





"""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     __lowerCAmelCase	(   UpperCamelCase__						,    UpperCamelCase__):
      _lowercase    : str            =      1







      @register_to_config
      def __init__(   self		,				lowerCAmelCase__=2_0_0_0		,				lowerCAmelCase__=0.1		,				lowerCAmelCase__=2_0		,				lowerCAmelCase__=1E-3							)       ->						Dict:



        '''simple docstring'''




        a__     : str  =None
        a__     : Optional[Any]  =None
        a__     : Optional[int]  =None







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__ = None							)       ->						Any:



        '''simple docstring'''




        a__     : Optional[Any]  =torch.linspace(1		,				self.config.sampling_eps		,				lowerCAmelCase__		,				device=lowerCAmelCase__							)







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__=None							)       ->						Optional[int]:



        '''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__     : List[Any]  =(
            -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
        )
        a__     : int  =torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff							)							)
        a__     : Any  =std.flatten()
        while len(std.shape							) < len(score.shape							):
          a__     : Union[str, Any]  =std.unsqueeze(-1							)
        a__     : Tuple  =-score / std

        # compute
        a__     : List[Any]  =-1.0 / len(self.timesteps							)

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

        a__     : Union[str, Any]  =torch.sqrt(lowerCAmelCase__							)
        a__     : List[str]  =drift - diffusion**2 * score
        a__     : Union[str, Any]  =x + drift * dt

        # add noise
        a__     : Dict  =randn_tensor(x.shape		,				layout=x.layout		,				generator=lowerCAmelCase__		,				device=x.device		,				dtype=x.dtype							)
        a__     : Optional[int]  =x_mean + diffusion * math.sqrt(-dt							) * noise

        return x, x_mean







      def __len__(   self							)       ->						Union[str, Any]:



        '''simple docstring'''




        return self.config.num_train_timesteps













from __future__ import annotations

import math
def 					_A	(		SCREAMING_SNAKE_CASE					:       int						):





  """simple docstring"""



  if num <= 0:
    a__     : List[str]  =f'''{num}: Invalid input, please enter a positive integer.'''
    raise ValueError(SCREAMING_SNAKE_CASE						)

  a__     : Union[str, Any]  =[True] * (num + 1)
  a__     : Union[str, Any]  =[]
  a__     : str  =2
  a__     : Any  =int(math.sqrt(SCREAMING_SNAKE_CASE						)						)

  while start <= end:
    # If start is a prime
    if sieve[start] is True:
      prime.append(SCREAMING_SNAKE_CASE						)

      # Set multiples of start be False
      for i in range(start * start	,	num + 1	,	SCREAMING_SNAKE_CASE						):
        if sieve[i] is True:
          a__     : Optional[int]  =False

    start += 1

  for j in range(end + 1	,	num + 1						):
    if sieve[j] is True:
      prime.append(SCREAMING_SNAKE_CASE						)

  return prime


if __name__ == "__main__":
     print(prime_sieve(int(input("""Enter a positive integer: """).strip())))






