





from typing import List, Optional, Tuple, Union

import torch

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

class    lowerCAmelCase							(					__UpperCamelCase			):
 UpperCAmelCase__													=		42
 UpperCAmelCase__													=		42
 def __init__(      self  :      Any			,     UpperCAmelCase  :      UNetaDModel			,     UpperCAmelCase  :      KarrasVeScheduler	)			->	List[str]:
     super().__init__()
     self.register_modules(unet=UpperCAmelCase			,     scheduler=UpperCAmelCase	)







 @torch.no_grad()
 def __call__(      self  :      List[Any]			,     UpperCAmelCase  :      int = 1			,     UpperCAmelCase  :      int = 50			,     UpperCAmelCase  :      Optional[Union[torch.Generator, List[torch.Generator]]] = None			,     UpperCAmelCase  :      Optional[str] = "pil"			,     UpperCAmelCase  :      bool = True			,     **UpperCAmelCase  :      Tuple			,     )			->	Union[Tuple, ImagePipelineOutput]:
     lowerCamelCase__    :      Any					 =		self.unet.config.sample_size
     lowerCamelCase__    :      Any					 =		(batch_size, 3, img_size, img_size)

     lowerCamelCase__    :      Dict					 =		self.unet

     # sample x_0 ~ N(0, sigma_0^2 * I)
     lowerCamelCase__    :      Dict					 =		randn_tensor(UpperCAmelCase			,     generator=UpperCAmelCase			,     device=self.device	) * self.scheduler.init_noise_sigma

     self.scheduler.set_timesteps(UpperCAmelCase	)

     for t in self.progress_bar(self.scheduler.timesteps	):
         # here sigma_t == t_i from the paper
         lowerCamelCase__    :      List[Any]					 =		self.scheduler.schedule[t]
         lowerCamelCase__    :      Any					 =		self.scheduler.schedule[t - 1] if t > 0 else 0

         # 1. Select temporarily increased noise level sigma_hat
         # 2. Add new noise to move from sample_i to sample_hat
         lowerCamelCase__ ,							lowerCamelCase__    :      Any					 =		self.scheduler.add_noise_to_input(UpperCAmelCase			,     UpperCAmelCase			,     generator=UpperCAmelCase	)

         # 3. Predict the noise residual given the noise magnitude `sigma_hat`
         # The model inputs and output are adjusted by following eq. (213) in [1].
         lowerCamelCase__    :      Optional[Any]					 =		(sigma_hat / 2) * model((sample_hat + 1) / 2			,     sigma_hat / 2	).sample

         # 4. Evaluate dx/dt at sigma_hat
         # 5. Take Euler step from sigma to sigma_prev
         lowerCamelCase__    :      Dict					 =		self.scheduler.step(UpperCAmelCase			,     UpperCAmelCase			,     UpperCAmelCase			,     UpperCAmelCase	)

         if sigma_prev != 0:
             # 6. Apply 2nd order correction
             # The model inputs and output are adjusted by following eq. (213) in [1].
             lowerCamelCase__    :      Optional[Any]					 =		(sigma_prev / 2) * model((step_output.prev_sample + 1) / 2			,     sigma_prev / 2	).sample
             lowerCamelCase__    :      Optional[int]					 =		self.scheduler.step_correct(
                 UpperCAmelCase			,     UpperCAmelCase			,     UpperCAmelCase			,     UpperCAmelCase			,     step_output.prev_sample			,     step_output['derivative']			,     )
         lowerCamelCase__    :      Union[str, Any]					 =		step_output.prev_sample

     lowerCamelCase__    :      Optional[int]					 =		(sample / 2 + 0.5).clamp(0			,     1	)
     lowerCamelCase__    :      Union[str, Any]					 =		sample.cpu().permute(0			,     2			,     3			,     1	).numpy()
     if output_type == "pil":
         lowerCamelCase__    :      List[Any]					 =		self.numpy_to_pil(UpperCAmelCase	)

     if not return_dict:
         return (image,)

     return ImagePipelineOutput(images=UpperCAmelCase	)












def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase = 100_0000 )			->     int:
    lowerCamelCase__    :      int					 =		limit + 1
    lowerCamelCase__    :      Optional[Any]					 =		[0] * limit
    for first_term in range(1						,	_UpperCAmelCase ):
        for n in range(_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase ):
            lowerCamelCase__    :      Optional[Any]					 =		first_term + n / first_term
            if common_difference % 4:  # d must be divisble by 4
                continue
            else:
                common_difference /= 4
                if (
                    first_term > common_difference
                    and first_term < 4 * common_difference
                ):  # since x,y,z are positive integers
                    frequency[n] += 1  # so z>0 and a>d ,also 4d<a

    lowerCamelCase__    :      List[str]					 =		sum(1 for x in frequency[1:limit] if x == 10 )

    return count


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





