






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 				lowerCAmelCase_	(		__SCREAMING_SNAKE_CASE			):


				def __init__(					self ,						_lowerCAmelCase ,						_lowerCAmelCase      ):
											super().__init__()

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

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


				@torch.no_grad()
				def __call__(					self ,						_lowerCAmelCase = 1 ,						_lowerCAmelCase = None ,						_lowerCAmelCase = 0.0 ,						_lowerCAmelCase = 5_0 ,						_lowerCAmelCase = None ,						_lowerCAmelCase = "pil" ,						_lowerCAmelCase = True ,						):




											if isinstance(self.unet.config.sample_size ,						lowerCAmelCase__      ):
																		_lowercase							:   Any 							=   (
																		    batch_size,
																		    self.unet.config.in_channels,
																		    self.unet.config.sample_size,
																		    self.unet.config.sample_size,
																		)
											else:
																		_lowercase							:   Dict 							=   (batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

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

											_lowercase							:   List[Any] 							=   randn_tensor(lowerCAmelCase__ ,						generator=lowerCAmelCase__ ,						device=self.device ,						dtype=self.unet.dtype      )

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

											for t in self.progress_bar(self.scheduler.timesteps      ):
																		# 1. predict noise model_output
																		_lowercase							:   List[str] 							=   self.unet(lowerCAmelCase__ ,						lowerCAmelCase__      ).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
																		_lowercase							:   List[str] 							=   self.scheduler.step(
																		    lowerCAmelCase__ ,						lowerCAmelCase__ ,						lowerCAmelCase__ ,						eta=lowerCAmelCase__ ,						use_clipped_model_output=lowerCAmelCase__ ,						generator=lowerCAmelCase__      ).prev_sample

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

											if not return_dict:
																		return (image,)

											return ImagePipelineOutput(images=lowerCAmelCase__      )








def 						a__			(				A__ = 5_0_0_0_0_0_0_0				):
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					set()
			SCREAMING_SNAKE_CASE_		:     Optional[int]					=					int((limit - 2_4) ** (1 / 2)				)

			SCREAMING_SNAKE_CASE_		:     Dict					=					set(range(3,      prime_square_limit + 1,      2				)				)
			primes.add(2				)
			for p in range(3,      prime_square_limit + 1,      2				):
						if p not in primes:
									continue
						primes.difference_update(set(range(p * p,      prime_square_limit + 1,      A__				)				)				)

			for primea in primes:
						SCREAMING_SNAKE_CASE_		:     int					=					primea * primea
						for primea in primes:
									SCREAMING_SNAKE_CASE_		:     Dict					=					primea * primea * primea
									if square + cube >= limit - 1_6:
												break
									for primea in primes:
												SCREAMING_SNAKE_CASE_		:     Optional[int]					=					primea * primea * primea * primea
												SCREAMING_SNAKE_CASE_		:     str					=					square + cube + tetr
												if total >= limit:
															break
												ret.add(A__				)

			return len(A__				)


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





