code: 
  
  
  
  
  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 __UpperCamelCase    (							_a		):
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  					__magic_name__     			=      4_2
  					__magic_name__     			=      4_2
  
  
  
  
  
  					def __init__(							self							,			lowerCamelCase__							,			lowerCamelCase__	):
  						super().__init__()
  
  						UpperCAmelCase__:  Union[str, Any]		       =   PNDMScheduler.from_config(scheduler.config	)
  
  						self.register_modules(unet=lowerCamelCase__							,			scheduler=lowerCamelCase__	)
  
  
  
  
  
  					@torch.no_grad()
  					def __call__(							self							,			lowerCamelCase__ = 1							,			lowerCamelCase__ = 5_0							,			lowerCamelCase__ = None							,			lowerCamelCase__ = "pil"							,			lowerCamelCase__ = True							,			**lowerCamelCase__							,			):
  						UpperCAmelCase__:  str		       =   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	):
  							UpperCAmelCase__:  List[str]		       =   self.unet(lowerCamelCase__							,			lowerCamelCase__	).sample
  
  							UpperCAmelCase__:  Tuple		       =   self.scheduler.step(lowerCamelCase__							,			lowerCamelCase__							,			lowerCamelCase__	).prev_sample
  
  						UpperCAmelCase__:  Tuple		       =   (image / 2 + 0.5).clamp(0							,			1	)
  						UpperCAmelCase__:  str		       =   image.cpu().permute(0							,			2							,			3							,			1	).numpy()
  						if output_type == "pil":
  							UpperCAmelCase__:  str		       =   self.numpy_to_pil(lowerCamelCase__	)
  
  						if not return_dict:
  							return (image,)
  
  						return ImagePipelineOutput(images=lowerCamelCase__	)
style_context: 
  
  from __future__ import annotations
  
  from collections import Counter
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE			):
  	UpperCAmelCase__:  Optional[Any]		       =   [True] * n
  	UpperCAmelCase__:  Any		       =   False
  	UpperCAmelCase__:  Tuple		       =   False
  	UpperCAmelCase__:  Optional[Any]		       =   True
  
  	for i in range(3  ,int(n**0.5 + 1			)  ,2			):
  		UpperCAmelCase__:  Any		       =   i * 2
  		while index < n:
  			UpperCAmelCase__:  Optional[int]		       =   False
  			UpperCAmelCase__:  Tuple		       =   index + i
  
  	UpperCAmelCase__:  int		       =   [2]
  
  	for i in range(3  ,SCREAMING_SNAKE_CASE  ,2			):
  		if is_prime[i]:
  			primes.append(SCREAMING_SNAKE_CASE			)
  
  	return primes
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE			):
  	UpperCAmelCase__:  List[Any]		       =   str(SCREAMING_SNAKE_CASE			)
  	UpperCAmelCase__:  Tuple		       =   []
  	UpperCAmelCase__:  Optional[int]		       =   ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
  
  	for duplicate in Counter(SCREAMING_SNAKE_CASE			) - Counter(set(SCREAMING_SNAKE_CASE			)			):
  		UpperCAmelCase__:  Optional[Any]		       =   [int(number_str.replace(SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE			)			) for digit in digits]
  		replacements.append(SCREAMING_SNAKE_CASE			)
  
  	return replacements
  
  
  
  def  _A  (			SCREAMING_SNAKE_CASE = 8			):
  	UpperCAmelCase__:  Union[str, Any]		       =   set()
  
  	# Filter primes with less than 3 replaceable digits
  	UpperCAmelCase__:  Optional[Any]		       =   {
  	    x for x in set(prime_sieve(1_0_0_0_0_0_0			)			) if len(str(SCREAMING_SNAKE_CASE			)			) - len(set(str(SCREAMING_SNAKE_CASE			)			)			) >= 3
  	}
  
  	for prime in primes:
  		if prime in numbers_checked:
  			continue
  
  		UpperCAmelCase__:  Optional[int]		       =   digit_replacements(SCREAMING_SNAKE_CASE			)
  
  		for family in replacements:
  			numbers_checked.update(SCREAMING_SNAKE_CASE			)
  			UpperCAmelCase__:  Dict		       =   primes.intersection(SCREAMING_SNAKE_CASE			)
  
  			if len(SCREAMING_SNAKE_CASE			) != family_length:
  				continue
  
  			return min(SCREAMING_SNAKE_CASE			)
  
  	return -1
  
  
  if __name__ == "__main__":
  					print(solution())