


from __future__ import annotations

from math import gcd




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

       for _ in range(snake_case					):
              # These track the position within the cycle detection logic.
              lowercase__:       List[str]        =       seed
              lowercase__:       str        =       seed

              while True:
                     # At each iteration, the tortoise moves one step and the hare moves two.
                     lowercase__:       List[Any]        =       rand_fn(snake_case      ,							snake_case      ,							snake_case					)
                     lowercase__:       Optional[Any]        =       rand_fn(snake_case      ,							snake_case      ,							snake_case					)
                     lowercase__:       Any        =       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``.
                     lowercase__:       List[str]        =       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.
              lowercase__:       Tuple        =       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

 __lowerCAmelCase			=							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''',
 )
 __lowerCAmelCase			=							parser.parse_args()

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






import os
from typing import Dict, List, Union

import tensorflow as tf
from keras_nlp.tokenizers import BytePairTokenizer
from tensorflow_text import pad_model_inputs

from .tokenization_gpta import GPTaTokenizer





class   __a      (   tf.keras.layers.Layer				):
 def __init__(       self    ,			lowerCAmelCase__    ,			lowerCAmelCase__    ,			lowerCAmelCase__ = None    ,			lowerCAmelCase__ = None			) ->    int:




        '''simple docstring'''
        super().__init__()
        lowercase__:       Union[str, Any]        =       pad_token_id
        lowercase__:       List[str]        =       max_length
        lowercase__:       int        =       vocab
        lowercase__:       List[Any]        =       merges
        lowercase__:       str        =       BytePairTokenizer(lowerCAmelCase__    ,			lowerCAmelCase__    ,			sequence_length=lowerCAmelCase__			)
 @classmethod
 def 		SCREAMING_SNAKE_CASE__       (       cls    ,			lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			) ->    Any:




        '''simple docstring'''
        lowercase__:       Tuple        =       [' '.join(lowerCAmelCase__			) for m in tokenizer.bpe_ranks.keys()]
        lowercase__:       List[Any]        =       tokenizer.get_vocab()
        return cls(lowerCAmelCase__    ,			lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			)
 @classmethod
 def 		SCREAMING_SNAKE_CASE__       (       cls    ,			lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			) ->    List[Any]:




        '''simple docstring'''
        lowercase__:       int        =       GPTaTokenizer.from_pretrained(lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			)
        return cls.from_tokenizer(lowerCAmelCase__    ,			*lowerCAmelCase__    ,			**lowerCAmelCase__			)
 @classmethod
 def 		SCREAMING_SNAKE_CASE__       (       cls    ,			lowerCAmelCase__			) ->    Dict:




        '''simple docstring'''
        return cls(**lowerCAmelCase__			)
 def 		SCREAMING_SNAKE_CASE__       (       self			) ->    List[Any]:




        '''simple docstring'''
        return {
            "vocab": self.vocab,
            "merges": self.merges,
            "max_length": self.max_length,
            "pad_token_id": self.pad_token_id,
        }
 def 		SCREAMING_SNAKE_CASE__       (       self    ,			lowerCAmelCase__    ,			lowerCAmelCase__ = None			) ->    Optional[Any]:




        '''simple docstring'''
        lowercase__:       Optional[Any]        =       self.tf_tokenizer(lowerCAmelCase__			)
        lowercase__:       List[Any]        =       tf.ones_like(lowerCAmelCase__			)

        if self.pad_token_id is not None:
               # pad the tokens up to max length
               lowercase__:       int        =       max_length if max_length is not None else self.max_length

               if max_length is not None:
                      lowercase__      ,						lowercase__:       List[Any]        =       pad_model_inputs(
                          lowerCAmelCase__    ,			max_seq_length=lowerCAmelCase__    ,			pad_value=self.pad_token_id			)

        return {"attention_mask": attention_mask, "input_ids": input_ids}


