





'''simple docstring'''


from __future__ import annotations

from math import gcd


def 	__a(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int = 2		,       SCREAMING_SNAKE_CASE_  :					int = 1		,       SCREAMING_SNAKE_CASE_  :					int = 3		,       ):



    '''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(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int    ) -> 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

       _SCREAMING_SNAKE_CASE	 =							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	 =							parser.parse_args()

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









'''simple docstring'''


from queue import Queue
from typing import TYPE_CHECKING, Optional


if TYPE_CHECKING:
       from ..models.auto import AutoTokenizer

class    lowerCAmelCase_		:




 def 							_snake_case   (	self			,     _lowerCAmelCase		)    ->							Tuple:
     raise NotImplementedError()





 def 							_snake_case   (	self		)    ->							Optional[int]:
     raise NotImplementedError()







class    lowerCAmelCase_		(		__magic_name__		):




 def __init__(	self			,     _lowerCAmelCase			,     _lowerCAmelCase = False			,     **_lowerCAmelCase		)    ->							str:
     _lowerCAmelCase				=      tokenizer
     _lowerCAmelCase				=      skip_prompt
     _lowerCAmelCase				=      decode_kwargs

     # variables used in the streaming process
     _lowerCAmelCase				=      []
     _lowerCAmelCase				=      0
     _lowerCAmelCase				=      True




 def 							_snake_case   (	self			,     _lowerCAmelCase		)    ->							List[Any]:
     if len(value.shape		) > 1 and value.shape[0] > 1:
         raise ValueError("TextStreamer only supports batch size 1"		)
     elif len(value.shape		) > 1:
         _lowerCAmelCase				=      value[0]

     if self.skip_prompt and self.next_tokens_are_prompt:
         _lowerCAmelCase				=      False
         return

     # Add the new token to the cache and decodes the entire thing.
     self.token_cache.extend(value.tolist()		)
     _lowerCAmelCase				=      self.tokenizer.decode(self.token_cache			,     **self.decode_kwargs		)

     # After the symbol for a new line, we flush the cache.
     if text.endswith("\n"		):
         _lowerCAmelCase				=      text[self.print_len :]
         _lowerCAmelCase				=      []
         _lowerCAmelCase				=      0
     # If the last token is a CJK character, we print the characters.
     elif len(_lowerCAmelCase		) > 0 and self._is_chinese_char(ord(text[-1]		)		):
         _lowerCAmelCase				=      text[self.print_len :]
         self.print_len += len(_lowerCAmelCase		)
     # Otherwise, prints until the last space char (simple heuristic to avoid printing incomplete words,
     # which may change with the subsequent token -- there are probably smarter ways to do this!)
     else:
         _lowerCAmelCase				=      text[self.print_len : text.rfind(" "		) + 1]
         self.print_len += len(_lowerCAmelCase		)

     self.on_finalized_text(_lowerCAmelCase		)




 def 							_snake_case   (	self		)    ->							Union[str, Any]:
     # Flush the cache, if it exists
     if len(self.token_cache		) > 0:
         _lowerCAmelCase				=      self.tokenizer.decode(self.token_cache			,     **self.decode_kwargs		)
         _lowerCAmelCase				=      text[self.print_len :]
         _lowerCAmelCase				=      []
         _lowerCAmelCase				=      0
     else:
         _lowerCAmelCase				=      ""

     _lowerCAmelCase				=      True
     self.on_finalized_text(_lowerCAmelCase			,     stream_end=_lowerCAmelCase		)




 def 							_snake_case   (	self			,     _lowerCAmelCase			,     _lowerCAmelCase = False		)    ->							List[Any]:
     print(_lowerCAmelCase			,     flush=_lowerCAmelCase			,     end="" if not stream_end else None		)





 def 							_snake_case   (	self			,     _lowerCAmelCase		)    ->							Tuple:
     # This defines a "chinese character" as anything in the CJK Unicode block:
     #   https://en.wikipedia.org/wiki/CJK_Unified_Ideographs_(Unicode_block)
     #
     # Note that the CJK Unicode block is NOT all Japanese and Korean characters,
     # despite its name. The modern Korean Hangul alphabet is a different block,
     # as is Japanese Hiragana and Katakana. Those alphabets are used to write
     # space-separated words, so they are not treated specially and handled
     # like the all of the other languages.
     if (
         (cp >= 0X4E_00 and cp <= 0X9F_FF)
         or (cp >= 0X34_00 and cp <= 0X4D_BF)  #
         or (cp >= 0X2_00_00 and cp <= 0X2_A6_DF)  #
         or (cp >= 0X2_A7_00 and cp <= 0X2_B7_3F)  #
         or (cp >= 0X2_B7_40 and cp <= 0X2_B8_1F)  #
         or (cp >= 0X2_B8_20 and cp <= 0X2_CE_AF)  #
         or (cp >= 0XF9_00 and cp <= 0XFA_FF)
         or (cp >= 0X2_F8_00 and cp <= 0X2_FA_1F)  #
     ):  #
         return True

     return False







class    lowerCAmelCase_		(		__magic_name__		):




 def __init__(	self			,     _lowerCAmelCase			,     _lowerCAmelCase = False			,     _lowerCAmelCase = None			,     **_lowerCAmelCase		)    ->							Dict:
     super().__init__(_lowerCAmelCase			,     _lowerCAmelCase			,     **_lowerCAmelCase		)
     _lowerCAmelCase				=      Queue()
     _lowerCAmelCase				=      None
     _lowerCAmelCase				=      timeout




 def 							_snake_case   (	self			,     _lowerCAmelCase			,     _lowerCAmelCase = False		)    ->							Any:
     self.text_queue.put(_lowerCAmelCase			,     timeout=self.timeout		)
     if stream_end:
         self.text_queue.put(self.stop_signal			,     timeout=self.timeout		)




 def __iter__(	self		)    ->							int:
     return self





 def 							_snake_case   (	self		)    ->							Tuple:
     _lowerCAmelCase				=      self.text_queue.get(timeout=self.timeout		)
     if value == self.stop_signal:
         raise StopIteration()
     else:
         return value


