code: 
  
  from __future__ import annotations
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> set[int]:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			List[str]    			=      {1}
      lowerCAmelCase				:			int    			=      [1]
      for _ in range(2,      depth + 1				):
          lowerCAmelCase				:			str    			=      [*previous_coefficients, 0]
          lowerCAmelCase				:			Optional[int]    			=      [0, *previous_coefficients]
          lowerCAmelCase				:			Tuple    			=      []
          for x, y in zip(_UpperCAmelCase,      _UpperCAmelCase				):
              coefficients.add(x + y				)
              previous_coefficients.append(x + y				)
      return coefficients
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> set[int]:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			str    			=      set()
      for number in unique_coefficients:
          lowerCAmelCase				:			Dict    			=      2
          lowerCAmelCase				:			Tuple    			=      number
          while divisor**2 <= copy_number:
              lowerCAmelCase				:			List[str]    			=      0
              while copy_number % divisor == 0:
                  copy_number //= divisor
                  multiplicity += 1
              if multiplicity >= 2:
                  non_squarefrees.add(_UpperCAmelCase				)
                  break
              divisor += 1
  
      return unique_coefficients.difference(_UpperCAmelCase				)
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase = 51				)					-> int:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			int    			=      get_pascal_triangle_unique_coefficients(_UpperCAmelCase				)
      lowerCAmelCase				:			Optional[int]    			=      get_squarefrees(_UpperCAmelCase				)
      return sum(_UpperCAmelCase				)
  
  
  if __name__ == "__main__":
   print(F'{solution() = }')
  
  
  
  
  
  
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
  
  
  
  
  
  