

from __future__ import annotations

from math import gcd



def 			_A	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 2	,SCREAMING_SNAKE_CASE = 1	,SCREAMING_SNAKE_CASE = 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(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.
		UpperCAmelCase__:	int									= seed
		UpperCAmelCase__:	Any									= seed

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

					_lowerCAmelCase  :      int			 =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""",
					)
					_lowerCAmelCase  :      List[Any]			 =parser.parse_args()

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


def 			_A	(      SCREAMING_SNAKE_CASE      ):
	UpperCAmelCase__							,						UpperCAmelCase__:	int									= [], []
	while len(SCREAMING_SNAKE_CASE      ) > 1:
		UpperCAmelCase__							,						UpperCAmelCase__:	str									= min(SCREAMING_SNAKE_CASE      ), max(SCREAMING_SNAKE_CASE      )
		start.append(SCREAMING_SNAKE_CASE      )
		end.append(SCREAMING_SNAKE_CASE      )
		collection.remove(SCREAMING_SNAKE_CASE      )
		collection.remove(SCREAMING_SNAKE_CASE      )
	end.reverse()
	return start + collection + end


if __name__ == "__main__":
					_lowerCAmelCase  :      Union[str, Any]			 =input("""Enter numbers separated by a comma:\n""").strip()
					_lowerCAmelCase  :      Dict			 =[int(item) for item in user_input.split(""",""")]
					print(*merge_sort(unsorted), sep=""",""")