




from __future__ import annotations

from math import gcd

def lowercase    (  SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE = 2       ,    SCREAMING_SNAKE_CASE = 1       ,    SCREAMING_SNAKE_CASE = 3       ,    )			->							int | None:


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

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

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

									# 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``.
									SCREAMING_SNAKE_CASE_								=						gcd(hare - tortoise       ,    SCREAMING_SNAKE_CASE )

									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.
						SCREAMING_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__     :     List[str]		    =       parser.parse_args()

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






def lowercase    (  SCREAMING_SNAKE_CASE )			->							str:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						len(SCREAMING_SNAKE_CASE )
			while cur > 1:
						# Find the maximum number in arr
						SCREAMING_SNAKE_CASE_								=						arr.index(max(arr[0:cur] ) )
						# Reverse from 0 to mi
						SCREAMING_SNAKE_CASE_								=						arr[mi::-1] + arr[mi + 1 : len(SCREAMING_SNAKE_CASE )]
						# Reverse whole list
						SCREAMING_SNAKE_CASE_								=						arr[cur - 1 :: -1] + arr[cur : len(SCREAMING_SNAKE_CASE )]
						cur -= 1
			return arr


if __name__ == "__main__":
				SCREAMING_SNAKE_CASE__     :     List[str]		    =       input("Enter numbers separated by a comma:\n").strip()
				SCREAMING_SNAKE_CASE__     :     Optional[int]		    =       [int(item) for item in user_input.split(",")]
				print(pancake_sort(unsorted))
