




"""simple docstring"""





from __future__ import annotations

import math
from itertools import permutations

def 		lowerCAmelCase				(			lowerCamelCase		):
						'''simple docstring'''


						if 1 < number < 4:
												# 2 and 3 are primes
												return True
						elif number < 2 or number % 2 == 0 or number % 3 == 0:
												# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
												return False

						# All primes number are in format of 6k +/- 1
						for i in range(5   ,      int(math.sqrt(UpperCAmelCase_		) + 1		)   ,      6		):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True

def 		lowerCAmelCase				(			lowerCamelCase = 7		):
						'''simple docstring'''


						snake_case__							:       Tuple				      =       ''.join(str(UpperCAmelCase_		) for i in range(1   ,      n + 1		)		)
						snake_case__							:       Any				      =       [int(''''''.join(UpperCAmelCase_		)		) for i in permutations(UpperCAmelCase_   ,      UpperCAmelCase_		)]
						snake_case__							:       Any				      =       [num for num in perm_list if is_prime(UpperCAmelCase_		)]
						return max(UpperCAmelCase_		) if pandigitals else 0


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





'''simple docstring'''

import torch

from diffusers import LMSDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest




class 			A_					(							_snake_case				):






     '''simple docstring'''



     UpperCAmelCase_		:      Dict    						=    (LMSDiscreteScheduler,)
     UpperCAmelCase_		:      Any    						=    10


     def   UpperCAmelCase_			(						self					:	str	,     **lowercase_					:	List[str]			)		->      str:
      UpperCAmelCase			:      Optional[Any]		   =					{
          'num_train_timesteps': 1_100,
          'beta_start': 0.0001,
          'beta_end': 0.02,
          'beta_schedule': 'linear',
      }

      config.update(**lowercase_			)
      return config


     def   UpperCAmelCase_			(						self					:	Optional[int]			)		->      Tuple:
      for timesteps in [10, 50, 100, 1_000]:
       self.check_over_configs(num_train_timesteps=lowercase_			)


     def   UpperCAmelCase_			(						self					:	int			)		->      Tuple:
      for beta_start, beta_end in zip([0.0_0001, 0.0001, 0.001]	,     [0.0002, 0.002, 0.02]			):
       self.check_over_configs(beta_start=lowercase_	,     beta_end=lowercase_			)


     def   UpperCAmelCase_			(						self					:	Dict			)		->      Union[str, Any]:
      for schedule in ["linear", "scaled_linear"]:
       self.check_over_configs(beta_schedule=lowercase_			)


     def   UpperCAmelCase_			(						self					:	Tuple			)		->      List[Any]:
      for prediction_type in ["epsilon", "v_prediction"]:
       self.check_over_configs(prediction_type=lowercase_			)


     def   UpperCAmelCase_			(						self					:	str			)		->      Union[str, Any]:
      for t in [0, 500, 800]:
       self.check_over_forward(time_step=lowercase_			)


     def   UpperCAmelCase_			(						self					:	Union[str, Any]			)		->      List[str]:
      UpperCAmelCase			:      Any		   =					self.scheduler_classes[0]
      UpperCAmelCase			:      Tuple		   =					self.get_scheduler_config()
      UpperCAmelCase			:      Any		   =					scheduler_class(**lowercase_			)

      scheduler.set_timesteps(self.num_inference_steps			)

      UpperCAmelCase			:      str		   =					self.dummy_model()
      UpperCAmelCase			:      str		   =					self.dummy_sample_deter * scheduler.init_noise_sigma

      for i, t in enumerate(scheduler.timesteps			):
       UpperCAmelCase			:      Optional[Any]		   =					scheduler.scale_model_input(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      Union[str, Any]		   =					model(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      Dict		   =					scheduler.step(lowercase_	,     lowercase_	,     lowercase_			)
       UpperCAmelCase			:      List[str]		   =					output.prev_sample

      UpperCAmelCase			:      Optional[Any]		   =					torch.sum(torch.abs(lowercase_			)			)
      UpperCAmelCase			:      Optional[Any]		   =					torch.mean(torch.abs(lowercase_			)			)

      assert abs(result_sum.item() - 1006.388			) < 1E-2
      assert abs(result_mean.item() - 1.31			) < 1E-3


     def   UpperCAmelCase_			(						self					:	str			)		->      Dict:
      UpperCAmelCase			:      Any		   =					self.scheduler_classes[0]
      UpperCAmelCase			:      Dict		   =					self.get_scheduler_config(prediction_type='v_prediction'			)
      UpperCAmelCase			:      Optional[int]		   =					scheduler_class(**lowercase_			)

      scheduler.set_timesteps(self.num_inference_steps			)

