





'''simple docstring'''

from __future__ import annotations

from math import gcd







def  a__    (    lowercase :					int, lowercase :					int = 2, lowercase :					int = 1, lowercase :					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(lowercase :					int, lowercase :					int, lowercase :					int				) -> int:
          return (pow(lowercase, 2				) + step) % modulus

     for _ in range(lowercase				):
          # 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(lowercase, lowercase, lowercase				)
               _UpperCamelCase       =	rand_fn(lowercase, lowercase, lowercase				)
               _UpperCamelCase       =	rand_fn(lowercase, lowercase, lowercase				)

               # 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, lowercase				)

               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

   lowercase__						:      Tuple	=    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',
   )
   lowercase__						:      Dict	=    parser.parse_args()

   lowercase__						:      Optional[int]	=    pollard_rho(args.num, attempts=args.attempts)
   if divisor is None:
      print(F"""{args.num} is probably prime""")
   else:
      lowercase__						:      List[Any]	=    args.num // divisor
      print(F"""{args.num} = {divisor} * {quotient}""")










'''simple docstring'''

import warnings

from ...utils import logging
from .image_processing_owlvit import OwlViTImageProcessor


lowercase__						:      Optional[Any]	=    logging.get_logger(__name__)
class     __lowerCAmelCase					(   __magic_name__			):






       """simple docstring"""





       def __init__(							self       :		List[Any]	,			*lowerCAmelCase__       :		List[str]	,			**lowerCAmelCase__       :		List[str]					)   ->					None:

            '''simple docstring'''




            warnings.warn(
                '''The class OwlViTFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please'''
                ''' use OwlViTImageProcessor instead.'''	,			lowerCAmelCase__	,			)
            super().__init__(*lowerCAmelCase__	,			**lowerCAmelCase__					)



