



'''simple docstring'''


import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

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

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class  SCREAMING_SNAKE_CASE (  _a		):






    """simple docstring"""





    _SCREAMING_SNAKE_CASE	  =  42
    _SCREAMING_SNAKE_CASE	  =  None







def 				__lowerCamelCase				(   A__    ,						A__=0.999    ,						A__="cosine"    ,						)       ->	Tuple:






   """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  SCREAMING_SNAKE_CASE (  _a   ,						_a		):






    """simple docstring"""





    @register_to_config
    def __init__(  self      :					List[str]  ,						UpperCamelCase__      :					int = 1_0_0_0  ,						UpperCamelCase__      :					str = "fixed_small_log"  ,						UpperCamelCase__      :					bool = True  ,						UpperCamelCase__      :					Optional[float] = 1.0  ,						UpperCamelCase__      :					str = "epsilon"  ,						UpperCamelCase__      :					str = "squaredcos_cap_v2"  ,						):


       """simple docstring"""







       if beta_schedule != "squaredcos_cap_v2":
          raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\'' )

       UpperCamelCase					=  betas_for_alpha_bar(UpperCamelCase__ )

       UpperCamelCase					=  1.0 - self.betas
       UpperCamelCase					=  torch.cumprod(self.alphas  ,						dim=0 )
       UpperCamelCase					=  torch.tensor(1.0 )

       # standard deviation of the initial noise distribution
       UpperCamelCase					=  1.0

       # setable values
       UpperCamelCase					=  None
       UpperCamelCase					=  torch.from_numpy(np.arange(0  ,						UpperCamelCase__ )[::-1].copy() )

       UpperCamelCase					=  variance_type






    def  A       (  self      :					Dict  ,						UpperCamelCase__      :					torch.FloatTensor  ,						UpperCamelCase__      :					Optional[int] = None ):


       """simple docstring"""







       return sample






    def  A       (  self      :					List[str]  ,						UpperCamelCase__      :					int  ,						UpperCamelCase__      :					Union[str, torch.device] = None ):


       """simple docstring"""







       UpperCamelCase					=  num_inference_steps
       UpperCamelCase					=  (self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
       UpperCamelCase					=  (np.arange(0  ,						UpperCamelCase__ ) * step_ratio).round()[::-1].copy().astype(np.intaa )
       UpperCamelCase					=  torch.from_numpy(UpperCamelCase__ ).to(UpperCamelCase__ )






    def  A       (  self      :					Dict  ,						UpperCamelCase__      :					Union[str, Any]  ,						UpperCamelCase__      :					Union[str, Any]=None  ,						UpperCamelCase__      :					Optional[int]=None  ,						UpperCamelCase__      :					Tuple=None ):


       """simple docstring"""







       if prev_timestep is None:
          UpperCamelCase					=  t - 1

       UpperCamelCase					=  self.alphas_cumprod[t]
       UpperCamelCase					=  self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
       UpperCamelCase					=  1 - alpha_prod_t
       UpperCamelCase					=  1 - alpha_prod_t_prev

       if prev_timestep == t - 1:
          UpperCamelCase					=  self.betas[t]
       else:
          UpperCamelCase					=  1 - alpha_prod_t / alpha_prod_t_prev

       # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
       # and sample from it to get previous sample
       # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
       UpperCamelCase					=  beta_prod_t_prev / beta_prod_t * beta

       if variance_type is None:
          UpperCamelCase					=  self.config.variance_type

       # hacks - were probably added for training stability
       if variance_type == "fixed_small_log":
          UpperCamelCase					=  torch.log(torch.clamp(UpperCamelCase__  ,						min=1E-2_0 ) )
          UpperCamelCase					=  torch.exp(0.5 * variance )
       elif variance_type == "learned_range":
          # NOTE difference with DDPM scheduler
          UpperCamelCase					=  variance.log()
          UpperCamelCase					=  beta.log()

          UpperCamelCase					=  (predicted_variance + 1) / 2
          UpperCamelCase					=  frac * max_log + (1 - frac) * min_log

       return variance






    def  A       (  self      :					int  ,						UpperCamelCase__      :					torch.FloatTensor  ,						UpperCamelCase__      :					int  ,						UpperCamelCase__      :					torch.FloatTensor  ,						UpperCamelCase__      :					Optional[int] = None  ,						UpperCamelCase__      :					str=None  ,						UpperCamelCase__      :					bool = True  ,						):


       """simple docstring"""







       UpperCamelCase					=  timestep

       if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
          UpperCamelCase				,      UpperCamelCase					=  torch.split(UpperCamelCase__  ,						sample.shape[1]  ,						dim=1 )
       else:
          UpperCamelCase					=  None

