


import inspect
from typing import List, Optional, Tuple, Union

import torch

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







class 	snake_case_       (lowerCamelCase_				):
					def __init__(				self       :int      ,__snake_case       :VQModel      ,__snake_case       :UNetaDModel      ,__snake_case       :DDIMScheduler				) ->   Any:
												super().__init__()
												self.register_modules(vqvae=__snake_case      ,unet=__snake_case      ,scheduler=__snake_case				)



					@torch.no_grad()
					def __call__(				self       :Dict      ,__snake_case       :int = 1      ,__snake_case       :Optional[Union[torch.Generator, List[torch.Generator]]] = None      ,__snake_case       :float = 0.0      ,__snake_case       :int = 50      ,__snake_case       :Optional[str] = "pil"      ,__snake_case       :bool = True      ,**__snake_case       :Union[str, Any]      ,) ->   Union[Tuple, ImagePipelineOutput]:
												a__					=					randn_tensor(
												    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)      ,generator=__snake_case      ,)
												a__					=					latents.to(self.device				)

												# scale the initial noise by the standard deviation required by the scheduler
												a__					=					latents * self.scheduler.init_noise_sigma

												self.scheduler.set_timesteps(__snake_case				)

												# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
												a__					=					'eta' in set(inspect.signature(self.scheduler.step				).parameters.keys()				)

												a__					=					{}
												if accepts_eta:
																			a__					=					eta

												for t in self.progress_bar(self.scheduler.timesteps				):
																			a__					=					self.scheduler.scale_model_input(__snake_case      ,__snake_case				)
																			# predict the noise residual
																			a__					=					self.unet(__snake_case      ,__snake_case				).sample
																			# compute the previous noisy sample x_t -> x_t-1
																			a__					=					self.scheduler.step(__snake_case      ,__snake_case      ,__snake_case      ,**__snake_case				).prev_sample

												# decode the image latents with the VAE
												a__					=					self.vqvae.decode(__snake_case				).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,)

												return ImagePipelineOutput(images=__snake_case				)








from math import ceil, sqrt






def 							__lowercase       (			__lowerCAmelCase							:    int = 1_0_0_0_0_0_0       ):
							a__					=					0

							for outer_width in range(3 ,   (limit // 4) + 2       ):
														if outer_width**2 > limit:
																					a__					=					max(ceil(sqrt(outer_width**2 - limit       )       ) ,   1       )
														else:
																					a__					=					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() = }""")




