

import random







def  _A		(     snake_case					)      ->     bool:
   _lowercase      :				Dict      					=       num - 1
   _lowercase      :				List[str]      					=       0

   while s % 2 == 0:
      _lowercase      :				Any      					=       s // 2
      t += 1

   for _ in range(5					):
      _lowercase      :				List[str]      					=       random.randrange(2		,							num - 1					)
      _lowercase      :				Tuple      					=       pow(snake_case		,							snake_case		,							snake_case					)
      if v != 1:
         _lowercase      :				Any      					=       0
         while v != (num - 1):
            if i == t - 1:
               return False
            else:
               _lowercase      :				List[str]      					=       i + 1
               _lowercase      :				List[str]      					=       (v**2) % num
   return True







def  _A		(     snake_case					)      ->     bool:
   if num < 2:
      return False

   _lowercase      :				Optional[Any]      					=       [
       2,
       3,
       5,
       7,
       11,
       13,
       17,
       19,
       23,
       29,
       31,
       37,
       41,
       43,
       47,
       53,
       59,
       61,
       67,
       71,
       73,
       79,
       83,
       89,
       97,
       1_01,
       1_03,
       1_07,
       1_09,
       1_13,
       1_27,
       1_31,
       1_37,
       1_39,
       1_49,
       1_51,
       1_57,
       1_63,
       1_67,
       1_73,
       1_79,
       1_81,
       1_91,
       1_93,
       1_97,
       1_99,
       2_11,
       2_23,
       2_27,
       2_29,
       2_33,
       2_39,
       2_41,
       2_51,
       2_57,
       2_63,
       2_69,
       2_71,
       2_77,
       2_81,
       2_83,
       2_93,
       3_07,
       3_11,
       3_13,
       3_17,
       3_31,
       3_37,
       3_47,
       3_49,
       3_53,
       3_59,
       3_67,
       3_73,
       3_79,
       3_83,
       3_89,
       3_97,
       4_01,
       4_09,
       4_19,
       4_21,
       4_31,
       4_33,
       4_39,
       4_43,
       4_49,
       4_57,
       4_61,
       4_63,
       4_67,
       4_79,
       4_87,
       4_91,
       4_99,
       5_03,
       5_09,
       5_21,
       5_23,
       5_41,
       5_47,
       5_57,
       5_63,
       5_69,
       5_71,
       5_77,
       5_87,
       5_93,
       5_99,
       6_01,
       6_07,
       6_13,
       6_17,
       6_19,
       6_31,
       6_41,
       6_43,
       6_47,
       6_53,
       6_59,
       6_61,
       6_73,
       6_77,
       6_83,
       6_91,
       7_01,
       7_09,
       7_19,
       7_27,
       7_33,
       7_39,
       7_43,
       7_51,
       7_57,
       7_61,
       7_69,
       7_73,
       7_87,
       7_97,
       8_09,
       8_11,
       8_21,
       8_23,
       8_27,
       8_29,
       8_39,
       8_53,
       8_57,
       8_59,
       8_63,
       8_77,
       8_81,
       8_83,
       8_87,
       9_07,
       9_11,
       9_19,
       9_29,
       9_37,
       9_41,
       9_47,
       9_53,
       9_67,
       9_71,
       9_77,
       9_83,
       9_91,
       9_97,
   ]

   if num in low_primes:
      return True

   for prime in low_primes:
      if (num % prime) == 0:
         return False

   return rabin_miller(snake_case					)







def  _A		(     snake_case = 10_24					)      ->     int:
   while True:
      _lowercase      :				List[Any]      					=       random.randrange(2 ** (keysize - 1)		,							2 ** (keysize)					)
      if is_prime_low_num(snake_case					):
         return num


if __name__ == "__main__":
    _snake_case         =  generate_large_prime()
    print(('Prime number:', num))
    print(('is_prime_low_num:', is_prime_low_num(num)))









'''simple docstring'''
import os
from shutil import copyfile
from typing import Any, Dict, List, Optional, Tuple

import sentencepiece as spm

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


_snake_case         =  '▁'

