"""simple docstring"""







from __future__ import annotations

import math
import random


def   __lowerCAmelCase(		__UpperCAmelCase  ,__UpperCAmelCase  ,__UpperCAmelCase      ):






	"""simple docstring"""





	_lowercase			:     Optional[int]      					=				d * e - 1
	_lowercase			:     int      					=				0
	_lowercase			:     Union[str, Any]      					=				0
	while p == 0:
		_lowercase			:     int      					=				random.randint(2  ,n - 1      )
		_lowercase			:     str      					=				k
		while True:
			if t % 2 == 0:
				_lowercase			:     List[Any]      					=				t // 2
				_lowercase			:     int      					=				(g**t) % n
				_lowercase			:     Tuple      					=				math.gcd(x - 1  ,__UpperCAmelCase      )
				if x > 1 and y > 1:
					_lowercase			:     List[str]      					=				y
					_lowercase			:     str      					=				n // y
					break  # find the correct factors
			else:
				break  # t is not divisible by 2, break and choose another g
	return sorted([p, q]      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()




"""simple docstring"""







from __future__ import annotations

import re


def   __lowerCAmelCase(		__UpperCAmelCase      ):






	"""simple docstring"""





	def alphanum_key(__UpperCAmelCase      ):
		return [int(__UpperCAmelCase      ) if s.isdigit() else s.lower() for s in re.split('([0-9]+)'  ,__UpperCAmelCase      )]

	return sorted(__UpperCAmelCase  ,key=__UpperCAmelCase      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



