




'''simple docstring'''





from __future__ import annotations

from math import gcd


def 	UpperCamelCase_(      snake_case				:			int				,							snake_case				:			int = 2				,							snake_case				:			int = 1				,							snake_case				:			int = 3				,							):

							'''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(snake_case				:			int				,							snake_case				:			int				,							snake_case				:			int	) -> int:
														return (pow(A__				,							2	) + step) % modulus

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

														while True:
																					# At each iteration, the tortoise moves one step and the hare moves two.
																					snake_case_         = rand_fn(A__				,							A__				,							A__	)
																					snake_case_         = rand_fn(A__				,							A__				,							A__	)
																					snake_case_         = 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_         = 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_         = 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				:  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				:  Tuple 						=					parser.parse_args()

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







def 	a (     A__      :  int	)       -> bool:





      """simple docstring"""



      return sum(i for i in range(1 ,  number // 2 + 1	) if number % i == 0	) == number


if __name__ == "__main__":
  print('Program to check whether a number is a Perfect number or not...')
  lowercase_   							=  int(input('Enter number: ').strip())
  print(f"{number} is {'' if perfect(number) else 'not '}a Perfect Number.")


