"""simple docstring"""



from math import gcd





def   _lowerCamelCase ( UpperCAmelCase__ = 1_20_00					)							->     str:


   '''simple docstring'''


   a__     				=		0
   for d in range(max_d + 1					):
      for n in range(d // 3 + 1,(d + 1) // 2					):
         if gcd(lowercase_,lowercase_					) == 1:
            fractions_number += 1
   return fractions_number


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





"""simple docstring"""



# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput

class SCREAMING_SNAKE_CASE     (    a	):







 """simple docstring"""


 def __init__(   self		:      Dict					,   _snake_case		:      List[str]					,   _snake_case		:      Any				)				->			Optional[Any]:




    '''simple docstring'''






    super().__init__()
    self.register_modules(unet=_snake_case					,   scheduler=_snake_case				)



 @torch.no_grad()
 def __call__(   self		:      int					,   _snake_case		:      int = 1					,   _snake_case		:      Optional[torch.Generator] = None					,   _snake_case		:      int = 50					,   _snake_case		:      Optional[str] = "pil"					,   _snake_case		:      bool = True					,   **_snake_case		:      str					,   )				->			Union[ImagePipelineOutput, Tuple]:




    '''simple docstring'''






    a__     				=		torch.randn(
        (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)					,   generator=_snake_case					,   )
    a__     				=		image.to(self.device				)

    # set step values
    self.scheduler.set_timesteps(_snake_case				)

    for t in self.progress_bar(self.scheduler.timesteps				):
       # 1. predict noise model_output
       a__     				=		self.unet(_snake_case					,   _snake_case				).sample

       # 2. predict previous mean of image x_t-1 and add variance depending on eta
       # eta corresponds to η in paper and should be between [0, 1]
       # do x_t -> x_t-1
       a__     				=		self.scheduler.step(_snake_case					,   _snake_case					,   _snake_case				).prev_sample

    a__     				=		(image / 2 + 0.5).clamp(0					,   1				)
    a__     				=		image.cpu().permute(0					,   2					,   3					,   1				).numpy()
    if output_type == "pil":
       a__     				=		self.numpy_to_pil(_snake_case				)

    if not return_dict:
       return (image,), "This is a local test"

    return ImagePipelineOutput(images=_snake_case				), "This is a local test"


