
from __future__ import annotations
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						list[int]:
			lowerCAmelCase__ : List[Any]   =						[0] * max_one

			for i in range(0			,				SCREAMING_SNAKE_CASE_	):
						lowerCAmelCase__ : List[Any]   =						i

			for i in range(2			,				SCREAMING_SNAKE_CASE_	):
						if totients[i] == i:
									for j in range(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	):
												totients[j] -= totients[j] // i

			return totients
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)							->						bool:
			return sorted(str(SCREAMING_SNAKE_CASE_	)	) == sorted(str(SCREAMING_SNAKE_CASE_	)	)
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_ = 10_000_000	)							->						int:
			lowerCAmelCase__ : Optional[int]   =						1  # i
			lowerCAmelCase__ : int   =						0  # φ(i)
			lowerCAmelCase__ : List[Any]   =						get_totients(max_n + 1	)

			for i in range(2			,				max_n + 1	):
						lowerCAmelCase__ : int   =						totients[i]

						if i * min_denominator < min_numerator * t and has_same_digits(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	):
									lowerCAmelCase__ : int   =						i
									lowerCAmelCase__ : List[str]   =						t

			return min_numerator


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

from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class 	A__				(	__magic_name__      ):






				def __init__(		self   : Any       ,	a   : Any       ,	a   : Optional[int]  ):






							'''simple docstring'''







							super().__init__()
							self.register_modules(unet=a       ,	scheduler=a  )






				@torch.no_grad()
				def __call__(		self   : Optional[Any]       ,	a   : int = 1       ,	a   : Optional[Union[torch.Generator, List[torch.Generator]]] = None       ,	a   : int = 1_000       ,	a   : Optional[str] = "pil"       ,	a   : bool = True       ,	):






							'''simple docstring'''







							if isinstance(self.unet.config.sample_size       ,	a  ):
										lowerCAmelCase__ : Union[str, Any]   =						(
										    batch_size,
										    self.unet.config.in_channels,
										    self.unet.config.sample_size,
										    self.unet.config.sample_size,
										)
							else:
										lowerCAmelCase__ : str   =						(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

							if self.device.type == "mps":
										# randn does not work reproducibly on mps
										lowerCAmelCase__ : Optional[int]   =						randn_tensor(a       ,	generator=a  )
										lowerCAmelCase__ : Optional[int]   =						image.to(self.device  )
							else:
										lowerCAmelCase__ : Dict   =						randn_tensor(a       ,	generator=a       ,	device=self.device  )

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

							for t in self.progress_bar(self.scheduler.timesteps  ):
										# 1. predict noise model_output
										lowerCAmelCase__ : Tuple   =						self.unet(a       ,	a  ).sample

										# 2. compute previous image: x_t -> x_t-1
										lowerCAmelCase__ : Optional[Any]   =						self.scheduler.step(a       ,	a       ,	a       ,	generator=a  ).prev_sample

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

							if not return_dict:
										return (image,)

							return ImagePipelineOutput(images=a  )