



"""simple docstring"""
import math
def        A_  (      _lowercase     ):







						'''simple docstring'''


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







						'''simple docstring'''


						if n <= 0:
												raise ValueError("""Only positive numbers are accepted"""     )
						snake_case_			:Tuple						=      1
						snake_case_			:Optional[Any]						=      1
						while n % 2 == 0:
												temp += 1
												snake_case_			:Union[str, Any]						=      int(n / 2     )
						div *= temp
						for i in range(3, int(math.sqrt(_lowercase     )     ) + 1, 2     ):
												snake_case_			:int						=      1
												while n % i == 0:
																		temp += 1
																		snake_case_			:Optional[int]						=      int(n / i     )
												div *= temp
						if n > 1:
												div *= 2
						return div
def        A_  (      _lowercase     ):







						'''simple docstring'''


						if n <= 0:
												raise ValueError("""Only positive numbers are accepted"""     )
						snake_case_			:int						=      1
						snake_case_			:Optional[Any]						=      1
						while n % 2 == 0:
												temp += 1
												snake_case_			:Optional[Any]						=      int(n / 2     )
						if temp > 1:
												s *= (2**temp - 1) / (2 - 1)
						for i in range(3, int(math.sqrt(_lowercase     )     ) + 1, 2     ):
												snake_case_			:Optional[int]						=      1
												while n % i == 0:
																		temp += 1
																		snake_case_			:Union[str, Any]						=      int(n / i     )
												if temp > 1:
																		s *= (i**temp - 1) / (i - 1)
						return int(_lowercase     )
def        A_  (      _lowercase     ):







						'''simple docstring'''


						snake_case_			:Tuple						=      n
						for x in set(prime_factors(_lowercase     )     ):
												s *= (x - 1) / x
						return int(_lowercase     )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





"""simple docstring"""
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


__a     =    {
    "configuration_xlm_prophetnet": ["XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMProphetNetConfig"],
}

try:
						if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a     =    ["XLMProphetNetTokenizer"]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a     =    [
						    "XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "XLMProphetNetDecoder",
						    "XLMProphetNetEncoder",
						    "XLMProphetNetForCausalLM",
						    "XLMProphetNetForConditionalGeneration",
						    "XLMProphetNetModel",
						    "XLMProphetNetPreTrainedModel",
						]


if TYPE_CHECKING:
						from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

						try:
												if not is_sentencepiece_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_xlm_prophetnet import (
												    XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
												    XLMProphetNetDecoder,
												    XLMProphetNetEncoder,
												    XLMProphetNetForCausalLM,
												    XLMProphetNetForConditionalGeneration,
												    XLMProphetNetModel,
												    XLMProphetNetPreTrainedModel,
												)

else:
						import sys

						__a     =    _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
