





from __future__ import annotations

from math import gcd






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

   for _ in range(lowerCamelCase   ):
      # These track the position within the cycle detection logic.
      a__	:						str      		=  seed
      a__	:						Optional[int]      		=  seed

      while True:
         # At each iteration, the tortoise moves one step and the hare moves two.
         a__	:						Union[str, Any]      		=  rand_fn(lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )
         a__	:						Optional[Any]      		=  rand_fn(lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )
         a__	:						Tuple      		=  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``.
         a__	:						Optional[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.
      a__	:						Optional[Any]      		=  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[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""",
  )
  SCREAMING_SNAKE_CASE__       :			Optional[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__       :			Optional[int]			      =						args.num // divisor
    print(f'{args.num} = {divisor} * {quotient}')








import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import CONFIG_MAPPING


SCREAMING_SNAKE_CASE__       :			int			      =						logging.get_logger(__name__)







class   __lowerCAmelCase			(					_UpperCamelCase  ):
   _UpperCamelCase :						int     		=				"""upernet"""





   def __init__( self					,			snake_case=None					,			snake_case=512					,			snake_case=0.02					,			snake_case=[1, 2, 3, 6]					,			snake_case=True					,			snake_case=0.4					,			snake_case=384					,			snake_case=256					,			snake_case=1					,			snake_case=False					,			snake_case=255					,			**snake_case					,			)				->  Optional[Any]:
      """simple docstring"""





      super().__init__(**snake_case      )

      if backbone_config is None:
         logger.info("`backbone_config` is `None`. Initializing the config with the default `ResNet` backbone."      )
         a__	:						List[str]      		=  CONFIG_MAPPING["resnet"](out_features=["stage1", "stage2", "stage3", "stage4"]      )
      elif isinstance(snake_case					,			snake_case      ):
         a__	:						Optional[int]      		=  backbone_config.get("model_type"      )
         a__	:						str      		=  CONFIG_MAPPING[backbone_model_type]
         a__	:						str      		=  config_class.from_dict(snake_case      )

      a__	:						int      		=  backbone_config
      a__	:						Optional[Any]      		=  hidden_size
      a__	:						Optional[Any]      		=  initializer_range
      a__	:						Tuple      		=  pool_scales
      a__	:						Optional[Any]      		=  use_auxiliary_head
      a__	:						Optional[Any]      		=  auxiliary_loss_weight
      a__	:						Dict      		=  auxiliary_in_channels
      a__	:						Optional[int]      		=  auxiliary_channels
      a__	:						Any      		=  auxiliary_num_convs
      a__	:						Any      		=  auxiliary_concat_input
      a__	:						int      		=  loss_ignore_index





   def 	_snake_case ( self      )				->  str:
      """simple docstring"""





      a__	:						Tuple      		=  copy.deepcopy(self.__dict__      )
      a__	:						Optional[Any]      		=  self.backbone_config.to_dict()
      a__	:						List[Any]      		=  self.__class__.model_type
      return output

