



from typing import List, Optional, Tuple, Union

import torch

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







class 		snake_case						(	lowercase__  ):



   '''simple docstring'''






   def __init__(					self							:			Optional[Any]				,		lowerCAmelCase							:			Optional[int]				,		lowerCAmelCase							:			int)				->				str:

    """simple docstring"""







    super().__init__()

    # make sure scheduler can always be converted to DDIM
    _snake_case    :  Any					=					DDIMScheduler.from_config(scheduler.config)

    self.register_modules(unet=UpperCAmelCase__				,		scheduler=UpperCAmelCase__)


   @torch.no_grad()
   def __call__(					self							:			List[Any]				,		lowerCAmelCase							:			int = 1				,		lowerCAmelCase							:			Optional[Union[torch.Generator, List[torch.Generator]]] = None				,		lowerCAmelCase							:			float = 0.0				,		lowerCAmelCase							:			int = 50				,		lowerCAmelCase							:			Optional[bool] = None				,		lowerCAmelCase							:			Optional[str] = "pil"				,		lowerCAmelCase							:			bool = True				,		)				->				List[str]:

    """simple docstring"""







    if isinstance(self.unet.config.sample_size				,		UpperCAmelCase__):
     _snake_case    :  Optional[int]					=					(
         batch_size,
         self.unet.config.in_channels,
         self.unet.config.sample_size,
         self.unet.config.sample_size,
     )
    else:
     _snake_case    :  Optional[int]					=					(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

    if isinstance(UpperCAmelCase__				,		UpperCAmelCase__) and len(UpperCAmelCase__) != batch_size:
     raise ValueError(
         F'''You have passed a list of generators of length {len(UpperCAmelCase__)}, but requested an effective batch'''
         F''' size of {batch_size}. Make sure the batch size matches the length of the generators.''')

    _snake_case    :  str					=					randn_tensor(UpperCAmelCase__				,		generator=UpperCAmelCase__				,		device=self.device				,		dtype=self.unet.dtype)

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

    for t in self.progress_bar(self.scheduler.timesteps):
     # 1. predict noise model_output
     _snake_case    :  Dict					=					self.unet(UpperCAmelCase__				,		UpperCAmelCase__).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
     _snake_case    :  Dict					=					self.scheduler.step(
         UpperCAmelCase__				,		UpperCAmelCase__				,		UpperCAmelCase__				,		eta=UpperCAmelCase__				,		use_clipped_model_output=UpperCAmelCase__				,		generator=UpperCAmelCase__).prev_sample

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

    if not return_dict:
     return (image,)

    return ImagePipelineOutput(images=UpperCAmelCase__)










from math import ceil, sqrt



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	int = 1_000_000				)  ->     int:
 _snake_case    :  Tuple					=					0

 for outer_width in range(3				,       (limit // 4) + 2				):
  if outer_width**2 > limit:
   _snake_case    :  int					=					max(ceil(sqrt(outer_width**2 - limit				)				)				,       1				)
  else:
   _snake_case    :  Any					=					1
  if (outer_width - hole_width_lower_bound) % 2:
   hole_width_lower_bound += 1

  answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

 return answer


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