






'''simple docstring'''
from __future__ import annotations

from math import gcd





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

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

            while True:
                  # At each iteration, the tortoise moves one step and the hare moves two.
                  SCREAMING_SNAKE_CASE__       :			List[str]													=rand_fn(UpperCamelCase__,		UpperCamelCase__,		UpperCamelCase__							)
                  SCREAMING_SNAKE_CASE__       :			Optional[int]													=rand_fn(UpperCamelCase__,		UpperCamelCase__,		UpperCamelCase__							)
                  SCREAMING_SNAKE_CASE__       :			Optional[int]													=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``.
                  SCREAMING_SNAKE_CASE__       :			List[str]													=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.
            SCREAMING_SNAKE_CASE__       :			List[Any]													=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_					=	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_					=	parser.parse_args()

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







'''simple docstring'''
import json
import os
from typing import Dict, List, Optional, Tuple

import regex as re

from ...tokenization_utils import PreTrainedTokenizer
from ...utils import logging


a_					=	logging.get_logger(__name__)


a_					=	{
    'vocab_file': 'vocab.json',
    'merges_file': 'merges.txt',
    'tokenizer_config_file': 'tokenizer_config.json',
}

a_					=	{
    'vocab_file': {
        'facebook/blenderbot_small-90M': 'https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/vocab.json'
    },
    'merges_file': {
        'facebook/blenderbot_small-90M': 'https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/merges.txt'
    },
    'tokenizer_config_file': {
        'facebook/blenderbot_small-90M': (
            'https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/tokenizer_config.json'
        )
    },
}

a_					=	{'facebook/blenderbot_small-90M': 5_1_2}





def 	_a(					UpperCamelCase__			:  Dict							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=set()
      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=word[0]
      for char in word[1:]:
            pairs.add((prev_char, char)							)
            SCREAMING_SNAKE_CASE__       :			Optional[Any]													=char

      SCREAMING_SNAKE_CASE__       :			Any													=set(UpperCamelCase__							)
      return pairs







class        __SCREAMING_SNAKE_CASE (     lowerCamelCase			):
 snake_case_												=							VOCAB_FILES_NAMES
 snake_case_												=							PRETRAINED_VOCAB_FILES_MAP
 snake_case_												=							PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 snake_case_												=							["""input_ids""", """attention_mask"""]




 def __init__( self		:							Tuple   , __lowercase		:							int   , __lowercase		:							Optional[int]   , __lowercase		:							List[str]="__start__"   , __lowercase		:							Union[str, Any]="__end__"   , __lowercase		:							str="__unk__"   , __lowercase		:							Union[str, Any]="__null__"   , **__lowercase		:							List[str]   , )		->  Optional[int]:
       super().__init__(unk_token=__lowercase   , bos_token=__lowercase   , eos_token=__lowercase   , pad_token=__lowercase   , **__lowercase )

       with open(__lowercase   , encoding='''utf-8''' ) as vocab_handle:
             SCREAMING_SNAKE_CASE__       :			Any													=json.load(__lowercase )
       SCREAMING_SNAKE_CASE__       :			Dict													={v: k for k, v in self.encoder.items()}
       with open(__lowercase   , encoding='''utf-8''' ) as merges_handle:
             SCREAMING_SNAKE_CASE__       :			int													=merges_handle.read().split('''\n''' )[1:-1]
       SCREAMING_SNAKE_CASE__       :			List[Any]													=[tuple(merge.split() ) for merge in merges]
       SCREAMING_SNAKE_CASE__       :			int													=dict(zip(__lowercase   , range(len(__lowercase ) ) ) )
       SCREAMING_SNAKE_CASE__       :			Dict													={}




 @property
 def        __magic_name__		( self		:							Any )		->  int:
       return len(self.encoder )




 def        __magic_name__		( self		:							Tuple )		->  Dict:
       return dict(self.encoder   , **self.added_tokens_encoder )




 def        __magic_name__		( self		:							Optional[Any]   , __lowercase		:							str )		->  str:
       if token in self.cache:
             return self.cache[token]
       SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=re.sub('''([.,!?()])'''   , r''' \1'''   , __lowercase )
       SCREAMING_SNAKE_CASE__       :			int													=re.sub('''(\')'''   , r''' \1 '''   , __lowercase )
       SCREAMING_SNAKE_CASE__       :			Dict													=re.sub(r'''\s{2,}'''   , ''' '''   , __lowercase )
       if "\n" in token:
             SCREAMING_SNAKE_CASE__       :			List[str]													=token.replace('''\n'''   , ''' __newln__''' )

       SCREAMING_SNAKE_CASE__       :			Dict													=token.split(''' ''' )
       SCREAMING_SNAKE_CASE__       :			Dict													=[]
       for token in tokens:
             if not len(__lowercase ):
                   continue

             SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=token.lower()
             SCREAMING_SNAKE_CASE__       :			Optional[Any]													=tuple(__lowercase )
             SCREAMING_SNAKE_CASE__       :			Optional[int]													=tuple(list(word[:-1] ) + [word[-1] + '''</w>'''] )
             SCREAMING_SNAKE_CASE__       :			Optional[Any]													=get_pairs(__lowercase )

             if not pairs:
                   words.append(__lowercase )
                   continue

             while True:
                   SCREAMING_SNAKE_CASE__       :			int													=min(__lowercase   , key=lambda __lowercase : self.bpe_ranks.get(__lowercase   , float('''inf''' ) ) )
                   if bigram not in self.bpe_ranks:
                         break
                   SCREAMING_SNAKE_CASE__						,		SCREAMING_SNAKE_CASE__       :			Any													=bigram
                   SCREAMING_SNAKE_CASE__       :			List[Any]													=[]
                   SCREAMING_SNAKE_CASE__       :			Tuple													=0

                   while i < len(__lowercase ):
                         try:
                               SCREAMING_SNAKE_CASE__       :			Optional[Any]													=word.index(__lowercase   , __lowercase )
                               new_word.extend(word[i:j] )
                               SCREAMING_SNAKE_CASE__       :			Optional[int]													=j
                         except ValueError:
                               new_word.extend(word[i:] )
                               break

                         if word[i] == first and i < len(__lowercase ) - 1 and word[i + 1] == second:
                               new_word.append(first + second )
                               i += 2
                         else:
                               new_word.append(word[i] )
                               i += 1
                   SCREAMING_SNAKE_CASE__       :			int													=tuple(__lowercase )
                   SCREAMING_SNAKE_CASE__       :			int													=new_word
                   if len(__lowercase ) == 1:
                         break
                   else:
                         SCREAMING_SNAKE_CASE__       :			Any													=get_pairs(__lowercase )
             SCREAMING_SNAKE_CASE__       :			Optional[int]													='''@@ '''.join(__lowercase )
             SCREAMING_SNAKE_CASE__       :			List[Any]													=word[:-4]

             SCREAMING_SNAKE_CASE__       :			str													=word
             words.append(__lowercase )
       return " ".join(__lowercase )




 def        __magic_name__		( self		:							str   , __lowercase		:							str )		->  List[str]:
       SCREAMING_SNAKE_CASE__       :			Dict													=[]

       SCREAMING_SNAKE_CASE__       :			List[Any]													=re.findall(r'''\S+\n?'''   , __lowercase )

       for token in words:
             split_tokens.extend(list(self.bpe(__lowercase ).split(''' ''' ) ) )
       return split_tokens




 def        __magic_name__		( self		:							List[Any]   , __lowercase		:							str )		->  int:
       SCREAMING_SNAKE_CASE__       :			int													=token.lower()
       return self.encoder.get(__lowercase   , self.encoder.get(self.unk_token ) )




 def        __magic_name__		( self		:							int   , __lowercase		:							int )		->  str:
       return self.decoder.get(__lowercase   , self.unk_token )




 def        __magic_name__		( self		:							List[Any]   , __lowercase		:							List[str] )		->  str:
       SCREAMING_SNAKE_CASE__       :			Optional[int]													=''' '''.join(__lowercase ).replace('''@@ '''   , '''''' ).strip()
       return out_string




 def        __magic_name__		( self		:							Tuple   , __lowercase		:							str   , __lowercase		:							Optional[str] = None )		->  Tuple[str]:
       if not os.path.isdir(__lowercase ):
             logger.error(F"Vocabulary path ({save_directory}) should be a directory" )
             return
       SCREAMING_SNAKE_CASE__       :			str													=os.path.join(
           __lowercase   , (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''vocab_file'''] )
       SCREAMING_SNAKE_CASE__       :			int													=os.path.join(
           __lowercase   , (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''merges_file'''] )

       with open(__lowercase   , '''w'''   , encoding='''utf-8''' ) as f:
             f.write(json.dumps(self.encoder   , indent=2   , sort_keys=__lowercase   , ensure_ascii=__lowercase ) + '''\n''' )

       SCREAMING_SNAKE_CASE__       :			List[str]													=0
       with open(__lowercase   , '''w'''   , encoding='''utf-8''' ) as writer:
             writer.write('''#version: 0.2\n''' )
             for bpe_tokens, token_index in sorted(self.bpe_ranks.items()   , key=lambda __lowercase : kv[1] ):
                   if index != token_index:
                         logger.warning(
                             F"Saving vocabulary to {merge_file}: BPE merge indices are not consecutive."
                             ''' Please check that the tokenizer is not corrupted!''' )
                         SCREAMING_SNAKE_CASE__       :			Any													=token_index
                   writer.write(''' '''.join(__lowercase ) + '''\n''' )
                   index += 1

       return vocab_file, merge_file