

import math
from collections.abc import Generator







def     A_   (					_UpperCAmelCase					):
						SCREAMING_SNAKE_CASE_:				Generator							= (i for i in range(1       ,			(max_n + 1)					))
						for i in (n for n in numbers if n > 1):
												for j in range(2       ,			_UpperCAmelCase					):
																		if (i % j) == 0:
																								break
												else:
																		yield i







def     A_   (					_UpperCAmelCase					):
						SCREAMING_SNAKE_CASE_:				Generator							= (i for i in range(1       ,			(max_n + 1)					))
						for i in (n for n in numbers if n > 1):
												# only need to check for factors up to sqrt(i)
												SCREAMING_SNAKE_CASE_:				List[str]							= int(math.sqrt(_UpperCAmelCase					)					) + 1
												for j in range(2       ,			_UpperCAmelCase					):
																		if (i % j) == 0:
																								break
												else:
																		yield i







def     A_   (					_UpperCAmelCase					):
						SCREAMING_SNAKE_CASE_:				Generator							= (i for i in range(1       ,			(max_n + 1)       ,			2					))
						# It's useless to test even numbers as they will not be prime
						if max_n > 2:
												yield 2  # Because 2 will not be tested, it's necessary to yield it now
						for i in (n for n in numbers if n > 1):
												SCREAMING_SNAKE_CASE_:				List[Any]							= int(math.sqrt(_UpperCAmelCase					)					) + 1
												for j in range(3       ,			_UpperCAmelCase       ,			2					):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i







def     A_   (					):
						from timeit import timeit

						SCREAMING_SNAKE_CASE_:				Tuple							= "from __main__ import slow_primes, primes, fast_primes"
						print(timeit("slow_primes(1_000_000_000_000)"       ,			setup=_UpperCAmelCase       ,			number=1_00_00_00					)					)
						print(timeit("primes(1_000_000_000_000)"       ,			setup=_UpperCAmelCase       ,			number=1_00_00_00					)					)
						print(timeit("fast_primes(1_000_000_000_000)"       ,			setup=_UpperCAmelCase       ,			number=1_00_00_00					)					)


if __name__ == "__main__":
						lowerCAmelCase							:						str     			=		int(input("""Calculate primes up to:\n>> """).strip())
						for ret in primes(number):
												print(ret)
						benchmark()









from typing import List, Optional, Tuple, Union

import torch

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



class 						__lowercase       (				UpperCAmelCase_			):




			"""simple docstring"""







			_UpperCAmelCase     :							UNetaDModel
			_UpperCAmelCase     :							PNDMScheduler



			def __init__(				self						:  Optional[int]     ,		lowerCAmelCase__						:  UNetaDModel     ,		lowerCAmelCase__						:  PNDMScheduler):
									super().__init__()

									SCREAMING_SNAKE_CASE_:				Dict							= PNDMScheduler.from_config(scheduler.config)

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




			@torch.no_grad()
			def __call__(				self						:  int     ,		lowerCAmelCase__						:  int = 1     ,		lowerCAmelCase__						:  int = 50     ,		lowerCAmelCase__						:  Optional[Union[torch.Generator, List[torch.Generator]]] = None     ,		lowerCAmelCase__						:  Optional[str] = "pil"     ,		lowerCAmelCase__						:  bool = True     ,		**lowerCAmelCase__						:  str     ,		):
									SCREAMING_SNAKE_CASE_:				Dict							= randn_tensor(
									    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)     ,		generator=lowerCAmelCase__     ,		device=self.device     ,		)

									self.scheduler.set_timesteps(lowerCAmelCase__)
									for t in self.progress_bar(self.scheduler.timesteps):
															SCREAMING_SNAKE_CASE_:				Union[str, Any]							= self.unet(lowerCAmelCase__     ,		lowerCAmelCase__).sample

															SCREAMING_SNAKE_CASE_:				Any							= self.scheduler.step(lowerCAmelCase__     ,		lowerCAmelCase__     ,		lowerCAmelCase__).prev_sample

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

									if not return_dict:
															return (image,)

									return ImagePipelineOutput(images=lowerCAmelCase__)






