




from __future__ import annotations

from math import gcd






def 					snake_case(				__magic_name__ ,		__magic_name__ = 2 ,		__magic_name__ = 1 ,		__magic_name__ = 3 ,		) ->							List[Any]:





     '''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(__magic_name__ ,		__magic_name__ ,		__magic_name__    ) -> int:
          return (pow(__lowerCamelCase ,		2    ) + step) % modulus

     for _ in range(__lowerCamelCase    ):
          # These track the position within the cycle detection logic.
          lowercase					:   str								= seed
          lowercase					:   List[Any]								= seed

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

               # 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``.
               lowercase					:   Any								= gcd(hare - tortoise ,		__lowerCamelCase    )

               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.
          lowercase					:   List[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

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

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







import copy
from dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Audio, Features, Value
from .base import TaskTemplate
@dataclass(frozen=lowercase__   )
class     a    ( lowercase__   ):



      """simple docstring"""


      a  : str							       =	field(default='automatic-speech-recognition'							,       metadata={'include_in_asdict_even_if_is_default': True}   )
      a  : ClassVar[Features]							       =	Features({'audio': Audio()}   )
      a  : ClassVar[Features]							       =	Features({'transcription': Value('string'   )}   )
      a  : str							       =	"audio"
      a  : str							       =	"transcription"
      def 	UpperCAmelCase      (      self					:			Optional[Any]		,      __lowercase					:			Optional[int]					)							->      str:
        if self.audio_column not in features:
          raise ValueError(f"""Column {self.audio_column} is not present in features."""					)
        if not isinstance(features[self.audio_column]		,      __lowercase					):
          raise ValueError(f"""Column {self.audio_column} is not an Audio type."""					)
        __UpperCAmelCase							:	int           =  copy.deepcopy(self					)
        __UpperCAmelCase							:	str           =  self.input_schema.copy()
        __UpperCAmelCase							:	List[str]           =  features[self.audio_column]
        __UpperCAmelCase							:	Optional[Any]           =  input_schema
        return task_template




      @property
      def 	UpperCAmelCase      (      self					:			Union[str, Any]					)							->      Dict[str, str]:
        return {self.audio_column: "audio", self.transcription_column: "transcription"}


