





'''simple docstring'''




import math





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





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





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





def      __lowerCamelCase       (	__lowerCAmelCase    :				Any						)						->   int:
   snake_case      		=					n
   for x in set(prime_factors(__lowerCAmelCase						)						):
      s *= (x - 1) / x
   return int(__lowerCAmelCase						)


if __name__ == "__main__":
 import doctest

 doctest.testmod()





'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


__UpperCAmelCase    				=							{
    '''configuration_switch_transformers''': [
        '''SWITCH_TRANSFORMERS_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''SwitchTransformersConfig''',
        '''SwitchTransformersOnnxConfig''',
    ]
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCAmelCase    				=							[
		    '''SWITCH_TRANSFORMERS_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''SwitchTransformersEncoderModel''',
		    '''SwitchTransformersForConditionalGeneration''',
		    '''SwitchTransformersModel''',
		    '''SwitchTransformersPreTrainedModel''',
		    '''SwitchTransformersTop1Router''',
		    '''SwitchTransformersSparseMLP''',
		]


if TYPE_CHECKING:
		from .configuration_switch_transformers import (
		    SWITCH_TRANSFORMERS_PRETRAINED_CONFIG_ARCHIVE_MAP,
		    SwitchTransformersConfig,
		    SwitchTransformersOnnxConfig,
		)

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_switch_transformers import (
				    SWITCH_TRANSFORMERS_PRETRAINED_MODEL_ARCHIVE_LIST,
				    SwitchTransformersEncoderModel,
				    SwitchTransformersForConditionalGeneration,
				    SwitchTransformersModel,
				    SwitchTransformersPreTrainedModel,
				    SwitchTransformersSparseMLP,
				    SwitchTransformersTopaRouter,
				)


else:
		import sys

		__UpperCAmelCase    				=							_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)