_snake_case         =  {'vocab_file': 'spiece.model'}

_snake_case         =  {
    'vocab_file': {'google/pegasus-xsum': 'https://huggingface.co/google/pegasus-xsum/resolve/main/spiece.model'}
}

_snake_case         =  {
    'google/pegasus-xsum': 512,
}


_snake_case         =  logging.get_logger(__name__)


class        a__  (							lowerCamelCase_  ):
   _SCREAMING_SNAKE_CASE   :					str     	=							VOCAB_FILES_NAMES

   _SCREAMING_SNAKE_CASE   :					Tuple     	=							VOCAB_FILES_NAMES
   _SCREAMING_SNAKE_CASE   :					Any     	=							PRETRAINED_VOCAB_FILES_MAP
   _SCREAMING_SNAKE_CASE   :					Tuple     	=							PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
   _SCREAMING_SNAKE_CASE   :					Union[str, Any]     	=							['input_ids', 'attention_mask']


   def __init__(			self      ,    _UpperCamelCase      ,    _UpperCamelCase="<pad>"      ,    _UpperCamelCase="</s>"      ,    _UpperCamelCase="<unk>"      ,    _UpperCamelCase="<mask_2>"      ,    _UpperCamelCase="<mask_1>"      ,    _UpperCamelCase=None      ,    _UpperCamelCase=103      ,    _UpperCamelCase = None      ,    **_UpperCamelCase      ,    ):





      """simple docstring"""





      _lowercase      :				Tuple      					=       offset
      if additional_special_tokens is not None:
         if not isinstance(_UpperCamelCase      ,    _UpperCamelCase  ):
            raise TypeError(
                f'''additional_special_tokens should be of type {type(_UpperCamelCase  )}, but is'''
                f''' {type(_UpperCamelCase  )}'''  )

         _lowercase      :				Dict      					=       (
             ([mask_token_sent] + additional_special_tokens)
             if mask_token_sent not in additional_special_tokens and mask_token_sent is not None
             else additional_special_tokens
         )
         # fill additional tokens with ..., <unk_token_102> in case not all additional tokens are already taken
         additional_special_tokens_extended += [
             f'''<unk_{i}>''' for i in range(len(_UpperCamelCase  )      ,    self.offset - 1  )
         ]

         if len(set(_UpperCamelCase  )  ) != len(_UpperCamelCase  ):
            raise ValueError(
                "Please make sure that the provided additional_special_tokens do not contain an incorrectly"
                f''' shifted list of <unk_x> tokens. Found {additional_special_tokens_extended}.'''  )
         _lowercase      :				List[str]      					=       additional_special_tokens_extended
      else:
         _lowercase      :				Dict      					=       [mask_token_sent] if mask_token_sent is not None else []
         additional_special_tokens += [f'''<unk_{i}>''' for i in range(2      ,    self.offset  )]

      _lowercase      :				int      					=       {} if sp_model_kwargs is None else sp_model_kwargs

      super().__init__(
          eos_token=_UpperCamelCase      ,    unk_token=_UpperCamelCase      ,    mask_token=_UpperCamelCase      ,    pad_token=_UpperCamelCase      ,    mask_token_sent=_UpperCamelCase      ,    offset=_UpperCamelCase      ,    additional_special_tokens=_UpperCamelCase      ,    sp_model_kwargs=self.sp_model_kwargs      ,    **_UpperCamelCase      ,    )
      _lowercase      :				Union[str, Any]      					=       mask_token_sent
      _lowercase      :				str      					=       vocab_file
      _lowercase      :				Dict      					=       spm.SentencePieceProcessor(**self.sp_model_kwargs  )
      self.sp_model.Load(_UpperCamelCase  )

      # add special tokens to encoder dict
      _lowercase      :				Dict[int, str]      					=       {
          0: self.pad_token,
          1: self.eos_token,
      }

      if self.mask_token_sent is not None:
         self.encoder.update(
             {
                 2: self.mask_token_sent,
                 3: self.mask_token,
             }  )

      if self.offset > 0:
         # entries 2-104 are only used for pretraining and called <mask_1>, <mask_2>, unk_2, ...unk_102
         # mask_token_sent is already added to list -> so start at 1
         self.encoder.update({i + 3: additional_special_tokens[i] for i in range(1      ,    self.offset - 1  )}  )

