


from __future__ import annotations

from math import gcd







def 	SCREAMING_SNAKE_CASE_						(      __A			:      int  ,   __A			:      int = 2  ,   __A			:      int = 1  ,   __A			:      int = 3  ,   )     ->		int | None:

       """simple docstring"""

       if num < 2:
              raise ValueError('The input value cannot be less than 2'    )

       # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
       # algorithm struggles to find factors that are divisible by two.
       # As a workaround, we specifically check for two and even inputs.
       #   See: https://math.stackexchange.com/a/2856214/165820
       if num > 2 and num % 2 == 0:
              return 2

       # Pollard's Rho algorithm requires a function that returns pseudorandom
       # values between 0 <= X < ``num``.  It doesn't need to be random in the
       # sense that the output value is cryptographically secure or difficult
       # to calculate, it only needs to be random in the sense that all output
       # values should be equally likely to appear.
       # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
       # However, the success of Pollard's algorithm isn't guaranteed and is
       # determined in part by the initial seed and the chosen random function.
       # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
       # where ``C`` is a value that we can modify between each attempt.
       def rand_fn(__A			:      int  ,   __A			:      int  ,   __A			:      int    ) -> int:
              return (pow(__A  ,   2    ) + step) % modulus

       for _ in range(__A    ):
              # These track the position within the cycle detection logic.
              a_ :		Optional[int]							=  seed
              a_ :		Optional[Any]							=  seed

              while True:
                     # At each iteration, the tortoise moves one step and the hare moves two.
                     a_ :		str							=  rand_fn(__A  ,   __A  ,   __A    )
                     a_ :		Optional[int]							=  rand_fn(__A  ,   __A  ,   __A    )
                     a_ :		Union[str, Any]							=  rand_fn(__A  ,   __A  ,   __A    )

                     # At some point both the tortoise and the hare will enter a cycle whose
                     # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
                     # the tortoise and hare will end up on the same value modulo ``p``.
                     # We can detect when this happens because the position difference between
                     # the tortoise and the hare will share a common divisor with ``num``.
                     a_ :		Union[str, Any]							=  gcd(hare - tortoise  ,   __A    )

                     if divisor == 1:
                            # No common divisor yet, just keep searching.
                            continue
                     else:
                            # We found a common divisor!
                            if divisor == num:
                                   # Unfortunately, the divisor is ``num`` itself and is useless.
                                   break
                            else:
                                   # The divisor is a nontrivial factor of ``num``!
                                   return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
              a_ :		str							=  hare

              # The new step value for the random function can just be incremented.
              # At first the results will be similar to what the old function would
              # have produced, but the value will quickly diverge after a bit.
              step += 1

       # We haven't found a divisor within the requested number of attempts.
       # We were unlucky or ``num`` itself is actually prime.
       return None


if __name__ == "__main__":
   import argparse

   UpperCAmelCase_				:			Any   =	argparse.ArgumentParser()
   parser.add_argument(
       'num',
       type=int,
       help='The value to find a divisor of',
   )
   parser.add_argument(
       '--attempts',
       type=int,
       default=3,
       help='The number of attempts before giving up',
   )
   UpperCAmelCase_				:			str   =	parser.parse_args()

   UpperCAmelCase_				:			Dict   =	pollard_rho(args.num, attempts=args.attempts)
   if divisor is None:
      print(F'{args.num} is probably prime')
   else:
      UpperCAmelCase_				:			Union[str, Any]   =	args.num // divisor
      print(F'{args.num} = {divisor} * {quotient}')






from typing import TYPE_CHECKING

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


UpperCAmelCase_				:			Any   =	{
    'configuration_mobilebert': [
        'MOBILEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'MobileBertConfig',
        'MobileBertOnnxConfig',
    ],
    'tokenization_mobilebert': ['MobileBertTokenizer'],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_				:			Union[str, Any]   =	['MobileBertTokenizerFast']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_				:			List[str]   =	[
       'MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'MobileBertForMaskedLM',
       'MobileBertForMultipleChoice',
       'MobileBertForNextSentencePrediction',
       'MobileBertForPreTraining',
       'MobileBertForQuestionAnswering',
       'MobileBertForSequenceClassification',
       'MobileBertForTokenClassification',
       'MobileBertLayer',
       'MobileBertModel',
       'MobileBertPreTrainedModel',
       'load_tf_weights_in_mobilebert',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_				:			Tuple   =	[
       'TF_MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFMobileBertForMaskedLM',
       'TFMobileBertForMultipleChoice',
       'TFMobileBertForNextSentencePrediction',
       'TFMobileBertForPreTraining',
       'TFMobileBertForQuestionAnswering',
       'TFMobileBertForSequenceClassification',
       'TFMobileBertForTokenClassification',
       'TFMobileBertMainLayer',
       'TFMobileBertModel',
       'TFMobileBertPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_mobilebert import (
       MOBILEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
       MobileBertConfig,
       MobileBertOnnxConfig,
   )
   from .tokenization_mobilebert import MobileBertTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_mobilebert_fast import MobileBertTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_mobilebert import (
          MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
          MobileBertForMaskedLM,
          MobileBertForMultipleChoice,
          MobileBertForNextSentencePrediction,
          MobileBertForPreTraining,
          MobileBertForQuestionAnswering,
          MobileBertForSequenceClassification,
          MobileBertForTokenClassification,
          MobileBertLayer,
          MobileBertModel,
          MobileBertPreTrainedModel,
          load_tf_weights_in_mobilebert,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_mobilebert import (
          TF_MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFMobileBertForMaskedLM,
          TFMobileBertForMultipleChoice,
          TFMobileBertForNextSentencePrediction,
          TFMobileBertForPreTraining,
          TFMobileBertForQuestionAnswering,
          TFMobileBertForSequenceClassification,
          TFMobileBertForTokenClassification,
          TFMobileBertMainLayer,
          TFMobileBertModel,
          TFMobileBertPreTrainedModel,
      )

else:
   import sys

   UpperCAmelCase_				:			Tuple   =	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


