





'''simple docstring'''
def 				lowercase__   (   __lowercase						:  int = 50000000     ) ->      int:



       """simple docstring"""






       __UpperCamelCase       =  set()
       __UpperCamelCase       =  int((limit - 24) ** (1 / 2)     )

       __UpperCamelCase       =  set(range(3				,  prime_square_limit + 1				,  2     )     )
       primes.add(2     )
       for p in range(3				,  prime_square_limit + 1				,  2     ):
              if p not in primes:
                     continue
              primes.difference_update(set(range(p * p				,  prime_square_limit + 1				,  __lowercase     )     )     )

       for primea in primes:
              __UpperCamelCase       =  primea * primea
              for primea in primes:
                     __UpperCamelCase       =  primea * primea * primea
                     if square + cube >= limit - 16:
                            break
                     for primea in primes:
                            __UpperCamelCase       =  primea * primea * primea * primea
                            __UpperCamelCase       =  square + cube + tetr
                            if total >= limit:
                                   break
                            ret.add(__lowercase     )

       return len(__lowercase     )


if __name__ == "__main__":
    print(f'{solution() = }')




'''simple docstring'''

from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import ScoreSdeVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput





class      snake_case    (    lowercase			):





  """simple docstring"""




  _lowerCamelCase		    =  42
  _lowerCamelCase		    =  42






  def __init__(    self			,  UpperCamelCase			,  UpperCamelCase     ):







   """simple docstring"""
   super().__init__()
   self.register_modules(unet=UpperCamelCase			,  scheduler=UpperCamelCase     )







  @torch.no_grad()
  def __call__(    self			,  UpperCamelCase = 1			,  UpperCamelCase = 2000			,  UpperCamelCase = None			,  UpperCamelCase = "pil"			,  UpperCamelCase = True			,  **UpperCamelCase			,  ):







   """simple docstring"""
   lowerCamelCase_      =  self.unet.config.sample_size
   lowerCamelCase_      =  (batch_size, 3, img_size, img_size)

   lowerCamelCase_      =  self.unet

   lowerCamelCase_      =  randn_tensor(UpperCamelCase			,  generator=UpperCamelCase     ) * self.scheduler.init_noise_sigma
   lowerCamelCase_      =  sample.to(self.device     )

   self.scheduler.set_timesteps(UpperCamelCase     )
   self.scheduler.set_sigmas(UpperCamelCase     )

   for i, t in enumerate(self.progress_bar(self.scheduler.timesteps     )     ):
    lowerCamelCase_      =  self.scheduler.sigmas[i] * torch.ones(shape[0]			,  device=self.device     )

    # correction step
    for _ in range(self.scheduler.config.correct_steps     ):
     lowerCamelCase_      =  self.unet(UpperCamelCase			,  UpperCamelCase     ).sample
     lowerCamelCase_      =  self.scheduler.step_correct(UpperCamelCase			,  UpperCamelCase			,  generator=UpperCamelCase     ).prev_sample

    # prediction step
    lowerCamelCase_      =  model(UpperCamelCase			,  UpperCamelCase     ).sample
    lowerCamelCase_      =  self.scheduler.step_pred(UpperCamelCase			,  UpperCamelCase			,  UpperCamelCase			,  generator=UpperCamelCase     )

    lowerCamelCase_ ,lowerCamelCase_      =  output.prev_sample, output.prev_sample_mean

   lowerCamelCase_      =  sample_mean.clamp(0			,  1     )
   lowerCamelCase_      =  sample.cpu().permute(0			,  2			,  3			,  1     ).numpy()
   if output_type == "pil":
    lowerCamelCase_      =  self.numpy_to_pil(UpperCamelCase     )

   if not return_dict:
    return (sample,)

   return ImagePipelineOutput(images=UpperCamelCase     )



