code: 
  
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase,      _UpperCAmelCase				)					-> Union[str, Any]:
  
  
  
  				'''simple docstring'''
  
  
  
  
  
  
  				if a < b:
  								return gcd(_UpperCAmelCase,      _UpperCAmelCase				)
  				if a % b == 0:
  								return b
  				return gcd(_UpperCAmelCase,      a % b				)
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase,      _UpperCAmelCase,      _UpperCAmelCase				)					-> List[str]:
  
  
  
  				'''simple docstring'''
  
  
  
  
  
  
  				if y == 0:
  								return 1
  				lowerCAmelCase				:			Tuple    			=      power(_UpperCAmelCase,      y // 2,      _UpperCAmelCase				) % mod
  				lowerCAmelCase				:			str    			=      (temp * temp) % mod
  				if y % 2 == 1:
  								lowerCAmelCase				:			int    			=      (temp * x) % mod
  				return temp
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> int:
  
  
  
  				'''simple docstring'''
  
  
  
  
  
  
  				lowerCAmelCase				:			Optional[Any]    			=      2
  				while b < n:
  								if gcd(_UpperCAmelCase,      _UpperCAmelCase				) == 1 and power(_UpperCAmelCase,      n - 1,      _UpperCAmelCase				) != 1:
  												return False
  								b += 1
  				return True
  
  
  if __name__ == "__main__":
  	__A   :     List[Any]      =			int(input('''Enter number: ''').strip())
  	if is_carmichael_number(number):
  		print(F'{number} is a Carmichael Number.')
  	else:
  		print(F'{number} is not a Carmichael Number.')
  
  
  
  
  
  
style_context: 
  
  import torch
  
  from diffusers import KDPMaAncestralDiscreteScheduler
  from diffusers.utils import torch_device
  
  from .test_schedulers import SchedulerCommonTest
  
  
  
  
  
  
  class    __A				(							lowerCAmelCase ):
      lowerCAmelCase_							:		List[str]						=							(KDPMaAncestralDiscreteScheduler,)
      lowerCAmelCase_							:		Dict						=							10
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Any    ,				**UpperCAmelCase_			:    List[Any]    ):
          lowerCAmelCase				:			int    			=      {
              'num_train_timesteps': 1100,
              'beta_start': 0.00_01,
              'beta_end': 0.02,
              'beta_schedule': 'linear',
          }
  
          config.update(**UpperCAmelCase_    )
          return config
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Optional[Any]    ):
          for timesteps in [10, 50, 100, 1000]:
              self.check_over_configs(num_train_timesteps=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    List[str]    ):
          for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]    ,				[0.00_02, 0.0_02, 0.02]    ):
              self.check_over_configs(beta_start=UpperCAmelCase_    ,				beta_end=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Optional[int]    ):
          for schedule in ["linear", "scaled_linear"]:
              self.check_over_configs(beta_schedule=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    int    ):
          if torch_device == "mps":
              return
          lowerCAmelCase				:			Any    			=      self.scheduler_classes[0]
          lowerCAmelCase				:			Optional[int]    			=      self.get_scheduler_config()
          lowerCAmelCase				:			List[str]    			=      scheduler_class(**UpperCAmelCase_    )
  
          scheduler.set_timesteps(self.num_inference_steps    )
  
          lowerCAmelCase				:			Any    			=      torch.manual_seed(0    )
  
          lowerCAmelCase				:			List[Any]    			=      self.dummy_model()
          lowerCAmelCase				:			List[Any]    			=      self.dummy_sample_deter * scheduler.init_noise_sigma
          lowerCAmelCase				:			Optional[int]    			=      sample.to(UpperCAmelCase_    )
  
          for i, t in enumerate(scheduler.timesteps    ):
              lowerCAmelCase				:			str    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Any    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Optional[Any]    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
              lowerCAmelCase				:			Union[str, Any]    			=      output.prev_sample
  
          lowerCAmelCase				:			List[Any]    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
          lowerCAmelCase				:			Any    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )
  
          assert abs(result_sum.item() - 1_38_49.38_77    ) < 1E-2
          assert abs(result_mean.item() - 18.03_31    ) < 5E-3
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Tuple    ):
          for prediction_type in ["epsilon", "v_prediction"]:
              self.check_over_configs(prediction_type=UpperCAmelCase_    )
  
  
  
  
  
  
      def 	lowercase__ (	self			:    List[str]    ):
          if torch_device == "mps":
              return
          lowerCAmelCase				:			Optional[Any]    			=      self.scheduler_classes[0]
          lowerCAmelCase				:			List[Any]    			=      self.get_scheduler_config(prediction_type='v_prediction'    )
          lowerCAmelCase				:			Any    			=      scheduler_class(**UpperCAmelCase_    )
  
          scheduler.set_timesteps(self.num_inference_steps    )
  
          lowerCAmelCase				:			Optional[int]    			=      self.dummy_model()
          lowerCAmelCase				:			Any    			=      self.dummy_sample_deter * scheduler.init_noise_sigma
          lowerCAmelCase				:			Optional[int]    			=      sample.to(UpperCAmelCase_    )
  
          lowerCAmelCase				:			Optional[int]    			=      torch.manual_seed(0    )
  
          for i, t in enumerate(scheduler.timesteps    ):
              lowerCAmelCase				:			Dict    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Optional[int]    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Optional[int]    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
              lowerCAmelCase				:			str    			=      output.prev_sample
  
          lowerCAmelCase				:			str    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
          lowerCAmelCase				:			Tuple    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )
  
          assert abs(result_sum.item() - 3_28.99_70    ) < 1E-2
          assert abs(result_mean.item() - 0.42_84    ) < 1E-3
  
  
  
  
  
  
      def 	lowercase__ (	self			:    Tuple    ):
          if torch_device == "mps":
              return
          lowerCAmelCase				:			str    			=      self.scheduler_classes[0]
          lowerCAmelCase				:			Dict    			=      self.get_scheduler_config()
          lowerCAmelCase				:			List[str]    			=      scheduler_class(**UpperCAmelCase_    )
  
          scheduler.set_timesteps(self.num_inference_steps    ,				device=UpperCAmelCase_    )
          lowerCAmelCase				:			int    			=      torch.manual_seed(0    )
  
          lowerCAmelCase				:			Tuple    			=      self.dummy_model()
          lowerCAmelCase				:			Optional[Any]    			=      self.dummy_sample_deter.to(UpperCAmelCase_    ) * scheduler.init_noise_sigma
  
          for t in scheduler.timesteps:
              lowerCAmelCase				:			str    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			List[Any]    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )
  
              lowerCAmelCase				:			Dict    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
              lowerCAmelCase				:			Dict    			=      output.prev_sample
  
          lowerCAmelCase				:			Union[str, Any]    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
          lowerCAmelCase				:			str    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )
  
          assert abs(result_sum.item() - 1_38_49.38_18    ) < 1E-1
          assert abs(result_mean.item() - 18.03_31    ) < 1E-3
  
  
  
  
  
  