"""simple docstring"""



from __future__ import annotations

from math import gcd



def 	_lowerCamelCase(	a   ,    a = 2   ,    a = 1   ,    a = 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   ,    a   ,    a				) -> int:
              return (pow(lowercase_   ,    2				) + step) % modulus

       for _ in range(lowercase_				):
              # These track the position within the cycle detection logic.
              __a       =    seed
              __a       =    seed

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

   SCREAMING_SNAKE_CASE__:List[str]									=			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""",
   )
   SCREAMING_SNAKE_CASE__:Any									=			parser.parse_args()

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







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowerCamelCase      							=   {
    'configuration_clipseg': [
        'CLIPSEG_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'CLIPSegConfig',
        'CLIPSegTextConfig',
        'CLIPSegVisionConfig',
    ],
    'processing_clipseg': ['CLIPSegProcessor'],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _lowerCamelCase      							=   [
           'CLIPSEG_PRETRAINED_MODEL_ARCHIVE_LIST',
           'CLIPSegModel',
           'CLIPSegPreTrainedModel',
           'CLIPSegTextModel',
           'CLIPSegVisionModel',
           'CLIPSegForImageSegmentation',
       ]

if TYPE_CHECKING:
       from .configuration_clipseg import (
           CLIPSEG_PRETRAINED_CONFIG_ARCHIVE_MAP,
           CLIPSegConfig,
           CLIPSegTextConfig,
           CLIPSegVisionConfig,
       )
       from .processing_clipseg import CLIPSegProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_clipseg import (
                  CLIPSEG_PRETRAINED_MODEL_ARCHIVE_LIST,
                  CLIPSegForImageSegmentation,
                  CLIPSegModel,
                  CLIPSegPreTrainedModel,
                  CLIPSegTextModel,
                  CLIPSegVisionModel,
              )

else:
       import sys

       _lowerCamelCase      							=   _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)

