" and torch.is_floating_point(lowercase			):
     # mps does not support float64
     __UpperCamelCase				      =  self.timesteps.to(original_samples.device		,	dtype=torch.floataa			)
     __UpperCamelCase				      =  timesteps.to(original_samples.device		,	dtype=torch.floataa			)
    else:
     __UpperCamelCase				      =  self.timesteps.to(original_samples.device			)
     __UpperCamelCase				      =  timesteps.to(original_samples.device			)
  
    __UpperCamelCase				      =  [(schedule_timesteps == t).nonzero().item() for t in timesteps]
  
    __UpperCamelCase				      =  sigmas[step_indices].flatten()
    while len(sigma.shape			) < len(original_samples.shape			):
     __UpperCamelCase				      =  sigma.unsqueeze(-1			)
  
    __UpperCamelCase				      =  original_samples + noise * sigma
    return noisy_samples
  
  
  
  
   def __len__(  self			)  ->							str:
    return self.config.num_train_timesteps
  
  
  
  
  
  
style_context: 
  
  
  
  '''simple docstring'''
  
  
  
  a__						:			str										=			[chr(i) for i in range(3_2, 1_2_6)]
  a__						:			List[Any]										=			list(range(len(alphabets)))
  a__						:			Union[str, Any]										=			list(range(len(alphabets)))
  a__						:			Dict										=			list(range(len(alphabets)))
  a__						:			Union[str, Any]										=			list(reversed(range(len(alphabets))))
  a__						:			List[str]										=			[]
  a__						:			int										=			0
  
  
  
  
  
  
  
  def _lowercase   (  ):
  
  
  
   '''simple docstring'''
  
  
  
   global gear_one_pos
   global gear_two_pos
   global gear_three_pos
   __UpperCamelCase				      =  gear_one[0]
   gear_one.append(__A       )
   del gear_one[0]
   gear_one_pos += 1
   if gear_one_pos % int(len(__A       )       ) == 0:
    __UpperCamelCase				      =  gear_two[0]
    gear_two.append(__A       )
    del gear_two[0]
    gear_two_pos += 1
    if gear_two_pos % int(len(__A       )       ) == 0:
     __UpperCamelCase				      =  gear_three[0]
     gear_three.append(__A       )
     del gear_three[0]
     gear_three_pos += 1
  
  
  
  
  
  
  
  def _lowercase   (  __A       ):
  
  
  
   '''simple docstring'''
  
  
  
   __UpperCamelCase				      =  alphabets.index(__A       )
   __UpperCamelCase				      =  gear_one[target]
   __UpperCamelCase				      =  gear_two[target]
   __UpperCamelCase				      =  gear_three[target]
   __UpperCamelCase				      =  reflector[target]
   __UpperCamelCase				      =  gear_three.index(__A       )
   __UpperCamelCase				      =  gear_two.index(__A       )
   __UpperCamelCase				      =  gear_one.index(__A       )
   code.append(alphabets[target]       )
   rotator()
  
  
  if __name__ == "__main__":
   a__						:			Any										=			list(input('Type your message:\n'))
   while True:
    try:
     a__						:			List[Any]										=			int(input('Please set token:(must be only digits)\n'))
     break
    except Exception as error:
     print(error)
   for _ in range(token):
    rotator()
   for j in decode:
    engine(j)
   print('\n' + ''.join(code))
   print(
       f'''\nYour Token is {token} please write it down.\nIf you want to decode '''
       'this message again you should input same digits as token!'
   )
  
  
  
  
  
  