
'''simple docstring'''





from __future__ import annotations

from math import gcd

def      A (       A_							:					int    ,							A_							:					int = 2    ,							A_							:					int = 1    ,							A_							:					int = 3    ,							):




						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_							:					int    ,							A_							:					int    ,							A_							:					int       ) -> int:
												return (pow(__a    ,							2       ) + step) % modulus

						for _ in range(__a       ):
												# These track the position within the cycle detection logic.
												snake_case       :     Optional[Any] =    seed
												snake_case       :     List[Any] =    seed

												while True:
																		# At each iteration, the tortoise moves one step and the hare moves two.
																		snake_case       :     Tuple =    rand_fn(__a    ,							__a    ,							__a       )
																		snake_case       :     List[Any] =    rand_fn(__a    ,							__a    ,							__a       )
																		snake_case       :     Dict =    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``.
																		snake_case       :     Optional[int] =    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.
												snake_case       :     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

						UpperCAmelCase    					=   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    					=   parser.parse_args()

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



'''simple docstring'''





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


UpperCAmelCase    					=   {
    "configuration_swiftformer": [
        "SWIFTFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "SwiftFormerConfig",
        "SwiftFormerOnnxConfig",
    ]
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						UpperCAmelCase    					=   [
						    "SWIFTFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "SwiftFormerForImageClassification",
						    "SwiftFormerModel",
						    "SwiftFormerPreTrainedModel",
						]

if TYPE_CHECKING:
						from .configuration_swiftformer import (
						    SWIFTFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
						    SwiftFormerConfig,
						    SwiftFormerOnnxConfig,
						)

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_swiftformer import (
												    SWIFTFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
												    SwiftFormerForImageClassification,
												    SwiftFormerModel,
												    SwiftFormerPreTrainedModel,
												)

else:
						import sys

						UpperCAmelCase    					=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

