


import math






def  _UpperCAmelCase						( __lowerCamelCase							)		->list:


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






def  _UpperCAmelCase						( __lowerCamelCase							)		->int:


 '''simple docstring'''
 if n <= 0:
  raise ValueError('''Only positive numbers are accepted'''							)
 snake_case :			Any							=   1
 snake_case :			List[str]							=   1
 while n % 2 == 0:
  temp += 1
  snake_case :			Dict							=   int(n / 2							)
 div *= temp
 for i in range(3			,  int(math.sqrt(__snake_case							)							) + 1			,  2							):
  snake_case :			List[str]							=   1
  while n % i == 0:
   temp += 1
   snake_case :			Dict							=   int(n / i							)
  div *= temp
 if n > 1:
  div *= 2
 return div






def  _UpperCAmelCase						( __lowerCamelCase							)		->int:


 '''simple docstring'''
 if n <= 0:
  raise ValueError('''Only positive numbers are accepted'''							)
 snake_case :			str							=   1
 snake_case :			Optional[Any]							=   1
 while n % 2 == 0:
  temp += 1
  snake_case :			int							=   int(n / 2							)
 if temp > 1:
  s *= (2**temp - 1) / (2 - 1)
 for i in range(3			,  int(math.sqrt(__snake_case							)							) + 1			,  2							):
  snake_case :			List[str]							=   1
  while n % i == 0:
   temp += 1
   snake_case :			Any							=   int(n / i							)
  if temp > 1:
   s *= (i**temp - 1) / (i - 1)
 return int(__snake_case							)






def  _UpperCAmelCase						( __lowerCamelCase							)		->int:


 '''simple docstring'''
 snake_case :			Optional[int]							=   n
 for x in set(prime_factors(__snake_case							)							):
  s *= (x - 1) / x
 return int(__snake_case							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()








import warnings
from dataclasses import dataclass, field
from typing import Optional, Tuple

from .training_args import TrainingArguments
from .utils import cached_property, is_tf_available, logging, requires_backends


lowerCamelCase_				:							Optional[Any]       =    logging.get_logger(__name__)

if is_tf_available():
 import tensorflow as tf







@dataclass
class  _lowerCamelCase			(lowerCamelCase					):
     lowercase__				  =			"""tf"""
     lowercase__				  =			field(
         default=lowerCamelCase							,					metadata={"""help""": """Name of TPU"""}							,					)

     lowercase__				  =			field(
         default=lowerCamelCase							,					metadata={"""help""": """Zone of TPU"""}							,					)

     lowercase__				  =			field(
         default=lowerCamelCase							,					metadata={"""help""": """Name of Cloud TPU-enabled project"""}							,					)

     lowercase__				  =			field(
         default=1.0							,					metadata={"""help""": """Power for the Polynomial decay LR scheduler."""}							,					)

     lowercase__				  =			field(default=lowerCamelCase							,					metadata={"""help""": """Whether to activate the XLA compilation or not"""}					)

     @cached_property
     def 						__lowerCamelCase				(  self    ):
            requires_backends(self							,       ['tf']    )
            logger.info('Tensorflow: setting up strategy'    )

            __snake_case						       =   tf.config.list_physical_devices('GPU'    )

            # Set to float16 at first
            if self.fpaa:
                   tf.keras.mixed_precision.set_global_policy('mixed_float16'    )

            if self.no_cuda:
                   __snake_case						       =   tf.distribute.OneDeviceStrategy(device='/cpu:0'    )
            else:
                   try:
                          if self.tpu_name:
                                 __snake_case						       =   tf.distribute.cluster_resolver.TPUClusterResolver(
                                     self.tpu_name							,       zone=self.tpu_zone							,       project=self.gcp_project    )
                          else:
                                 __snake_case						       =   tf.distribute.cluster_resolver.TPUClusterResolver()
                   except ValueError:
                          if self.tpu_name:
                                 raise RuntimeError(f'''Couldn\'t connect to TPU {self.tpu_name}!'''    )
                          else:
                                 __snake_case						       =   None

                   if tpu:
                          # Set to bfloat16 in case of TPU
                          if self.fpaa:
                                 tf.keras.mixed_precision.set_global_policy('mixed_bfloat16'    )

                          tf.config.experimental_connect_to_cluster(SCREAMING_SNAKE_CASE_    )
                          tf.tpu.experimental.initialize_tpu_system(SCREAMING_SNAKE_CASE_    )

                          __snake_case						       =   tf.distribute.TPUStrategy(SCREAMING_SNAKE_CASE_    )

                   elif len(SCREAMING_SNAKE_CASE_    ) == 0:
                          __snake_case						       =   tf.distribute.OneDeviceStrategy(device='/cpu:0'    )
                   elif len(SCREAMING_SNAKE_CASE_    ) == 1:
                          __snake_case						       =   tf.distribute.OneDeviceStrategy(device='/gpu:0'    )
                   elif len(SCREAMING_SNAKE_CASE_    ) > 1:
                          # If you only want to use a specific subset of GPUs use `CUDA_VISIBLE_DEVICES=0`
                          __snake_case						       =   tf.distribute.MirroredStrategy()
                   else:
                          raise ValueError('Cannot find the proper strategy, please check your environment properties.'    )

            return strategy

     @property
     def 						__lowerCamelCase				(  self    ):
            requires_backends(self							,       ['tf']    )
            return self._setup_strategy

     @property
     def 						__lowerCamelCase				(  self    ):
            requires_backends(self							,       ['tf']    )
            return self._setup_strategy.num_replicas_in_sync

     @property
     def 						__lowerCamelCase				(  self    ):
            return False  # TF Logging is handled by Keras not the Trainer

     @property
     def 						__lowerCamelCase				(  self    ):
            if self.per_gpu_train_batch_size:
                   logger.warning(
                       'Using deprecated `--per_gpu_train_batch_size` argument which will be removed in a future '
                       'version. Using `--per_device_train_batch_size` is preferred.'    )
            __snake_case						       =   self.per_gpu_train_batch_size or self.per_device_train_batch_size
            return per_device_batch_size * self.n_replicas

     @property
     def 						__lowerCamelCase				(  self    ):
            if self.per_gpu_eval_batch_size:
                   logger.warning(
                       'Using deprecated `--per_gpu_eval_batch_size` argument which will be removed in a future '
                       'version. Using `--per_device_eval_batch_size` is preferred.'    )
            __snake_case						       =   self.per_gpu_eval_batch_size or self.per_device_eval_batch_size
            return per_device_batch_size * self.n_replicas

     @property
     def 						__lowerCamelCase				(  self    ):
            requires_backends(self							,       ['tf']    )
            warnings.warn(
                'The n_gpu argument is deprecated and will be removed in a future version, use n_replicas instead.'							,       SCREAMING_SNAKE_CASE_							,       )
            return self._setup_strategy.num_replicas_in_sync
