'''simple docstring'''




from __future__ import annotations

from math import gcd






def __lowerCAmelCase			(							UpperCamelCase__    ,  UpperCamelCase__ = 2    ,  UpperCamelCase__ = 1    ,  UpperCamelCase__ = 3    ,  )     ->   int | None:
    # 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(UpperCamelCase__    ,  UpperCamelCase__    ,  UpperCamelCase__    ) -> int:
        return (pow(UpperCamelCase__    ,  2    ) + step) % modulus

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

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

            # 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``.
            __lowerCamelCase          =  gcd(hare - tortoise    ,  UpperCamelCase__    )

            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.
        __lowerCamelCase          =  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

  __UpperCAmelCase												=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",
  )
  __UpperCAmelCase												=parser.parse_args()

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

'''simple docstring'''




__UpperCAmelCase												="ABCDEFGHIJKLMNOPQRSTUVWXYZ"






def __lowerCAmelCase			(							)     ->   None:
    __lowerCamelCase          =  input('''Enter message: '''    )
    __lowerCamelCase          =  input('''Enter key [alphanumeric]: '''    )
    __lowerCamelCase          =  input('''Encrypt/Decrypt [e/d]: '''    )

    if mode.lower().startswith('''e'''    ):
        __lowerCamelCase          =  '''encrypt'''
        __lowerCamelCase          =  encrypt_message(UpperCamelCase__    ,  UpperCamelCase__    )
    elif mode.lower().startswith('''d'''    ):
        __lowerCamelCase          =  '''decrypt'''
        __lowerCamelCase          =  decrypt_message(UpperCamelCase__    ,  UpperCamelCase__    )

    print(f"""\n{mode.title()}ed message:"""    )
    print(UpperCamelCase__    )






def __lowerCAmelCase			(							UpperCamelCase__    ,  UpperCamelCase__    )     ->   str:
    return translate_message(UpperCamelCase__    ,  UpperCamelCase__    ,  '''encrypt'''    )






def __lowerCAmelCase			(							UpperCamelCase__    ,  UpperCamelCase__    )     ->   str:
    return translate_message(UpperCamelCase__    ,  UpperCamelCase__    ,  '''decrypt'''    )






def __lowerCAmelCase			(							UpperCamelCase__    ,  UpperCamelCase__    ,  UpperCamelCase__    )     ->   str:
    __lowerCamelCase          =  []
    __lowerCamelCase          =  0
    __lowerCamelCase          =  key.upper()

    for symbol in message:
        __lowerCamelCase          =  LETTERS.find(symbol.upper()    )
        if num != -1:
            if mode == "encrypt":
                num += LETTERS.find(key[key_index]    )
            elif mode == "decrypt":
                num -= LETTERS.find(key[key_index]    )

            num %= len(UpperCamelCase__    )

            if symbol.isupper():
                translated.append(LETTERS[num]    )
            elif symbol.islower():
                translated.append(LETTERS[num].lower()    )

            key_index += 1
            if key_index == len(UpperCamelCase__    ):
                __lowerCamelCase          =  0
        else:
            translated.append(UpperCamelCase__    )
    return "".join(UpperCamelCase__    )


if __name__ == "__main__":
  main()
