



import math
import sys


def 	UpperCAmelCase__(      UpperCAmelCase__ :int					):






 '''simple docstring'''

 if number != int(UpperCamelCase__					):
  raise ValueError("the value of input must be a natural number"					)
 if number < 0:
  raise ValueError("the value of input must not be a negative number"					)
 if number == 0:
  return 1
 a						=		[-1] * (number + 1)
 a						=		0
 for i in range(1 ,					number + 1					):
  a						=		sys.maxsize
  a						=		int(math.sqrt(UpperCamelCase__					)					)
  for j in range(1 ,					root + 1					):
   a						=		1 + answers[i - (j**2)]
   a						=		min(UpperCamelCase__ ,					UpperCamelCase__					)
  a						=		answer
 return answers[number]


if __name__ == "__main__":
     import doctest

     doctest.testmod()






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 		_lowercase		(       UpperCAmelCase__	):
   _UpperCAmelCase     	=			42
   _UpperCAmelCase     	=			42

   def __init__(      self			:       Optional[Any]							,   __lowerCAmelCase			:       UNetaDModel							,   __lowerCAmelCase			:       ScoreSdeVeScheduler							)       ->				str:


    """simple docstring"""






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




   @torch.no_grad()
   def __call__(      self			:       int							,   __lowerCAmelCase			:       int = 1							,   __lowerCAmelCase			:       int = 2000							,   __lowerCAmelCase			:       Optional[Union[torch.Generator, List[torch.Generator]]] = None							,   __lowerCAmelCase			:       Optional[str] = "pil"							,   __lowerCAmelCase			:       bool = True							,   **__lowerCAmelCase			:       Any							,   )       ->				Union[ImagePipelineOutput, Tuple]:


    """simple docstring"""






    a						=		self.unet.config.sample_size
    a						=		(batch_size, 3, img_size, img_size)

    a						=		self.unet

    a						=		randn_tensor(__lowerCAmelCase							,   generator=__lowerCAmelCase							) * self.scheduler.init_noise_sigma
    a						=		sample.to(self.device							)

    self.scheduler.set_timesteps(__lowerCAmelCase							)
    self.scheduler.set_sigmas(__lowerCAmelCase							)

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

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

     # prediction step
     a						=		model(__lowerCAmelCase							,   __lowerCAmelCase							).sample
     a						=		self.scheduler.step_pred(__lowerCAmelCase							,   __lowerCAmelCase							,   __lowerCAmelCase							,   generator=__lowerCAmelCase							)

     a		,  a						=		output.prev_sample, output.prev_sample_mean

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

    if not return_dict:
     return (sample,)

    return ImagePipelineOutput(images=__lowerCAmelCase							)

