





import torch

from diffusers import EulerDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest




class 			__UpperCamelCase    (							A__    ):
     __A	:  List[str]							  =   (EulerDiscreteScheduler,)
     __A	:  Optional[int]							  =   10





     def 		UpperCamelCase(     self				,							**_UpperCamelCase					):
        _UpperCAmelCase           =   {
            '''num_train_timesteps''': 1100,
            '''beta_start''': 0.0001,
            '''beta_end''': 0.02,
            '''beta_schedule''': '''linear''',
        }

        config.update(**_UpperCamelCase					)
        return config





     def 		UpperCamelCase(     self					):
        for timesteps in [10, 50, 100, 1000]:
           self.check_over_configs(num_train_timesteps=_UpperCamelCase					)





     def 		UpperCamelCase(     self					):
        for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]				,							[0.0002, 0.002, 0.02]					):
           self.check_over_configs(beta_start=_UpperCamelCase				,							beta_end=_UpperCamelCase					)





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





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





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.scheduler_classes[0]
        _UpperCAmelCase           =   self.get_scheduler_config()
        _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

        scheduler.set_timesteps(self.num_inference_steps					)

        _UpperCAmelCase           =   torch.manual_seed(0					)

        _UpperCAmelCase           =   self.dummy_model()
        _UpperCAmelCase           =   self.dummy_sample_deter * scheduler.init_noise_sigma
        _UpperCAmelCase           =   sample.to(_UpperCamelCase					)

        for i, t in enumerate(scheduler.timesteps					):
           _UpperCAmelCase           =   scheduler.scale_model_input(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   model(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							generator=_UpperCamelCase					)
           _UpperCAmelCase           =   output.prev_sample

        _UpperCAmelCase           =   torch.sum(torch.abs(_UpperCamelCase					)					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_sum.item() - 10.0807					) < 1e-2
        assert abs(result_mean.item() - 0.0131					) < 1e-3





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.scheduler_classes[0]
        _UpperCAmelCase           =   self.get_scheduler_config(prediction_type='''v_prediction'''					)
        _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

        scheduler.set_timesteps(self.num_inference_steps					)

        _UpperCAmelCase           =   torch.manual_seed(0					)

        _UpperCAmelCase           =   self.dummy_model()
        _UpperCAmelCase           =   self.dummy_sample_deter * scheduler.init_noise_sigma
        _UpperCAmelCase           =   sample.to(_UpperCamelCase					)

        for i, t in enumerate(scheduler.timesteps					):
           _UpperCAmelCase           =   scheduler.scale_model_input(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   model(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							generator=_UpperCamelCase					)
           _UpperCAmelCase           =   output.prev_sample

        _UpperCAmelCase           =   torch.sum(torch.abs(_UpperCamelCase					)					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_sum.item() - 0.0002					) < 1e-2
        assert abs(result_mean.item() - 2.2676e-06					) < 1e-3





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.scheduler_classes[0]
        _UpperCAmelCase           =   self.get_scheduler_config()
        _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

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

        _UpperCAmelCase           =   torch.manual_seed(0					)

        _UpperCAmelCase           =   self.dummy_model()
        _UpperCAmelCase           =   self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
        _UpperCAmelCase           =   sample.to(_UpperCamelCase					)

        for t in scheduler.timesteps:
           _UpperCAmelCase           =   scheduler.scale_model_input(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   model(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							generator=_UpperCamelCase					)
           _UpperCAmelCase           =   output.prev_sample

        _UpperCAmelCase           =   torch.sum(torch.abs(_UpperCamelCase					)					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_sum.item() - 10.0807					) < 1e-2
        assert abs(result_mean.item() - 0.0131					) < 1e-3





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.scheduler_classes[0]
        _UpperCAmelCase           =   self.get_scheduler_config()
        _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase				,							use_karras_sigmas=_UpperCamelCase					)

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

        _UpperCAmelCase           =   torch.manual_seed(0					)

        _UpperCAmelCase           =   self.dummy_model()
        _UpperCAmelCase           =   self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
        _UpperCAmelCase           =   sample.to(_UpperCamelCase					)

        for t in scheduler.timesteps:
           _UpperCAmelCase           =   scheduler.scale_model_input(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   model(_UpperCamelCase				,							_UpperCamelCase					)

           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							generator=_UpperCamelCase					)
           _UpperCAmelCase           =   output.prev_sample

        _UpperCAmelCase           =   torch.sum(torch.abs(_UpperCamelCase					)					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_sum.item() - 124.52299499511719					) < 1e-2
        assert abs(result_mean.item() - 0.16213932633399963					) < 1e-3






from math import sqrt
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  bool:






   """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(sqrt(SCREAMING_SNAKE_CASE_						) + 1						)				,	6						):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 1_00_01						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   1
   while count != nth and number < 3:
      number += 1
      if is_prime(SCREAMING_SNAKE_CASE_						):
         count += 1
   while count != nth:
      number += 2
      if is_prime(SCREAMING_SNAKE_CASE_						):
         count += 1
   return number


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