






"""simple docstring"""



import math




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

					lowerCamelCase__					=3

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

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

					if n > 2:
										count += 1
					return count


if __name__ == "__main__":
						_snake_case							:   List[str]	  =       51_242_183
						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}")







"""simple docstring"""



import inspect

from diffusers.utils import is_flax_available
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
						import jax




@require_flax
class 							__lowercase:






						def 		lowerCAmelCase (       self)      ->	str:




											"""simple docstring"""





											lowerCamelCase__					,  lowerCamelCase__					=self.prepare_init_args_and_inputs_for_common()

											lowerCamelCase__					=self.model_class(**_SCREAMING_SNAKE_CASE)
											lowerCamelCase__					=model.init(inputs_dict['prng_key']     ,    inputs_dict['sample'])
											jax.lax.stop_gradient(_SCREAMING_SNAKE_CASE)

											lowerCamelCase__					=model.apply(_SCREAMING_SNAKE_CASE     ,    inputs_dict['sample'])

											if isinstance(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE):
																lowerCamelCase__					=output.sample

											self.assertIsNotNone(_SCREAMING_SNAKE_CASE)
											lowerCamelCase__					=inputs_dict['sample'].shape
											self.assertEqual(output.shape     ,    _SCREAMING_SNAKE_CASE     ,    'Input and output shapes do not match')






						def 		lowerCAmelCase (       self)      ->	Optional[Any]:




											"""simple docstring"""





											lowerCamelCase__					,  lowerCamelCase__					=self.prepare_init_args_and_inputs_for_common()

											lowerCamelCase__					=16
											lowerCamelCase__					=(16, 32)

											lowerCamelCase__					=self.model_class(**_SCREAMING_SNAKE_CASE)
											lowerCamelCase__					=model.init(inputs_dict['prng_key']     ,    inputs_dict['sample'])
											jax.lax.stop_gradient(_SCREAMING_SNAKE_CASE)

											lowerCamelCase__					=model.apply(_SCREAMING_SNAKE_CASE     ,    inputs_dict['sample'])

											if isinstance(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE):
																lowerCamelCase__					=output.sample

											self.assertIsNotNone(_SCREAMING_SNAKE_CASE)
											lowerCamelCase__					=inputs_dict['sample'].shape
											self.assertEqual(output.shape     ,    _SCREAMING_SNAKE_CASE     ,    'Input and output shapes do not match')






						def 		lowerCAmelCase (       self)      ->	Optional[Any]:




											"""simple docstring"""





											lowerCamelCase__					='kwargs' in inspect.signature(self.model_class.__init__).parameters
											lowerCamelCase__					=len(self.model_class._deprecated_kwargs) > 0

											if has_kwarg_in_model_class and not has_deprecated_kwarg:
																raise ValueError(
																    F"{self.model_class} has `**kwargs` in its __init__ method but has not defined any deprecated kwargs"
																    ' under the `_deprecated_kwargs` class attribute. Make sure to either remove `**kwargs` if there are'
																    ' no deprecated arguments or add the deprecated argument with `_deprecated_kwargs ='
																    ' [<deprecated_argument>]`')

											if not has_kwarg_in_model_class and has_deprecated_kwarg:
																raise ValueError(
																    F"{self.model_class} doesn't have `**kwargs` in its __init__ method but has defined deprecated kwargs"
																    ' under the `_deprecated_kwargs` class attribute. Make sure to either add the `**kwargs` argument to'
																    F" {self.model_class}.__init__ if there are deprecated arguments or remove the deprecated argument"
																    ' from `_deprecated_kwargs = [<deprecated_argument>]`')