'''simple docstring'''





from __future__ import annotations

from math import gcd





def       lowerCAmelCase_							(   snake_case_			:					int   ,       snake_case_			:					int = 2   ,       snake_case_			:					int = 1   ,       snake_case_			:					int = 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(snake_case_			:					int   ,       snake_case_			:					int   ,       snake_case_			:					int     ) -> int:
          return (pow(snake_case_   ,       2     ) + step) % modulus

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

          while True:
               # At each iteration, the tortoise moves one step and the hare moves two.
               UpperCAmelCase_			       =  rand_fn(snake_case_   ,       snake_case_   ,       snake_case_     )
               UpperCAmelCase_			       =  rand_fn(snake_case_   ,       snake_case_   ,       snake_case_     )
               UpperCAmelCase_			       =  rand_fn(snake_case_   ,       snake_case_   ,       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_			       =  gcd(hare - tortoise   ,       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_			       =  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_:	str    =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_:	Optional[int]    =parser.parse_args()

    SCREAMING_SNAKE_CASE_:	List[Any]    =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}")







import random

class    _lowercase				:

   @staticmethod
   def     UpperCamelCase					(				lowerCamelCase__	:    str       ) ->			tuple[list[int], list[int]]:
         """simple docstring"""





         A_							       =		[ord(lowerCamelCase__       ) for i in text]
         A_							       =		[]
         A_							       =		[]
         for i in plain:
               A_							       =		random.randint(1			,						3_0_0       )
               A_							       =		(i + k) * k
               cipher.append(lowerCamelCase__       )
               key.append(lowerCamelCase__       )
         return cipher, key





   @staticmethod
   def     UpperCamelCase					(				lowerCamelCase__	:    list[int]			,						lowerCamelCase__	:    list[int]       ) ->			str:
         """simple docstring"""





         A_							       =		[]
         for i in range(len(lowerCamelCase__       )       ):
               A_							       =		int((cipher[i] - (key[i]) ** 2) / key[i]       )
               plain.append(chr(lowerCamelCase__       )       )
         return "".join(lowerCamelCase__       )


if __name__ == "__main__":
      __lowercase      ,				__lowercase				      =						Onepad().encrypt("""Hello""")
      print(c, k)
      print(Onepad().decrypt(c, k))





