"""simple docstring"""




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
class 		__A							(				__lowercase	):
     _UpperCamelCase							:    torch.FloatTensor
     _UpperCamelCase							:    torch.FloatTensor
     _UpperCamelCase							:    Optional[torch.FloatTensor]	      =	None







class 		__A							(				__lowercase					,			__lowercase	):
     _UpperCamelCase							:    Any	      =	2






     @register_to_config
     def __init__(	self       ,  a__ = 0.0_2       ,  a__ = 100       ,  a__ = 1.0_0_7       ,  a__ = 80       ,  a__ = 0.0_5       ,  a__ = 50       ,  ):
       # standard deviation of the initial noise distribution
       _lowerCAmelCase		: Tuple						    =  sigma_max

       # setable values
       _lowerCAmelCase		: int						    =  None
       _lowerCAmelCase		: np.IntTensor						    =  None
       _lowerCAmelCase		: torch.FloatTensor						    =  None  # sigma(t_i)






     def 					__A						(	self       ,  a__       ,  a__ = None						):
       return sample






     def 					__A						(	self       ,  a__       ,  a__ = None						):
       _lowerCAmelCase		: Optional[Any]						    =  num_inference_steps
       _lowerCAmelCase		: Union[str, Any]						    =  np.arange(0       ,  self.num_inference_steps						)[::-1].copy()
       _lowerCAmelCase		: Dict						    =  torch.from_numpy(__a						).to(__a						)
       _lowerCAmelCase		: int						    =  [
           (
               self.config.sigma_max**2
               * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
           )
           for i in self.timesteps
       ]
       _lowerCAmelCase		: List[Any]						    =  torch.tensor(__a       ,  dtype=torch.floataa       ,  device=__a						)






     def 					__A						(	self       ,  a__       ,  a__       ,  a__ = None						):
       if self.config.s_min <= sigma <= self.config.s_max:
         _lowerCAmelCase		: str						    =  min(self.config.s_churn / self.num_inference_steps       ,  2**0.5 - 1						)
       else:
         _lowerCAmelCase		: Optional[Any]						    =  0

       # sample eps ~ N(0, S_noise^2 * I)
       _lowerCAmelCase		: str						    =  self.config.s_noise * randn_tensor(sample.shape       ,  generator=__a						).to(sample.device						)
       _lowerCAmelCase		: str						    =  sigma + gamma * sigma
       _lowerCAmelCase		: Dict						    =  sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

       return sample_hat, sigma_hat






     def 					__A						(	self       ,  a__       ,  a__       ,  a__       ,  a__       ,  a__ = True       ,  ):
       _lowerCAmelCase		: List[str]						    =  sample_hat + sigma_hat * model_output
       _lowerCAmelCase		: Tuple						    =  (sample_hat - pred_original_sample) / sigma_hat
       _lowerCAmelCase		: Optional[Any]						    =  sample_hat + (sigma_prev - sigma_hat) * derivative

       if not return_dict:
         return (sample_prev, derivative)

       return KarrasVeOutput(
           prev_sample=__a       ,  derivative=__a       ,  pred_original_sample=__a						)






     def 					__A						(	self       ,  a__       ,  a__       ,  a__       ,  a__       ,  a__       ,  a__       ,  a__ = True       ,  ):
       _lowerCAmelCase		: List[str]						    =  sample_prev + sigma_prev * model_output
       _lowerCAmelCase		: List[str]						    =  (sample_prev - pred_original_sample) / sigma_prev
       _lowerCAmelCase		: Any						    =  sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

       if not return_dict:
         return (sample_prev, derivative)

       return KarrasVeOutput(
           prev_sample=__a       ,  derivative=__a       ,  pred_original_sample=__a						)






     def 					__A						(	self       ,  a__       ,  a__       ,  a__						):
       raise NotImplementedError()





"""simple docstring"""




def 							SCREAMING_SNAKE_CASE  (    _lowerCamelCase		: int = 1000000			) ->   int:
  _lowerCAmelCase		: List[str]						    =  [i - 1 for i in range(limit + 1			)]

  for i in range(2    ,limit + 1			):
    if phi[i] == i - 1:
      for j in range(2 * i    ,limit + 1    ,_lowerCamelCase			):
        phi[j] -= phi[j] // i

  return sum(phi[2 : limit + 1]			)


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




