




'''simple docstring'''







from __future__ import annotations

from math import gcd





def 		snake_case_							(_a			:							int					,     _a			:							int = 2					,     _a			:							int = 1					,     _a			:							int = 3					,     ):
    # A value less than 2 can cause an infinite loop in the algorithm.
    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.
        UpperCAmelCase     =	seed
        UpperCAmelCase     =	seed

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            UpperCAmelCase     =	rand_fn(_a					,     _a					,     _a  )
            UpperCAmelCase     =	rand_fn(_a					,     _a					,     _a  )
            UpperCAmelCase     =	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``.
            UpperCAmelCase     =	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.
        UpperCAmelCase     =	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

   A									=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',
   )
   A									=parser.parse_args()

   A									=pollard_rho(args.num, attempts=args.attempts)
   if divisor is None:
      print(f"""{args.num} is probably prime""")
   else:
      A									=args.num // divisor
      print(f"""{args.num} = {divisor} * {quotient}""")










'''simple docstring'''







import os

from bleurt import score  # From: git+https://github.com/google-research/bleurt.git

import datasets


A									=datasets.logging.get_logger(__name__)


A									='\\n@inproceedings{bleurt,\n  title={BLEURT: Learning Robust Metrics for Text Generation},\n  author={Thibault Sellam and Dipanjan Das and Ankur P. Parikh},\n  booktitle={ACL},\n  year={2020},\n  url={https://arxiv.org/abs/2004.04696}\n}\n'

A									='\\nBLEURT a learnt evaluation metric for Natural Language Generation. It is built using multiple phases of transfer learning starting from a pretrained BERT model (Devlin et al. 2018)\nand then employing another pre-training phrase using synthetic data. Finally it is trained on WMT human annotations. You may run BLEURT out-of-the-box or fine-tune\nit for your specific application (the latter is expected to perform better).\n\nSee the project\'s README at https://github.com/google-research/bleurt#readme for more information.\n'

A									='\nBLEURT score.\n\nArgs:\n    `predictions` (list of str): prediction/candidate sentences\n    `references` (list of str): reference sentences\n    `checkpoint` BLEURT checkpoint. Will default to BLEURT-tiny if None.\n\nReturns:\n    \'scores\': List of scores.\nExamples:\n\n    >>> predictions = ["hello there", "general kenobi"]\n    >>> references = ["hello there", "general kenobi"]\n    >>> bleurt = datasets.load_metric("bleurt")\n    >>> results = bleurt.compute(predictions=predictions, references=references)\n    >>> print([round(v, 2) for v in results["scores"]])\n    [1.03, 1.04]\n'

A									={
    'bleurt-tiny-128': 'https://storage.googleapis.com/bleurt-oss/bleurt-tiny-128.zip',
    'bleurt-tiny-512': 'https://storage.googleapis.com/bleurt-oss/bleurt-tiny-512.zip',
    'bleurt-base-128': 'https://storage.googleapis.com/bleurt-oss/bleurt-base-128.zip',
    'bleurt-base-512': 'https://storage.googleapis.com/bleurt-oss/bleurt-base-512.zip',
    'bleurt-large-128': 'https://storage.googleapis.com/bleurt-oss/bleurt-large-128.zip',
    'bleurt-large-512': 'https://storage.googleapis.com/bleurt-oss/bleurt-large-512.zip',
    'BLEURT-20-D3': 'https://storage.googleapis.com/bleurt-oss-21/BLEURT-20-D3.zip',
    'BLEURT-20-D6': 'https://storage.googleapis.com/bleurt-oss-21/BLEURT-20-D6.zip',
    'BLEURT-20-D12': 'https://storage.googleapis.com/bleurt-oss-21/BLEURT-20-D12.zip',
    'BLEURT-20': 'https://storage.googleapis.com/bleurt-oss-21/BLEURT-20.zip',
}


@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION							,							_KWARGS_DESCRIPTION				)
class     _a						(			datasets.Metric				):
       def 					A   (			self		:			Dict       ):



           '''simple docstring'''

           return datasets.MetricInfo(
               description=_DESCRIPTION     ,       citation=_CITATION     ,       homepage='''https://github.com/google-research/bleurt'''     ,       inputs_description=_KWARGS_DESCRIPTION     ,       features=datasets.Features(
                   {
                       '''predictions''': datasets.Value('''string'''     ,       id='''sequence'''       ),
                       '''references''': datasets.Value('''string'''     ,       id='''sequence'''       ),
                   }       )     ,       codebase_urls=['''https://github.com/google-research/bleurt''']     ,       reference_urls=['''https://github.com/google-research/bleurt''', '''https://arxiv.org/abs/2004.04696''']     ,       )
       def 					A   (			self		:			List[Any]     ,       lowercase		:			Union[str, Any]       ):



           '''simple docstring'''

           if self.config_name == "default":
               logger.warning(
                   '''Using default BLEURT-Base checkpoint for sequence maximum length 128. '''
                   '''You can use a bigger model for better results with e.g.: datasets.load_metric(\'bleurt\', \'bleurt-large-512\').'''       )
               UpperCAmelCase     =	'''bleurt-base-128'''

           if self.config_name.lower() in CHECKPOINT_URLS:
               UpperCAmelCase     =	self.config_name.lower()

           elif self.config_name.upper() in CHECKPOINT_URLS:
               UpperCAmelCase     =	self.config_name.upper()

           else:
               raise KeyError(
                   f"{self.config_name} model not found. You should supply the name of a model checkpoint for bleurt in {CHECKPOINT_URLS.keys()}"       )

           # download the model checkpoint specified by self.config_name and set up the scorer
           UpperCAmelCase     =	dl_manager.download_and_extract(CHECKPOINT_URLS[checkpoint_name]       )
           UpperCAmelCase     =	score.BleurtScorer(os.path.join(lowercase     ,       lowercase       )       )







       def 					A   (			self		:			str     ,       lowercase		:			str     ,       lowercase		:			str       ):



           '''simple docstring'''

           UpperCAmelCase     =	self.scorer.score(references=lowercase     ,       candidates=lowercase       )
           return {"scores": scores}




