




from __future__ import annotations

from collections import Counter




def      __magic_name__							(					A						:   int  ):






			'''simple docstring'''







			a       =     [True] * n
			a       =     False
			a       =     False
			a       =     True

			for i in range(3,    int(n**0.5 + 1  ),    2  ):
						a       =     i * 2
						while index < n:
									a       =     False
									a       =     index + i

			a       =     [2]

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

			return primes




def      __magic_name__							(					A						:   int  ):






			'''simple docstring'''







			a       =     str(A  )
			a       =     []
			a       =     ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]

			for duplicate in Counter(A  ) - Counter(set(A  )  ):
						a       =     [int(number_str.replace(A,    A  )  ) for digit in digits]
						replacements.append(A  )

			return replacements




def      __magic_name__							(					A						:   int = 8  ):






			'''simple docstring'''







			a       =     set()

			# Filter primes with less than 3 replaceable digits
			a       =     {
			    x for x in set(prime_sieve(1000000  )  ) if len(str(A  )  ) - len(set(str(A  )  )  ) >= 3
			}

			for prime in primes:
						if prime in numbers_checked:
									continue

						a       =     digit_replacements(A  )

						for family in replacements:
									numbers_checked.update(A  )
									a       =     primes.intersection(A  )

									if len(A  ) != family_length:
												continue

									return min(A  )

			return -1


if __name__ == "__main__":
		print(solution())












import tempfile
import unittest

import torch

from diffusers import UNetaDConditionModel
from diffusers.training_utils import EMAModel
from diffusers.utils.testing_utils import enable_full_determinism, skip_mps, torch_device


enable_full_determinism()




class        snake_case__				(unittest.TestCase  ):
				"""simple docstring"""



				SCREAMING_SNAKE_CASE_			:				Optional[int]									=   """hf-internal-testing/tiny-stable-diffusion-pipe"""
				SCREAMING_SNAKE_CASE_			:				str									=   1
				SCREAMING_SNAKE_CASE_			:				Dict									=   77
				SCREAMING_SNAKE_CASE_			:				List[str]									=   32
				SCREAMING_SNAKE_CASE_			:				List[str]									=   4
				SCREAMING_SNAKE_CASE_			:				Union[str, Any]									=   64
				SCREAMING_SNAKE_CASE_			:				int									=   torch.manual_seed(0  )





				def 				__UpperCAmelCase				( self							:	List[Any]   , __lowerCamelCase							:	List[Any]=0.9_999				)   ->	Tuple:
							a       =     UNetaDConditionModel.from_pretrained(self.model_id   , subfolder="unet"				)
							a       =     unet.to(__lowerCamelCase				)
							a       =     EMAModel(unet.parameters()   , decay=__lowerCamelCase   , model_cls=__lowerCamelCase   , model_config=unet.config				)
							return unet, ema_unet





				def 				__UpperCAmelCase				( self							:	Tuple				)   ->	Any:
							a       =     torch.randn(
							    self.batch_size   , self.num_in_channels   , self.latent_height   , self.latent_width   , generator=self.generator				).to(__lowerCamelCase				)
							a       =     torch.randint(0   , 10_00   , size=(self.batch_size,)   , generator=self.generator				).to(__lowerCamelCase				)
							a       =     torch.randn(
							    self.batch_size   , self.prompt_length   , self.text_encoder_hidden_dim   , generator=self.generator				).to(__lowerCamelCase				)
							return noisy_latents, timesteps, encoder_hidden_states





				def 				__UpperCAmelCase				( self							:	Optional[int]   , __lowerCamelCase							:	Any				)   ->	Optional[int]:
							a       =     {}
							for k, param in unet.state_dict().items():
										a       =     torch.randn_like(__lowerCamelCase				) + (param * torch.randn_like(__lowerCamelCase				))
										updated_state_dict.update({k: updated_param}				)
							unet.load_state_dict(__lowerCamelCase				)
							return unet





				def 				__UpperCAmelCase				( self							:	Optional[Any]				)   ->	Union[str, Any]:
							a       ,						a       =     self.get_models()
							# Take the first (hypothetical) EMA step.
							ema_unet.step(unet.parameters()				)
							assert ema_unet.optimization_step == 1

