



'''simple docstring'''

import math



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



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



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



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		_a  :   Dict				 =							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,
)


__lowerCAmelCase		    =     {'''configuration_t5''': ['''T5_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''T5Config''', '''T5OnnxConfig''']}

try:
							if not is_sentencepiece_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase		    =     ['''T5Tokenizer''']

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase		    =     ['''T5TokenizerFast''']

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase		    =     [
							    '''T5_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''T5EncoderModel''',
							    '''T5ForConditionalGeneration''',
							    '''T5Model''',
							    '''T5PreTrainedModel''',
							    '''load_tf_weights_in_t5''',
							    '''T5ForQuestionAnswering''',
							]

try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase		    =     [
							    '''TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''TFT5EncoderModel''',
							    '''TFT5ForConditionalGeneration''',
							    '''TFT5Model''',
							    '''TFT5PreTrainedModel''',
							]

try:
							if not is_flax_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase		    =     [
							    '''FlaxT5EncoderModel''',
							    '''FlaxT5ForConditionalGeneration''',
							    '''FlaxT5Model''',
							    '''FlaxT5PreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_ta import T5_PRETRAINED_CONFIG_ARCHIVE_MAP, TaConfig, TaOnnxConfig

							try:
														if not is_sentencepiece_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_ta import TaTokenizer

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_ta_fast import TaTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_ta import (
														    T5_PRETRAINED_MODEL_ARCHIVE_LIST,
														    TaEncoderModel,
														    TaForConditionalGeneration,
														    TaForQuestionAnswering,
														    TaModel,
														    TaPreTrainedModel,
														    load_tf_weights_in_ta,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_ta import (
														    TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST,
														    TFTaEncoderModel,
														    TFTaForConditionalGeneration,
														    TFTaModel,
														    TFTaPreTrainedModel,
														)

							try:
														if not is_flax_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_flax_ta import (
														    FlaxTaEncoderModel,
														    FlaxTaForConditionalGeneration,
														    FlaxTaModel,
														    FlaxTaPreTrainedModel,
														)


else:
							import sys

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




