



from __future__ import annotations

from math import gcd

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

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

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

                  # 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``.
                  lowercase__     =  gcd(hare - tortoise						,  A__	)

                  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.
            lowercase__     =  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

       a__      :				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",
       )
       a__      :				Union[str, Any]   	=			parser.parse_args()

       a__      :				Union[str, Any]   	=			pollard_rho(args.num, attempts=args.attempts)
       if divisor is None:
              print(F'''{args.num} is probably prime''')
       else:
              a__      :				Any   	=			args.num // divisor
              print(F'''{args.num} = {divisor} * {quotient}''')





import argparse
import hashlib  # hashlib is only used inside the Test class
import struct



class       UpperCAmelCase__:

   '''simple docstring'''




   def __init__(						self  :			Optional[Any]			,				lowerCAmelCase  :			str)	->				Optional[int]:




         """simple docstring"""

         lowercase__     =  data
         lowercase__     =  [0X6_7_4_5_2_3_0_1, 0XE_F_C_D_A_B_8_9, 0X9_8_B_A_D_C_F_E, 0X1_0_3_2_5_4_7_6, 0XC_3_D_2_E_1_F_0]


   @staticmethod
   def 			UpperCAmelCase		(						lowerCAmelCase  :			Union[str, Any]			,				lowerCAmelCase  :			Optional[int])	->				str:




         """simple docstring"""

         return ((n << b) | (n >> (32 - b))) & 0XF_F_F_F_F_F_F_F


   def 			UpperCAmelCase		(						self  :			Dict)	->				Dict:




         """simple docstring"""

         lowercase__     =  B'\x80' + B'\x00' * (63 - (len(self.data) + 8) % 64)
         lowercase__     =  self.data + padding + struct.pack('>Q'			,				8 * len(self.data))
         return padded_data


   def 			UpperCAmelCase		(						self  :			int)	->				Tuple:




         """simple docstring"""

         return [
             self.padded_data[i : i + 64] for i in range(0			,				len(self.padded_data)			,				64)
         ]


   def 			UpperCAmelCase		(						self  :			Tuple			,				lowerCAmelCase  :			int)	->				List[Any]:




         """simple docstring"""

         lowercase__     =  list(struct.unpack('>16L'			,				lowerCAmelCase)) + [0] * 64
         for i in range(16			,				80):
               lowercase__     =  self.rotate((w[i - 3] ^ w[i - 8] ^ w[i - 14] ^ w[i - 16])			,				1)
         return w



   def 			UpperCAmelCase		(						self  :			str)	->				Dict:




         """simple docstring"""

         lowercase__     =  self.padding()
         lowercase__     =  self.split_blocks()
         for block in self.blocks:
               lowercase__     =  self.expand_block(lowerCAmelCase)
               lowercase__,	lowercase__,	lowercase__,	lowercase__,	lowercase__     =  self.h
               for i in range(0			,				80):
                     if 0 <= i < 20:
                           lowercase__     =  (b & c) | ((~b) & d)
                           lowercase__     =  0X5_A_8_2_7_9_9_9
                     elif 20 <= i < 40:
                           lowercase__     =  b ^ c ^ d
                           lowercase__     =  0X6_E_D_9_E_B_A_1
                     elif 40 <= i < 60:
                           lowercase__     =  (b & c) | (b & d) | (c & d)
                           lowercase__     =  0X8_F_1_B_B_C_D_C
                     elif 60 <= i < 80:
                           lowercase__     =  b ^ c ^ d
                           lowercase__     =  0XC_A_6_2_C_1_D_6
                     lowercase__,	lowercase__,	lowercase__,	lowercase__,	lowercase__     =  (
                         self.rotate(lowerCAmelCase			,				5) + f + e + k + expanded_block[i] & 0XF_F_F_F_F_F_F_F,
                         a,
                         self.rotate(lowerCAmelCase			,				30),
                         c,
                         d,
                     )
               lowercase__     =  (
                   self.h[0] + a & 0XF_F_F_F_F_F_F_F,
                   self.h[1] + b & 0XF_F_F_F_F_F_F_F,
                   self.h[2] + c & 0XF_F_F_F_F_F_F_F,
                   self.h[3] + d & 0XF_F_F_F_F_F_F_F,
                   self.h[4] + e & 0XF_F_F_F_F_F_F_F,
               )
         return ("{:08x}" * 5).format(*self.h)

def   _lowerCAmelCase   (						):
      lowercase__     =  B'Test String'
      assert SHAaHash(A__	).final_hash() == hashlib.shaa(A__	).hexdigest()  # noqa: S324

def   _lowerCAmelCase   (						):
      lowercase__     =  argparse.ArgumentParser(description='Process some strings or files'	)
      parser.add_argument(
          '--string'						,  dest='input_string'						,  default='Hello World!! Welcome to Cryptography'						,  help='Hash the string'						,  )
      parser.add_argument('--file'						,  dest='input_file'						,  help='Hash contents of a file'	)
      lowercase__     =  parser.parse_args()
      lowercase__     =  args.input_string
      # In any case hash input should be a bytestring
      if args.input_file:
            with open(args.input_file						,  'rb'	) as f:
                  lowercase__     =  f.read()
      else:
            lowercase__     =  bytes(A__						,  'utf-8'	)
      print(SHAaHash(A__	).final_hash()	)


if __name__ == "__main__":
       main()
       import doctest

       doctest.testmod()