							# Take two more.
							for _ in range(2				):
										ema_unet.step(unet.parameters()				)
							assert ema_unet.optimization_step == 3





				def 				__UpperCAmelCase				( self							:	Optional[int]				)   ->	Optional[int]:
							a       ,						a       =     self.get_models()
							# Since the `unet` is not being updated (i.e., backprop'd)
							# there won't be any difference between the `params` of `unet`
							# and `ema_unet` even if we call `ema_unet.step(unet.parameters())`.
							ema_unet.step(unet.parameters()				)
							a       =     list(unet.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert torch.allclose(__lowerCamelCase   , __lowerCamelCase				)

							# The above holds true even if we call `ema.step()` multiple times since
							# `unet` params are still not being updated.
							for _ in range(4				):
										ema_unet.step(unet.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				def 				__UpperCAmelCase				( self							:	Any				)   ->	Dict:
							a       ,						a       =     self.get_models()
							# Here we simulate the parameter updates for `unet`. Since there might
							# be some parameters which are initialized to zero we take extra care to
							# initialize their values to something non-zero before the multiplication.
							a       =     self.simulate_backprop(__lowerCamelCase				)

							# Take the EMA step.
							ema_unet.step(unet_pseudo_updated_step_one.parameters()				)

							# Now the EMA'd parameters won't be equal to the original model parameters.
							a       =     list(unet_pseudo_updated_step_one.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert ~torch.allclose(__lowerCamelCase   , __lowerCamelCase				)

							# Ensure this is the case when we take multiple EMA steps.
							for _ in range(4				):
										ema_unet.step(unet.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert ~torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				def 				__UpperCAmelCase				( self							:	Optional[Any]				)   ->	Any:
							# If we call EMA step after a backpropagation consecutively for two times,
							# the shadow params from those two steps should be different.
							a       ,						a       =     self.get_models()

							# First backprop + EMA
							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_one.parameters()				)
							a       =     ema_unet.shadow_params

							# Second backprop + EMA
							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_two.parameters()				)
							a       =     ema_unet.shadow_params

							for step_one, step_two in zip(__lowerCamelCase   , __lowerCamelCase				):
										assert ~torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				def 				__UpperCAmelCase				( self							:	Any				)   ->	List[Any]:
							# If there's no decay even if there are backprops, EMA steps
							# won't take any effect i.e., the shadow params would remain the
							# same.
							a       ,						a       =     self.get_models(decay=0.0				)
							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_one.parameters()				)
							a       =     ema_unet.shadow_params

							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_two.parameters()				)
							a       =     ema_unet.shadow_params

							for step_one, step_two in zip(__lowerCamelCase   , __lowerCamelCase				):
										assert torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				@skip_mps
				def 				__UpperCAmelCase				( self							:	List[str]				)   ->	Dict:
							a       ,						a       =     self.get_models()
							a       ,						a       ,						a       =     self.get_dummy_inputs()

							with tempfile.TemporaryDirectory() as tmpdir:
										ema_unet.save_pretrained(__lowerCamelCase				)
										a       =     UNetaDConditionModel.from_pretrained(__lowerCamelCase   , model_cls=__lowerCamelCase				)
										a       =     loaded_unet.to(unet.device				)

							# Since no EMA step has been performed the outputs should match.
							a       =     unet(__lowerCamelCase   , __lowerCamelCase   , __lowerCamelCase				).sample
							a       =     loaded_unet(__lowerCamelCase   , __lowerCamelCase   , __lowerCamelCase				).sample

							assert torch.allclose(__lowerCamelCase   , __lowerCamelCase   , atol=1e-4				)






