





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 		lowerCamelCase  (__lowerCamelCase     ):







							"""simple docstring"""




							def __init__(   self      :	List[Any],					_UpperCAmelCase      :	Tuple,					_UpperCAmelCase      :	List[str],					_UpperCAmelCase      :	List[Any]		) ->					Optional[Any]:





														"""simple docstring"""
														super().__init__()
														self.register_modules(vqvae=__a,					unet=__a,					scheduler=__a		)






							@torch.no_grad()
							def __call__(   self      :	List[Any],					_UpperCAmelCase      :	List[Any] = 1,					_UpperCAmelCase      :	int = None,					_UpperCAmelCase      :	Any = 0.0,					_UpperCAmelCase      :	List[str] = 5_0,					_UpperCAmelCase      :	List[Any] = "pil",					_UpperCAmelCase      :	Any = True,					**_UpperCAmelCase      :	List[Any],					) ->					Union[Tuple, ImagePipelineOutput]:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__  :     Dict           =		randn_tensor(
														    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size),					generator=__a,					)
														SCREAMING_SNAKE_CASE__  :     Optional[int]           =		latents.to(self.device		)

														# scale the initial noise by the standard deviation required by the scheduler
														SCREAMING_SNAKE_CASE__  :     List[str]           =		latents * self.scheduler.init_noise_sigma

														self.scheduler.set_timesteps(__a		)

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

														SCREAMING_SNAKE_CASE__  :     Dict           =		{}
														if accepts_eta:
																					SCREAMING_SNAKE_CASE__  :     int           =		eta

														for t in self.progress_bar(self.scheduler.timesteps		):
																					SCREAMING_SNAKE_CASE__  :     int           =		self.scheduler.scale_model_input(__a,					__a		)
																					# predict the noise residual
																					SCREAMING_SNAKE_CASE__  :     Optional[Any]           =		self.unet(__a,					__a		).sample
																					# compute the previous noisy sample x_t -> x_t-1
																					SCREAMING_SNAKE_CASE__  :     Tuple           =		self.scheduler.step(__a,					__a,					__a,					**__a		).prev_sample

														# decode the image latents with the VAE
														SCREAMING_SNAKE_CASE__  :     int           =		self.vqvae.decode(__a		).sample

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

														if not return_dict:
																					return (image,)

														return ImagePipelineOutput(images=__a		)








"""simple docstring"""





from __future__ import annotations

from functools import lru_cache
from math import ceil

_a								=						100

_a								=						set(range(3, NUM_PRIMES, 2))
primes.add(2)
_a								=						42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
				if prime not in primes:
								continue
				primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))



@lru_cache(maxsize=1_00      )
def  lowerCamelCase__						(     __snake_case      )				->						set[int]:


					"""simple docstring"""





					if number_to_partition < 0:
										return set()
					elif number_to_partition == 0:
										return {1}

					_UpperCamelCase									=    set()
					_UpperCamelCase									=    42
					_UpperCamelCase									=    42

					for prime in primes:
										if prime > number_to_partition:
															continue
										for sub in partition(number_to_partition - prime      ):
															ret.add(sub * prime      )

					return ret



def  lowerCamelCase__						(     __snake_case = 50_00      )				->						int | None:


					"""simple docstring"""





					for number_to_partition in range(1,	__snake_case      ):
										if len(partition(__snake_case      )      ) > number_unique_partitions:
															return number_to_partition
					return None


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






