



'''simple docstring'''






from __future__ import annotations


def  snake_case_     (					_lowerCAmelCase  :						int  )      ->   list[int]:
							UpperCAmelCase :       Tuple 							=		[True] * limit
							UpperCAmelCase :       Any 							=		False
							UpperCAmelCase :       Optional[int] 							=		False
							UpperCAmelCase :       Optional[Any] 							=		True

							for i in range(3   ,      int(limit**0.5 + 1  )   ,      2  ):
														UpperCAmelCase :       Optional[int] 							=		i * 2
														while index < limit:
																					UpperCAmelCase :       int 							=		False
																					UpperCAmelCase :       Optional[Any] 							=		index + i

							UpperCAmelCase :       Optional[int] 							=		[2]

							for i in range(3   ,      _lowerCAmelCase   ,      2  ):
														if is_prime[i]:
																					primes.append(_lowerCAmelCase  )

							return primes


def  snake_case_     (					_lowerCAmelCase  :						int = 1000000  )      ->   int:
							UpperCAmelCase :       Optional[int] 							=		prime_sieve(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[Any] 							=		0
							UpperCAmelCase :       List[Any] 							=		0

							for i in range(len(_lowerCAmelCase  )  ):
														for j in range(i + length   ,      len(_lowerCAmelCase  )  ):
																					UpperCAmelCase :       Any 							=		sum(primes[i:j]  )
																					if sol >= ceiling:
																												break

																					if sol in primes:
																												UpperCAmelCase :       List[str] 							=		j - i
																												UpperCAmelCase :       str 							=		sol

							return largest


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










'''simple docstring'''






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 				SCREAMING_SNAKE_CASE(							A__			):







	"""simple docstring"""






	lowerCamelCase__			 =       42
	lowerCamelCase__			 =       42







	def __init__(						self			:     Union[str, Any]		,			__snake_case			:     UNetaDModel		,			__snake_case			:     ScoreSdeVeScheduler		)			->		int:
								super().__init__()
								self.register_modules(unet=__snake_case		,			scheduler=__snake_case		)







	@torch.no_grad()
	def __call__(						self			:     Optional[int]		,			__snake_case			:     int = 1		,			__snake_case			:     int = 2000		,			__snake_case			:     Optional[Union[torch.Generator, List[torch.Generator]]] = None		,			__snake_case			:     Optional[str] = "pil"		,			__snake_case			:     bool = True		,			**__snake_case			:     Optional[int]		,			)			->		Union[ImagePipelineOutput, Tuple]:
								UpperCAmelCase :       str 							=		self.unet.config.sample_size
								UpperCAmelCase :       Union[str, Any] 							=		(batch_size, 3, img_size, img_size)

								UpperCAmelCase :       int 							=		self.unet

								UpperCAmelCase :       Any 							=		randn_tensor(__snake_case		,			generator=__snake_case		) * self.scheduler.init_noise_sigma
								UpperCAmelCase :       List[Any] 							=		sample.to(self.device		)

								self.scheduler.set_timesteps(__snake_case		)
								self.scheduler.set_sigmas(__snake_case		)

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

															# correction step
															for _ in range(self.scheduler.config.correct_steps		):
																						UpperCAmelCase :       Union[str, Any] 							=		self.unet(__snake_case		,			__snake_case		).sample
																						UpperCAmelCase :       Optional[Any] 							=		self.scheduler.step_correct(__snake_case		,			__snake_case		,			generator=__snake_case		).prev_sample

															# prediction step
															UpperCAmelCase :       Optional[Any] 							=		model(__snake_case		,			__snake_case		).sample
															UpperCAmelCase :       List[str] 							=		self.scheduler.step_pred(__snake_case		,			__snake_case		,			__snake_case		,			generator=__snake_case		)

															UpperCAmelCase							,		UpperCAmelCase :       Optional[Any] 							=		output.prev_sample, output.prev_sample_mean

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

								if not return_dict:
															return (sample,)

								return ImagePipelineOutput(images=__snake_case		)