      UpperCAmelCase			:      Optional[Any]		   =					self.dummy_model()
      UpperCAmelCase			:      List[str]		   =					self.dummy_sample_deter * scheduler.init_noise_sigma

      for i, t in enumerate(scheduler.timesteps			):
       UpperCAmelCase			:      List[Any]		   =					scheduler.scale_model_input(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      Optional[Any]		   =					model(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      Dict		   =					scheduler.step(lowercase_	,     lowercase_	,     lowercase_			)
       UpperCAmelCase			:      List[str]		   =					output.prev_sample

      UpperCAmelCase			:      Union[str, Any]		   =					torch.sum(torch.abs(lowercase_			)			)
      UpperCAmelCase			:      Any		   =					torch.mean(torch.abs(lowercase_			)			)

      assert abs(result_sum.item() - 0.0017			) < 1E-2
      assert abs(result_mean.item() - 2.2676E-06			) < 1E-3


     def   UpperCAmelCase_			(						self					:	Optional[Any]			)		->      Dict:
      UpperCAmelCase			:      Dict		   =					self.scheduler_classes[0]
      UpperCAmelCase			:      Optional[int]		   =					self.get_scheduler_config()
      UpperCAmelCase			:      List[str]		   =					scheduler_class(**lowercase_			)

      scheduler.set_timesteps(self.num_inference_steps	,     device=lowercase_			)

      UpperCAmelCase			:      Tuple		   =					self.dummy_model()
      UpperCAmelCase			:      Tuple		   =					self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
      UpperCAmelCase			:      Any		   =					sample.to(lowercase_			)

      for i, t in enumerate(scheduler.timesteps			):
       UpperCAmelCase			:      Dict		   =					scheduler.scale_model_input(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      Optional[Any]		   =					model(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      Tuple		   =					scheduler.step(lowercase_	,     lowercase_	,     lowercase_			)
       UpperCAmelCase			:      List[Any]		   =					output.prev_sample

      UpperCAmelCase			:      Union[str, Any]		   =					torch.sum(torch.abs(lowercase_			)			)
      UpperCAmelCase			:      Union[str, Any]		   =					torch.mean(torch.abs(lowercase_			)			)

      assert abs(result_sum.item() - 1006.388			) < 1E-2
      assert abs(result_mean.item() - 1.31			) < 1E-3




     def   UpperCAmelCase_			(						self					:	Dict			)		->      Optional[Any]:
      UpperCAmelCase			:      int		   =					self.scheduler_classes[0]
      UpperCAmelCase			:      Union[str, Any]		   =					self.get_scheduler_config()
      UpperCAmelCase			:      Optional[Any]		   =					scheduler_class(**lowercase_	,     use_karras_sigmas=lowercase_			)

      scheduler.set_timesteps(self.num_inference_steps	,     device=lowercase_			)

      UpperCAmelCase			:      List[Any]		   =					self.dummy_model()
      UpperCAmelCase			:      Dict		   =					self.dummy_sample_deter.to(lowercase_			) * scheduler.init_noise_sigma
      UpperCAmelCase			:      Union[str, Any]		   =					sample.to(lowercase_			)

      for t in scheduler.timesteps:
       UpperCAmelCase			:      Optional[int]		   =					scheduler.scale_model_input(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      List[str]		   =					model(lowercase_	,     lowercase_			)

       UpperCAmelCase			:      List[Any]		   =					scheduler.step(lowercase_	,     lowercase_	,     lowercase_			)
       UpperCAmelCase			:      Any		   =					output.prev_sample

      UpperCAmelCase			:      List[Any]		   =					torch.sum(torch.abs(lowercase_			)			)
      UpperCAmelCase			:      Any		   =					torch.mean(torch.abs(lowercase_			)			)

      assert abs(result_sum.item() - 3812.9927			) < 2E-2
      assert abs(result_mean.item() - 4.9648			) < 1E-3




