






import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest




class 							_lowerCAmelCase(			UpperCAmelCase_   ):





       """simple docstring"""







       a							:						Dict										=(KDPMaDiscreteScheduler,)
       a							:						str										=10





       def      _a       (   self    ,     **_lowerCamelCase				):
         UpperCamelCase_:   Optional[int]        =							{
             'num_train_timesteps': 1_1_0_0,
             'beta_start': 0.0_0_0_1,
             'beta_end': 0.0_2,
             'beta_schedule': 'linear',
         }

         config.update(**_lowercase				)
         return config





       def      _a       (   self				):
         for timesteps in [1_0, 5_0, 1_0_0, 1_0_0_0]:
           self.check_over_configs(num_train_timesteps=_lowercase				)





       def      _a       (   self				):
         for beta_start, beta_end in zip([0.0_0_0_0_1, 0.0_0_0_1, 0.0_0_1]    ,     [0.0_0_0_2, 0.0_0_2, 0.0_2]				):
           self.check_over_configs(beta_start=_lowercase    ,     beta_end=_lowercase				)





       def      _a       (   self				):
         for schedule in ["linear", "scaled_linear"]:
           self.check_over_configs(beta_schedule=_lowercase				)





       def      _a       (   self				):
         for prediction_type in ["epsilon", "v_prediction"]:
           self.check_over_configs(prediction_type=_lowercase				)





       def      _a       (   self				):
         UpperCamelCase_:   str        =							self.scheduler_classes[0]
         UpperCamelCase_:   Optional[Any]        =							self.get_scheduler_config(prediction_type='v_prediction'				)
         UpperCamelCase_:   Union[str, Any]        =							scheduler_class(**_lowercase				)

         scheduler.set_timesteps(self.num_inference_steps				)

         UpperCamelCase_:   Dict        =							self.dummy_model()
         UpperCamelCase_:   Optional[int]        =							self.dummy_sample_deter * scheduler.init_noise_sigma
         UpperCamelCase_:   Optional[int]        =							sample.to(_lowercase				)

         for i, t in enumerate(scheduler.timesteps				):
           UpperCamelCase_:   Any        =							scheduler.scale_model_input(_lowercase    ,     _lowercase				)

           UpperCamelCase_:   Any        =							model(_lowercase    ,     _lowercase				)

           UpperCamelCase_:   Optional[int]        =							scheduler.step(_lowercase    ,     _lowercase    ,     _lowercase				)
           UpperCamelCase_:   int        =							output.prev_sample

         UpperCamelCase_:   Union[str, Any]        =							torch.sum(torch.abs(_lowercase				)				)
         UpperCamelCase_:   Any        =							torch.mean(torch.abs(_lowercase				)				)

         if torch_device in ["cpu", "mps"]:
           assert abs(result_sum.item() - 4.6934e-07				) < 1e-2
           assert abs(result_mean.item() - 6.1112e-10				) < 1e-3
         else:
           # CUDA
           assert abs(result_sum.item() - 4.693428650170972e-07				) < 1e-2
           assert abs(result_mean.item() - 0.0_0_0_2				) < 1e-3





       def      _a       (   self				):
         if torch_device == "mps":
           return
         UpperCamelCase_:   Tuple        =							self.scheduler_classes[0]
         UpperCamelCase_:   Optional[Any]        =							self.get_scheduler_config()
         UpperCamelCase_:   str        =							scheduler_class(**_lowercase				)

         scheduler.set_timesteps(self.num_inference_steps				)

         UpperCamelCase_:   Optional[int]        =							self.dummy_model()
         UpperCamelCase_:   str        =							self.dummy_sample_deter * scheduler.init_noise_sigma
         UpperCamelCase_:   List[Any]        =							sample.to(_lowercase				)

         for i, t in enumerate(scheduler.timesteps				):
           UpperCamelCase_:   List[str]        =							scheduler.scale_model_input(_lowercase    ,     _lowercase				)

           UpperCamelCase_:   Union[str, Any]        =							model(_lowercase    ,     _lowercase				)

           UpperCamelCase_:   int        =							scheduler.step(_lowercase    ,     _lowercase    ,     _lowercase				)
           UpperCamelCase_:   List[Any]        =							output.prev_sample

         UpperCamelCase_:   Optional[Any]        =							torch.sum(torch.abs(_lowercase				)				)
         UpperCamelCase_:   Union[str, Any]        =							torch.mean(torch.abs(_lowercase				)				)

         if torch_device in ["cpu", "mps"]:
           assert abs(result_sum.item() - 2_0.4_1_2_5				) < 1e-2
           assert abs(result_mean.item() - 0.0_2_6_6				) < 1e-3
         else:
           # CUDA
           assert abs(result_sum.item() - 2_0.4_1_2_5				) < 1e-2
           assert abs(result_mean.item() - 0.0_2_6_6				) < 1e-3





       def      _a       (   self				):
         if torch_device == "mps":
           return
         UpperCamelCase_:   Dict        =							self.scheduler_classes[0]
         UpperCamelCase_:   List[Any]        =							self.get_scheduler_config()
         UpperCamelCase_:   List[Any]        =							scheduler_class(**_lowercase				)

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

         UpperCamelCase_:   Optional[int]        =							self.dummy_model()
         UpperCamelCase_:   List[str]        =							self.dummy_sample_deter.to(_lowercase				) * scheduler.init_noise_sigma

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

           UpperCamelCase_:   Any        =							model(_lowercase    ,     _lowercase				)

           UpperCamelCase_:   Dict        =							scheduler.step(_lowercase    ,     _lowercase    ,     _lowercase				)
           UpperCamelCase_:   Any        =							output.prev_sample

         UpperCamelCase_:   Union[str, Any]        =							torch.sum(torch.abs(_lowercase				)				)
         UpperCamelCase_:   Optional[int]        =							torch.mean(torch.abs(_lowercase				)				)

         if str(_lowercase				).startswith('cpu'				):
           # The following sum varies between 148 and 156 on mps. Why?
           assert abs(result_sum.item() - 2_0.4_1_2_5				) < 1e-2
           assert abs(result_mean.item() - 0.0_2_6_6				) < 1e-3
         else:
           # CUDA
           assert abs(result_sum.item() - 2_0.4_1_2_5				) < 1e-2
           assert abs(result_mean.item() - 0.0_2_6_6				) < 1e-3


def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0			)->						int:



    """simple docstring"""






    UpperCamelCase_			  =						[i - 1 for i in range(limit + 1			)]

    for i in range(2			,						limit + 1			):
        if phi[i] == i - 1:
            for j in range(2 * i			,						limit + 1			,						SCREAMING_SNAKE_CASE_			):
                phi[j] -= phi[j] // i

    return sum(phi[2 : limit + 1]			)


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