       # 1. compute alphas, betas
       if prev_timestep is None:
          UpperCamelCase					=  t - 1

       UpperCamelCase					=  self.alphas_cumprod[t]
       UpperCamelCase					=  self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
       UpperCamelCase					=  1 - alpha_prod_t
       UpperCamelCase					=  1 - alpha_prod_t_prev

       if prev_timestep == t - 1:
          UpperCamelCase					=  self.betas[t]
          UpperCamelCase					=  self.alphas[t]
       else:
          UpperCamelCase					=  1 - alpha_prod_t / alpha_prod_t_prev
          UpperCamelCase					=  1 - beta

       # 2. compute predicted original sample from predicted noise also called
       # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
       if self.config.prediction_type == "epsilon":
          UpperCamelCase					=  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
       elif self.config.prediction_type == "sample":
          UpperCamelCase					=  model_output
       else:
          raise ValueError(
              f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"""
              ' for the UnCLIPScheduler.' )

       # 3. Clip "predicted x_0"
       if self.config.clip_sample:
          UpperCamelCase					=  torch.clamp(
              UpperCamelCase__  ,						-self.config.clip_sample_range  ,						self.config.clip_sample_range )

       # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
       # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
       UpperCamelCase					=  (alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
       UpperCamelCase					=  alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

       # 5. Compute predicted previous sample µ_t
       # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
       UpperCamelCase					=  pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

       # 6. Add noise
       UpperCamelCase					=  0
       if t > 0:
          UpperCamelCase					=  randn_tensor(
              model_output.shape  ,						dtype=model_output.dtype  ,						generator=UpperCamelCase__  ,						device=model_output.device )

          UpperCamelCase					=  self._get_variance(
              UpperCamelCase__  ,						predicted_variance=UpperCamelCase__  ,						prev_timestep=UpperCamelCase__  ,						)

          if self.variance_type == "fixed_small_log":
             UpperCamelCase					=  variance
          elif self.variance_type == "learned_range":
             UpperCamelCase					=  (0.5 * variance).exp()
          else:
             raise ValueError(
                 f"""variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"""
                 ' for the UnCLIPScheduler.' )

          UpperCamelCase					=  variance * variance_noise

       UpperCamelCase					=  pred_prev_sample + variance

       if not return_dict:
          return (pred_prev_sample,)

       return UnCLIPSchedulerOutput(prev_sample=UpperCamelCase__  ,						pred_original_sample=UpperCamelCase__ )






    def  A       (  self      :					int  ,						UpperCamelCase__      :					torch.FloatTensor  ,						UpperCamelCase__      :					torch.FloatTensor  ,						UpperCamelCase__      :					torch.IntTensor  ,						):


       """simple docstring"""







       UpperCamelCase					=  self.alphas_cumprod.to(device=original_samples.device  ,						dtype=original_samples.dtype )
       UpperCamelCase					=  timesteps.to(original_samples.device )

       UpperCamelCase					=  alphas_cumprod[timesteps] ** 0.5
       UpperCamelCase					=  sqrt_alpha_prod.flatten()
       while len(sqrt_alpha_prod.shape ) < len(original_samples.shape ):
          UpperCamelCase					=  sqrt_alpha_prod.unsqueeze(-1 )

       UpperCamelCase					=  (1 - alphas_cumprod[timesteps]) ** 0.5
       UpperCamelCase					=  sqrt_one_minus_alpha_prod.flatten()
       while len(sqrt_one_minus_alpha_prod.shape ) < len(original_samples.shape ):
          UpperCamelCase					=  sqrt_one_minus_alpha_prod.unsqueeze(-1 )

       UpperCamelCase					=  sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
       return noisy_samples



from __future__ import annotations

from fractions import Fraction




def  __magic_name__ (   __lowerCAmelCase	:						int		,  __lowerCAmelCase	:						int							)			->   bool:
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def  __magic_name__ (   __lowerCAmelCase	:						int							)			->   list[str]:
				__lowerCamelCase    					=	[]
				__lowerCamelCase    					=	11
				__lowerCamelCase    					=	int('''1''' + '''0''' * digit_len							)
				for num in range(__lowerCAmelCase		,  __lowerCAmelCase							):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(__lowerCAmelCase		,  __lowerCAmelCase							):
																				solutions.append(f'''{num}/{den}'''							)
												den += 1
								num += 1
								__lowerCamelCase    					=	10
				return solutions




def  __magic_name__ (   __lowerCAmelCase	:						int = 2							)			->   int:
				__lowerCamelCase    					=	1.0
				for fraction in fraction_list(__lowerCAmelCase							):
								__lowerCamelCase    					=	Fraction(__lowerCAmelCase							)
								result *= frac.denominator / frac.numerator
				return int(__lowerCAmelCase							)


if __name__ == "__main__":
					print(solution())



