




import math




def       __magic_name__    (			A		: int       ):






			'''simple docstring'''







			a   =      0
			if n % 2 == 0:
						count += 1
						while n % 2 == 0:
									a   =      int(n / 2       )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

			a   =      3

			while i <= int(math.sqrt(__UpperCamelCase       )       ):
						if n % i == 0:
									count += 1
									while n % i == 0:
												a   =      int(n / i       )
						a   =      i + 2

			# this condition checks the prime
			# number n is greater than 2

			if n > 2:
						count += 1
			return count


if __name__ == "__main__":
		__lowerCAmelCase		:    Tuple	      =		5124_2183
		print(F'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
		print(F'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')












import torch
import torch.nn.functional as F

from diffusers import VQDiffusionScheduler

from .test_schedulers import SchedulerCommonTest




class    snake_case__							(_UpperCamelCase       ):
				"""simple docstring"""



				SCREAMING_SNAKE_CASE_	:							Dict										= (VQDiffusionScheduler,)





				def 							__UpperCAmelCase							(				self    :					Tuple ,				**__lowerCamelCase    :					Optional[int]							) ->					Optional[Any]:
							a   =      {
							    "num_vec_classes": 40_97,
							    "num_train_timesteps": 1_00,
							}

							config.update(**__lowerCamelCase							)
							return config





				def 							__UpperCAmelCase							(				self    :					List[str] ,				__lowerCamelCase    :					Any							) ->					Union[str, Any]:
							a   =      4
							a   =      8
							a   =      8

							a   =      torch.randint(0 ,				__lowerCamelCase ,				(batch_size, height * width)							)

							return sample





				@property
				def 							__UpperCAmelCase							(				self    :					List[str]							) ->					Optional[Any]:
							assert False





				def 							__UpperCAmelCase							(				self    :					Any ,				__lowerCamelCase    :					Optional[int]							) ->					int:
							def model(__lowerCamelCase    :					Tuple ,				__lowerCamelCase    :					Any ,				*__lowerCamelCase    :					Optional[Any]							):
										a   ,		a   =      sample.shape
										a   =      torch.rand((batch_size, num_vec_classes - 1, num_latent_pixels)							)
										a   =      F.log_softmax(logits.double() ,				dim=1							).float()
										return return_value

							return model





				def 							__UpperCAmelCase							(				self    :					Optional[Any]							) ->					Any:
							for timesteps in [2, 5, 1_00, 10_00]:
										self.check_over_configs(num_train_timesteps=__lowerCamelCase							)





				def 							__UpperCAmelCase							(				self    :					Any							) ->					List[Any]:
							for num_vec_classes in [5, 1_00, 10_00, 40_00]:
										self.check_over_configs(num_vec_classes=__lowerCamelCase							)





				def 							__UpperCAmelCase							(				self    :					Optional[Any]							) ->					List[Any]:
							for t in [0, 50, 99]:
										self.check_over_forward(time_step=__lowerCamelCase							)





				def 							__UpperCAmelCase							(				self    :					List[Any]							) ->					Optional[Any]:
							pass






