


'''simple docstring'''






from __future__ import annotations

from math import gcd


def       _snake_case     (  A				,					A = 2				,					A = 1				,					A = 3				,					)		->					int:
							# 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(A				,					2 ) + step) % modulus

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

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

		__UpperCAmelCase     :   Union[str, 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''',
		)
		__UpperCAmelCase     :   Dict					       =							parser.parse_args()

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



'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


__UpperCAmelCase					       =							{
    '''configuration_poolformer''': [
        '''POOLFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''PoolFormerConfig''',
        '''PoolFormerOnnxConfig''',
    ]
}

try:
		if not is_vision_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCAmelCase					       =							['''PoolFormerFeatureExtractor''']
		__UpperCAmelCase					       =							['''PoolFormerImageProcessor''']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCAmelCase					       =							[
		    '''POOLFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''PoolFormerForImageClassification''',
		    '''PoolFormerModel''',
		    '''PoolFormerPreTrainedModel''',
		]


if TYPE_CHECKING:
		from .configuration_poolformer import (
		    POOLFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
		    PoolFormerConfig,
		    PoolFormerOnnxConfig,
		)

		try:
				if not is_vision_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .feature_extraction_poolformer import PoolFormerFeatureExtractor
				from .image_processing_poolformer import PoolFormerImageProcessor

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_poolformer import (
				    POOLFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
				    PoolFormerForImageClassification,
				    PoolFormerModel,
				    PoolFormerPreTrainedModel,
				)


else:
		import sys

		__UpperCAmelCase					       =							_LazyModule(__name__, globals()['''__file__'''], _import_structure)