from __future__ import annotations

from math import gcd

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

    for _ in range(_lowerCamelCase):
        # These track the position within the cycle detection logic.
        lowercase__ :   Optional[int]    					=				seed
        lowercase__ :   int    					=				seed

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

            # 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__ :   Any    					=				gcd(hare - tortoise		,	_lowerCamelCase)

            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__ :   Dict    					=				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}")




import json
from typing import TYPE_CHECKING, List, Optional, Tuple

from tokenizers import pre_tokenizers

from ...tokenization_utils_base import BatchEncoding
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging


if TYPE_CHECKING:
    from transformers.pipelines.conversational import Conversation


__lowercase							 =					logging.get_logger(__name__)

__lowercase							 =					{'''tokenizer_file''': '''tokenizer.json'''}

__lowercase							 =					{
    '''tokenizer_file''': {
        '''bigscience/tokenizer''': '''https://huggingface.co/bigscience/tokenizer/blob/main/tokenizer.json''',
        '''bigscience/bloom-560m''': '''https://huggingface.co/bigscience/bloom-560m/blob/main/tokenizer.json''',
        '''bigscience/bloom-1b1''': '''https://huggingface.co/bigscience/bloom-1b1/blob/main/tokenizer.json''',
        '''bigscience/bloom-1b7''': '''https://huggingface.co/bigscience/bloom-1b7/blob/main/tokenizer.json''',
        '''bigscience/bloom-3b''': '''https://huggingface.co/bigscience/bloom-3b/blob/main/tokenizer.json''',
        '''bigscience/bloom-7b1''': '''https://huggingface.co/bigscience/bloom-7b1/blob/main/tokenizer.json''',
        '''bigscience/bloom''': '''https://huggingface.co/bigscience/bloom/blob/main/tokenizer.json''',
    },
}


class 	lowerCamelCase_     (   UpperCAmelCase_ ):






    '''simple docstring'''






    a__	:						int						=      VOCAB_FILES_NAMES
    a__	:						Tuple						=      PRETRAINED_VOCAB_FILES_MAP
    a__	:						List[str]						=      ["""input_ids""", """attention_mask"""]
    a__	:						int						=      None







    def __init__(	self , __lowercase=None , __lowercase=None , __lowercase=None , __lowercase="<unk>" , __lowercase="<s>" , __lowercase="</s>" , __lowercase="<pad>" , __lowercase=False , __lowercase=False , **__lowercase , )       ->	List[str]:
        super().__init__(
            __lowercase , __lowercase , tokenizer_file=__lowercase , unk_token=__lowercase , bos_token=__lowercase , eos_token=__lowercase , pad_token=__lowercase , add_prefix_space=__lowercase , clean_up_tokenization_spaces=__lowercase , **__lowercase , )
        __UpperCamelCase     :int			  =		json.loads(self.backend_tokenizer.pre_tokenizer.__getstate__())
        if pre_tok_state.get('''add_prefix_space''' , __lowercase) != add_prefix_space:
            __UpperCamelCase     :Any			  =		getattr(__lowercase , pre_tok_state.pop('''type'''))
            __UpperCamelCase     :str			  =		add_prefix_space
            __UpperCamelCase     :List[str]			  =		pre_tok_class(**__lowercase)

        __UpperCamelCase     :Tuple			  =		add_prefix_space







    def 			UpperCamelCase__   (	self , *__lowercase , **__lowercase)       ->	BatchEncoding:
        __UpperCamelCase     :Tuple			  =		kwargs.get('''is_split_into_words''' , __lowercase)
        if not (self.add_prefix_space or not is_split_into_words):
            raise Exception(
                f"""You need to instantiate {self.__class__.__name__} with add_prefix_space=True to use it with"""
                ''' pretokenized inputs.''')

        return super()._batch_encode_plus(*__lowercase , **__lowercase)







    def 			UpperCamelCase__   (	self , *__lowercase , **__lowercase)       ->	BatchEncoding:
        __UpperCamelCase     :List[str]			  =		kwargs.get('''is_split_into_words''' , __lowercase)

        if not (self.add_prefix_space or not is_split_into_words):
            raise Exception(
                f"""You need to instantiate {self.__class__.__name__} with add_prefix_space=True to use it with"""
                ''' pretokenized inputs.''')

        return super()._encode_plus(*__lowercase , **__lowercase)







    def 			UpperCamelCase__   (	self , __lowercase , __lowercase = None)       ->	Tuple[str]:
        __UpperCamelCase     :Optional[Any]			  =		self._tokenizer.model.save(__lowercase , name=__lowercase)
        return tuple(__lowercase)







    def 			UpperCamelCase__   (	self , __lowercase)       ->	List[int]:
        __UpperCamelCase     :str			  =		[]
        for is_user, text in conversation.iter_texts():
            input_ids.extend(self.encode(__lowercase , add_special_tokens=__lowercase) + [self.eos_token_id])

        if len(__lowercase) > self.model_max_length:
            __UpperCamelCase     :Any			  =		input_ids[-self.model_max_length :]
        return input_ids





