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

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






class  UpperCAmelCase_					(						_snake_case       ):





 def __init__(     self			,							lowercase_			,							lowercase_):
     super().__init__()
     self.register_modules(unet=A_			,							scheduler=A_)





 @torch.no_grad()
 def __call__(     self			,							lowercase_ = 1			,							lowercase_ = None			,							lowercase_ = 10_00			,							lowercase_ = "pil"			,							lowercase_ = True			,							):
     # Sample gaussian noise to begin loop
     if isinstance(self.unet.config.sample_size			,							A_):
         snake_case_			:     Dict        =    (
             batch_size,
             self.unet.config.in_channels,
             self.unet.config.sample_size,
             self.unet.config.sample_size,
         )
     else:
         snake_case_			:     Dict        =    (batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

     if self.device.type == "mps":
         # randn does not work reproducibly on mps
         snake_case_			:     int        =    randn_tensor(A_			,							generator=A_)
         snake_case_			:     List[Any]        =    image.to(self.device)
     else:
         snake_case_			:     List[Any]        =    randn_tensor(A_			,							generator=A_			,							device=self.device)

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

     for t in self.progress_bar(self.scheduler.timesteps):
         # 1. predict noise model_output
         snake_case_			:     List[Any]        =    self.unet(A_			,							A_).sample

         # 2. compute previous image: x_t -> x_t-1
         snake_case_			:     Dict        =    self.scheduler.step(A_			,							A_			,							A_			,							generator=A_).prev_sample

     snake_case_			:     str        =    (image / 2 + 0.5).clamp(0			,							1)
     snake_case_			:     int        =    image.cpu().permute(0			,							2			,							3			,							1).numpy()
     if output_type == "pil":
         snake_case_			:     List[Any]        =    self.numpy_to_pil(A_)

     if not return_dict:
         return (image,)

     return ImagePipelineOutput(images=A_)







from __future__ import annotations





def 				__a							(       __A						):
    SCREAMING_SNAKE_CASE__         =    {1}
    SCREAMING_SNAKE_CASE__         =    [1]
    for _ in range(2			,							depth + 1						):
        SCREAMING_SNAKE_CASE__         =    [*previous_coefficients, 0]
        SCREAMING_SNAKE_CASE__         =    [0, *previous_coefficients]
        SCREAMING_SNAKE_CASE__         =    []
        for x, y in zip(__A			,							__A						):
            coefficients.add(x + y						)
            previous_coefficients.append(x + y						)
    return coefficients





def 				__a							(       __A						):
    SCREAMING_SNAKE_CASE__         =    set()
    for number in unique_coefficients:
        SCREAMING_SNAKE_CASE__         =    2
        SCREAMING_SNAKE_CASE__         =    number
        while divisor**2 <= copy_number:
            SCREAMING_SNAKE_CASE__         =    0
            while copy_number % divisor == 0:
                copy_number //= divisor
                multiplicity += 1
            if multiplicity >= 2:
                non_squarefrees.add(__A						)
                break
            divisor += 1

    return unique_coefficients.difference(__A						)





def 				__a							(       __A = 51						):
    SCREAMING_SNAKE_CASE__         =    get_pascal_triangle_unique_coefficients(__A						)
    SCREAMING_SNAKE_CASE__         =    get_squarefrees(__A						)
    return sum(__A						)


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


