
'''simple docstring'''
import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput







class  __A				( _SCREAMING_SNAKE_CASE    ,						_SCREAMING_SNAKE_CASE			):
 lowerCamelCase				       =1
 @register_to_config
 def __init__(   self			:    Any				,   lowerCamelCase			:    int = 10_00				,   lowerCamelCase			:    Optional[Union[np.ndarray, List[float]]] = None       ):



   """simple docstring"""





   self.set_timesteps(lowerCamelCase       )

   # standard deviation of the initial noise distribution
   __A		:     Dict												=		1.0

   # For now we only support F-PNDM, i.e. the runge-kutta method
   # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
   # mainly at formula (9), (12), (13) and the Algorithm 2.
   __A		:     Optional[int]												=		4

   # running values
   __A		:     Optional[Any]												=		[]
 def 		lowercase_(   self			:    int				,   lowerCamelCase			:    int				,   lowerCamelCase			:    Union[str, torch.device] = None       ):



   """simple docstring"""





   __A		:     Union[str, Any]												=		num_inference_steps
   __A		:     int												=		torch.linspace(1				,   0				,   num_inference_steps + 1       )[:-1]
   __A		:     Union[str, Any]												=		torch.cat([steps, torch.tensor([0.0]       )]       )

   if self.config.trained_betas is not None:
     __A		:     List[str]												=		torch.tensor(self.config.trained_betas				,   dtype=torch.floataa       )
   else:
     __A		:     str												=		torch.sin(steps * math.pi / 2       ) ** 2

   __A		:     List[Any]												=		(1.0 - self.betas**2) ** 0.5

   __A		:     Any												=		(torch.atana(self.betas				,   self.alphas       ) / math.pi * 2)[:-1]
   __A		:     List[str]												=		timesteps.to(lowerCamelCase       )

   __A		:     int												=		[]
 def 		lowercase_(   self			:    Optional[int]				,   lowerCamelCase			:    torch.FloatTensor				,   lowerCamelCase			:    int				,   lowerCamelCase			:    torch.FloatTensor				,   lowerCamelCase			:    bool = True				,   ):



   """simple docstring"""





   if self.num_inference_steps is None:
     raise ValueError(
         """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"""       )

   __A		:     List[str]												=		(self.timesteps == timestep).nonzero().item()
   __A		:     str												=		timestep_index + 1

   __A		:     Optional[Any]												=		sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
   self.ets.append(lowerCamelCase       )

   if len(self.ets       ) == 1:
     __A		:     Optional[Any]												=		self.ets[-1]
   elif len(self.ets       ) == 2:
     __A		:     Dict												=		(3 * self.ets[-1] - self.ets[-2]) / 2
   elif len(self.ets       ) == 3:
     __A		:     Tuple												=		(23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
   else:
     __A		:     Union[str, Any]												=		(1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

   __A		:     List[Any]												=		self._get_prev_sample(lowerCamelCase				,   lowerCamelCase				,   lowerCamelCase				,   lowerCamelCase       )

   if not return_dict:
     return (prev_sample,)

   return SchedulerOutput(prev_sample=lowerCamelCase       )
 def 		lowercase_(   self			:    Tuple				,   lowerCamelCase			:    torch.FloatTensor				,   *lowerCamelCase			:    str				,   **lowerCamelCase			:    List[str]       ):



   """simple docstring"""





   return sample
 def 		lowercase_(   self			:    Tuple				,   lowerCamelCase			:    Optional[int]				,   lowerCamelCase			:    Any				,   lowerCamelCase			:    Dict				,   lowerCamelCase			:    str       ):



   """simple docstring"""





   __A		:     List[Any]												=		self.alphas[timestep_index]
   __A		:     List[str]												=		self.betas[timestep_index]

   __A		:     int												=		self.alphas[prev_timestep_index]
   __A		:     Any												=		self.betas[prev_timestep_index]

   __A		:     Optional[int]												=		(sample - sigma * ets) / max(lowerCamelCase				,   1e-8       )
   __A		:     Union[str, Any]												=		next_alpha * pred + ets * next_sigma

   return prev_sample






 def __len__(   self			:    Dict       ):



   """simple docstring"""





   return self.config.num_train_timesteps





'''simple docstring'''
def        A_     (						__SCREAMING_SNAKE_CASE						:  int )				->       int:





  """simple docstring"""

  __A		:     Optional[int]												=		1
  for i in range(1			,     num + 1 ):
    fact *= i
  return fact







def        A_     (						__SCREAMING_SNAKE_CASE						:  int )				->       int:





  """simple docstring"""

  __A		:     List[str]												=		0
  while number > 0:
    __A		:     Union[str, Any]												=		number % 10
    sum_of_digits += last_digit
    __A		:     int												=		number // 10  # Removing the last_digit from the given number
  return sum_of_digits







def        A_     (						__SCREAMING_SNAKE_CASE						:  int = 100 )				->       int:





  """simple docstring"""

  __A		:     Union[str, Any]												=		factorial(__SCREAMING_SNAKE_CASE )
  __A		:     Any												=		split_and_add(__SCREAMING_SNAKE_CASE )
  return result


if __name__ == "__main__":
     print(solution(int(input('Enter the Number: ').strip())))



