

"""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 					snake_case			:

				def 							lowercase_  (			self							:       Dict)->     Dict:



											'''simple docstring'''


											__lowerCAmelCase: List[Any]					   =    self.prepare_init_args_and_inputs_for_common()

											__lowerCAmelCase: List[str]					   =    self.model_class(**UpperCamelCase__)
											__lowerCAmelCase: Dict					   =    model.init(inputs_dict["prng_key"]  ,						inputs_dict["sample"])
											jax.lax.stop_gradient(UpperCamelCase__)

											__lowerCAmelCase: Optional[int]					   =    model.apply(UpperCamelCase__  ,						inputs_dict["sample"])

											if isinstance(UpperCamelCase__  ,						UpperCamelCase__):
																		__lowerCAmelCase: List[Any]					   =    output.sample

											self.assertIsNotNone(UpperCamelCase__)
											__lowerCAmelCase: Union[str, Any]					   =    inputs_dict["sample"].shape
											self.assertEqual(output.shape  ,						UpperCamelCase__  ,						"Input and output shapes do not match")

				def 							lowercase_  (			self							:       Optional[Any])->     Optional[int]:



											'''simple docstring'''


											__lowerCAmelCase: Any					   =    self.prepare_init_args_and_inputs_for_common()

											__lowerCAmelCase: str					   =    1_6
											__lowerCAmelCase: List[Any]					   =    (1_6, 3_2)

											__lowerCAmelCase: Dict					   =    self.model_class(**UpperCamelCase__)
											__lowerCAmelCase: int					   =    model.init(inputs_dict["prng_key"]  ,						inputs_dict["sample"])
											jax.lax.stop_gradient(UpperCamelCase__)

											__lowerCAmelCase: Union[str, Any]					   =    model.apply(UpperCamelCase__  ,						inputs_dict["sample"])

											if isinstance(UpperCamelCase__  ,						UpperCamelCase__):
																		__lowerCAmelCase: Union[str, Any]					   =    output.sample

											self.assertIsNotNone(UpperCamelCase__)
											__lowerCAmelCase: Any					   =    inputs_dict["sample"].shape
											self.assertEqual(output.shape  ,						UpperCamelCase__  ,						"Input and output shapes do not match")




				def 							lowercase_  (			self							:       List[Any])->     List[Any]:



											'''simple docstring'''


											__lowerCAmelCase: Any					   =    "kwargs" in inspect.signature(self.model_class.__init__).parameters
											__lowerCAmelCase: int					   =    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>]`")





"""simple docstring"""


import math






def 					a__					(					__SCREAMING_SNAKE_CASE				)			->			list:
		if n <= 0:
				raise ValueError("Only positive integers have prime factors"				)
		__lowerCAmelCase: Tuple					   =    []
		while n % 2 == 0:
				pf.append(2				)
				__lowerCAmelCase: str					   =    int(n / 2				)
		for i in range(3      ,				int(math.sqrt(__SCREAMING_SNAKE_CASE				)				) + 1      ,				2				):
				while n % i == 0:
						pf.append(__SCREAMING_SNAKE_CASE				)
						__lowerCAmelCase: List[Any]					   =    int(n / i				)
		if n > 2:
				pf.append(__SCREAMING_SNAKE_CASE				)
		return pf






def 					a__					(					__SCREAMING_SNAKE_CASE				)			->			int:
		if n <= 0:
				raise ValueError("Only positive numbers are accepted"				)
		__lowerCAmelCase: int					   =    1
		__lowerCAmelCase: str					   =    1
		while n % 2 == 0:
				temp += 1
				__lowerCAmelCase: Dict					   =    int(n / 2				)
		div *= temp
		for i in range(3      ,				int(math.sqrt(__SCREAMING_SNAKE_CASE				)				) + 1      ,				2				):
				__lowerCAmelCase: int					   =    1
				while n % i == 0:
						temp += 1
						__lowerCAmelCase: Tuple					   =    int(n / i				)
				div *= temp
		if n > 1:
				div *= 2
		return div






def 					a__					(					__SCREAMING_SNAKE_CASE				)			->			int:
		if n <= 0:
				raise ValueError("Only positive numbers are accepted"				)
		__lowerCAmelCase: Dict					   =    1
		__lowerCAmelCase: int					   =    1
		while n % 2 == 0:
				temp += 1
				__lowerCAmelCase: Tuple					   =    int(n / 2				)
		if temp > 1:
				s *= (2**temp - 1) / (2 - 1)
		for i in range(3      ,				int(math.sqrt(__SCREAMING_SNAKE_CASE				)				) + 1      ,				2				):
				__lowerCAmelCase: List[Any]					   =    1
				while n % i == 0:
						temp += 1
						__lowerCAmelCase: List[str]					   =    int(n / i				)
				if temp > 1:
						s *= (i**temp - 1) / (i - 1)
		return int(__SCREAMING_SNAKE_CASE				)






def 					a__					(					__SCREAMING_SNAKE_CASE				)			->			int:
		__lowerCAmelCase: Optional[int]					   =    n
		for x in set(prime_factors(__SCREAMING_SNAKE_CASE				)				):
				s *= (x - 1) / x
		return int(__SCREAMING_SNAKE_CASE				)


if __name__ == "__main__":
			import doctest

			doctest.testmod()