      _lowercase      :				Dict[str, int]      					=       {v: k for k, v in self.encoder.items()}


   @property
   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      return len(self.sp_model  ) + self.offset


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      _lowercase      :				Tuple      					=       {self.convert_ids_to_tokens(_UpperCamelCase  ): i for i in range(self.vocab_size  )}
      vocab.update(self.added_tokens_encoder  )
      return vocab


   def __getstate__(			self  ):





      """simple docstring"""





      _lowercase      :				Optional[Any]      					=       self.__dict__.copy()
      _lowercase      :				Union[str, Any]      					=       None
      return state


   def __setstate__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				int      					=       d

      # for backward compatibility
      if not hasattr(self      ,    "sp_model_kwargs"  ):
         _lowercase      :				List[Any]      					=       {}

      _lowercase      :				Any      					=       spm.SentencePieceProcessor(**self.sp_model_kwargs  )
      self.sp_model.Load(self.vocab_file  )


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      return self.sp_model.encode(_UpperCamelCase      ,    out_type=_UpperCamelCase  )


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      if token in self.decoder:
         return self.decoder[token]
      elif token in self.added_tokens_decoder:
         return self.added_tokens_decoder[token]
      _lowercase      :				int      					=       self.sp_model.piece_to_id(_UpperCamelCase  )
      return sp_id + self.offset


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      if index in self.encoder:
         return self.encoder[index]
      elif index in self.added_tokens_encoder:
         return self.added_tokens_encoder[index]
      else:
         _lowercase      :				Any      					=       self.sp_model.IdToPiece(index - self.offset  )
      return token


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				Optional[int]      					=       []
      _lowercase      :				Optional[Any]      					=       ""
      for token in tokens:
         # make sure that special tokens are not decoded using sentencepiece model
         if token in self.all_special_tokens:
            out_string += self.sp_model.decode(_UpperCamelCase  ) + token
            _lowercase      :				Tuple      					=       []
         else:
            current_sub_tokens.append(_UpperCamelCase  )
      out_string += self.sp_model.decode(_UpperCamelCase  )
      return out_string.strip()


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase=False  ):





      """simple docstring"""





      return 1


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				int      					=       set(self.all_special_ids  )  # call it once instead of inside list comp
      all_special_ids.remove(self.unk_token_id  )  # <unk> is only sometimes special

      return [1 if x in all_special_ids else 0 for x in seq]


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    _UpperCamelCase = None      ,    _UpperCamelCase = False  ):





      """simple docstring"""





      if already_has_special_tokens:
         return self._special_token_mask(_UpperCamelCase  )
      elif token_ids_a is None:
         return self._special_token_mask(_UpperCamelCase  ) + [1]
      else:
         return self._special_token_mask(token_ids_a + token_ids_a  ) + [1]


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    _UpperCamelCase=None  ):





      """simple docstring"""





      if token_ids_a is None:
         return token_ids_a + [self.eos_token_id]
      # We don't expect to process pairs, but leave the pair logic for API consistency
      return token_ids_a + token_ids_a + [self.eos_token_id]






   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    _UpperCamelCase = None  ):





      """simple docstring"""





      if not os.path.isdir(_UpperCamelCase  ):
         logger.error(f'''Vocabulary path ({save_directory}) should be a directory'''  )
         return
      _lowercase      :				List[Any]      					=       os.path.join(
          _UpperCamelCase      ,    (filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["vocab_file"]  )

      if os.path.abspath(self.vocab_file  ) != os.path.abspath(_UpperCamelCase  ) and os.path.isfile(self.vocab_file  ):
         copyfile(self.vocab_file      ,    _UpperCamelCase  )
      elif not os.path.isfile(self.vocab_file  ):
         with open(_UpperCamelCase      ,    "wb"  ) as fi:
            _lowercase      :				Optional[int]      					=       self.sp_model.serialized_model_proto()
            fi.write(_UpperCamelCase  )

      return (out_vocab_file,)






