






import torch

from diffusers import DDIMScheduler

from .test_schedulers import SchedulerCommonTest


class        _lowerCAmelCase( UpperCAmelCase_      ):





       """simple docstring"""







       a       :	Optional[int]								=(DDIMScheduler,)
       a       :	Any								=(('''eta''', 0.0), ('''num_inference_steps''', 50))





       def     _a					(      self						,    **_lowerCamelCase							):
         UpperCamelCase_:      Union[str, Any]					   =       {
             'num_train_timesteps': 1_0_0_0,
             'beta_start': 0.0_0_0_1,
             'beta_end': 0.0_2,
             'beta_schedule': 'linear',
             'clip_sample': True,
         }

         config.update(**A_							)
         return config





       def     _a					(      self						,    **_lowerCamelCase							):
         UpperCamelCase_:      str					   =       self.scheduler_classes[0]
         UpperCamelCase_:      List[Any]					   =       self.get_scheduler_config(**A_							)
         UpperCamelCase_:      List[Any]					   =       scheduler_class(**A_							)

         UpperCamelCase_   ,UpperCamelCase_:      Optional[Any]					   =       1_0, 0.0

         UpperCamelCase_:      List[Any]					   =       self.dummy_model()
         UpperCamelCase_:      List[Any]					   =       self.dummy_sample_deter

         scheduler.set_timesteps(A_							)

         for t in scheduler.timesteps:
           UpperCamelCase_:      List[Any]					   =       model(A_						,    A_							)
           UpperCamelCase_:      str					   =       scheduler.step(A_						,    A_						,    A_						,    A_							).prev_sample

         return sample





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





       def     _a					(      self							):
         for steps_offset in [0, 1]:
           self.check_over_configs(steps_offset=A_							)

         UpperCamelCase_:      Union[str, Any]					   =       self.scheduler_classes[0]
         UpperCamelCase_:      Any					   =       self.get_scheduler_config(steps_offset=1							)
         UpperCamelCase_:      List[Any]					   =       scheduler_class(**A_							)
         scheduler.set_timesteps(5							)
         assert torch.equal(scheduler.timesteps						,    torch.LongTensor([8_0_1, 6_0_1, 4_0_1, 2_0_1, 1]							)							)





       def     _a					(      self							):
         for beta_start, beta_end in zip([0.0_0_0_1, 0.0_0_1, 0.0_1, 0.1]						,    [0.0_0_2, 0.0_2, 0.2, 2]							):
           self.check_over_configs(beta_start=A_						,    beta_end=A_							)





       def     _a					(      self							):
         for schedule in ["linear", "squaredcos_cap_v2"]:
           self.check_over_configs(beta_schedule=A_							)





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





       def     _a					(      self							):
         for clip_sample in [True, False]:
           self.check_over_configs(clip_sample=A_							)





       def     _a					(      self							):
         for timestep_spacing in ["trailing", "leading"]:
           self.check_over_configs(timestep_spacing=A_							)





       def     _a					(      self							):
         for rescale_betas_zero_snr in [True, False]:
           self.check_over_configs(rescale_betas_zero_snr=A_							)





       def     _a					(      self							):
         self.check_over_configs(thresholding=A_							)
         for threshold in [0.5, 1.0, 2.0]:
           for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(
                 thresholding=A_						,    prediction_type=A_						,    sample_max_value=A_						,    )





       def     _a					(      self							):
         for t in [1, 1_0, 4_9]:
           self.check_over_forward(time_step=A_							)





       def     _a					(      self							):
         for t, num_inference_steps in zip([1, 1_0, 5_0]						,    [1_0, 5_0, 5_0_0]							):
           self.check_over_forward(time_step=A_						,    num_inference_steps=A_							)





       def     _a					(      self							):
         for t, eta in zip([1, 1_0, 4_9]						,    [0.0, 0.5, 1.0]							):
           self.check_over_forward(time_step=A_						,    eta=A_							)





       def     _a					(      self							):
         UpperCamelCase_:      str					   =       self.scheduler_classes[0]
         UpperCamelCase_:      Tuple					   =       self.get_scheduler_config()
         UpperCamelCase_:      Tuple					   =       scheduler_class(**A_							)

         assert torch.sum(torch.abs(scheduler._get_variance(0						,    0							) - 0.0							)							) < 1e-5
         assert torch.sum(torch.abs(scheduler._get_variance(4_2_0						,    4_0_0							) - 0.1_4_7_7_1							)							) < 1e-5
         assert torch.sum(torch.abs(scheduler._get_variance(9_8_0						,    9_6_0							) - 0.3_2_4_6_0							)							) < 1e-5
         assert torch.sum(torch.abs(scheduler._get_variance(0						,    0							) - 0.0							)							) < 1e-5
         assert torch.sum(torch.abs(scheduler._get_variance(4_8_7						,    4_8_6							) - 0.0_0_9_7_9							)							) < 1e-5
         assert torch.sum(torch.abs(scheduler._get_variance(9_9_9						,    9_9_8							) - 0.0_2							)							) < 1e-5





       def     _a					(      self							):
         UpperCamelCase_:      str					   =       self.full_loop()

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

         assert abs(result_sum.item() - 1_7_2.0_0_6_7							) < 1e-2
         assert abs(result_mean.item() - 0.2_2_3_9_6_7							) < 1e-3





       def     _a					(      self							):
         UpperCamelCase_:      Union[str, Any]					   =       self.full_loop(prediction_type='v_prediction'							)

         UpperCamelCase_:      Optional[int]					   =       torch.sum(torch.abs(A_							)							)
         UpperCamelCase_:      Any					   =       torch.mean(torch.abs(A_							)							)

         assert abs(result_sum.item() - 5_2.5_3_0_2							) < 1e-2
         assert abs(result_mean.item() - 0.0_6_8_4							) < 1e-3





       def     _a					(      self							):
         # We specify different beta, so that the first alpha is 0.99
         UpperCamelCase_:      Tuple					   =       self.full_loop(set_alpha_to_one=A_						,    beta_start=0.0_1							)
         UpperCamelCase_:      Optional[Any]					   =       torch.sum(torch.abs(A_							)							)
         UpperCamelCase_:      int					   =       torch.mean(torch.abs(A_							)							)

         assert abs(result_sum.item() - 1_4_9.8_2_9_5							) < 1e-2
         assert abs(result_mean.item() - 0.1_9_5_1							) < 1e-3





       def     _a					(      self							):
         # We specify different beta, so that the first alpha is 0.99
         UpperCamelCase_:      Optional[int]					   =       self.full_loop(set_alpha_to_one=A_						,    beta_start=0.0_1							)
         UpperCamelCase_:      Dict					   =       torch.sum(torch.abs(A_							)							)
         UpperCamelCase_:      List[Any]					   =       torch.mean(torch.abs(A_							)							)

         assert abs(result_sum.item() - 1_4_9.0_7_8_4							) < 1e-2
         assert abs(result_mean.item() - 0.1_9_4_1							) < 1e-3







from math import factorial

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       Dict:
  return factorial(UpperCAmelCase__						) / (factorial(UpperCAmelCase__						) * factorial(n - r						))

def 						snake_case      () ->       Optional[Any]:
  UpperCamelCase_:      int					   =       0

  for i in range(1			,					1_0_1						):
    for j in range(1			,					i + 1						):
      if combinations(UpperCAmelCase__			,					UpperCAmelCase__						) > 1E6:
        total += 1
  return total


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