from __future__ import annotations

from math import ceil, floor, sqrt






def  snake_case(    __magic_name__ = 2_00_00_00   )			->							int:





     '''simple docstring'''


     lowercase :       list[int]       =			[0]
     lowercase :       int

     for idx in range(1			,		ceil(sqrt(target * 2   ) * 1.1   )   ):
          triangle_numbers.append(triangle_numbers[-1] + idx   )

     # we want this to be as close as possible to target
     lowercase :       int       =			0
     # the area corresponding to the grid that gives the product closest to target
     lowercase :       int       =			0
     # an estimate of b, using the quadratic formula
     lowercase :       float
     # the largest integer less than b_estimate
     lowercase :       int
     # the largest integer less than b_estimate
     lowercase :       int
     # the triangle number corresponding to b_floor
     lowercase :       int
     # the triangle number corresponding to b_ceil
     lowercase :       int

     for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,		1   ):
          lowercase :       Dict       =			(-1 + sqrt(1 + 8 * target / triangle_a   )) / 2
          lowercase :       int       =			floor(__magic_name__   )
          lowercase :       Union[str, Any]       =			ceil(__magic_name__   )
          lowercase :       Any       =			triangle_numbers[b_floor]
          lowercase :       Any       =			triangle_numbers[b_ceil]

          if abs(target - triangle_b_first_guess * triangle_a   ) < abs(
              target - best_product   ):
               lowercase :       Optional[int]       =			triangle_b_first_guess * triangle_a
               lowercase :       Union[str, Any]       =			idx_a * b_floor

          if abs(target - triangle_b_second_guess * triangle_a   ) < abs(
              target - best_product   ):
               lowercase :       Dict       =			triangle_b_second_guess * triangle_a
               lowercase :       Any       =			idx_a * b_ceil

     return area


if __name__ == "__main__":
 print(f'''{solution() = }''')





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

import sentencepiece as spm

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import logging


lowerCAmelCase_						=			logging.get_logger(__name__)

lowerCAmelCase_						=			{'vocab_file': 'sentencepiece.bpe.model'}

lowerCAmelCase_						=			{
    'vocab_file': {
        'moussaKam/mbarthez': 'https://huggingface.co/moussaKam/mbarthez/resolve/main/sentencepiece.bpe.model',
        'moussaKam/barthez': 'https://huggingface.co/moussaKam/barthez/resolve/main/sentencepiece.bpe.model',
        'moussaKam/barthez-orangesum-title': (
            'https://huggingface.co/moussaKam/barthez-orangesum-title/resolve/main/sentencepiece.bpe.model'
        ),
    },
}

lowerCAmelCase_						=			{
    'moussaKam/mbarthez': 10_24,
    'moussaKam/barthez': 10_24,
    'moussaKam/barthez-orangesum-title': 10_24,
}

lowerCAmelCase_						=			'▁'
class 						_A (  _lowerCamelCase				):
  _UpperCamelCase       :      Optional[Any]			=      VOCAB_FILES_NAMES
  _UpperCamelCase       :      Union[str, Any]			=      PRETRAINED_VOCAB_FILES_MAP
  _UpperCamelCase       :      Optional[Any]			=      PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  _UpperCamelCase       :      List[Any]			=      ['''input_ids''', '''attention_mask''']






  def __init__(  self		:     Any				,						_A		:     Optional[int]				,						_A		:     List[str]="<s>"				,						_A		:     Tuple="</s>"				,						_A		:     Dict="</s>"				,						_A		:     Dict="<s>"				,						_A		:     List[str]="<unk>"				,						_A		:     str="<pad>"				,						_A		:     Any="<mask>"				,						_A		:     Optional[Dict[str, Any]] = None				,						**_A		:     Union[str, Any]				,						)		->   None:






       """simple docstring"""







       lowercase :       List[str]       =			AddedToken(_A				,						lstrip=_A				,						rstrip=_A				) if isinstance(_A				,						_A				) else mask_token

       lowercase :       List[Any]       =			{} if sp_model_kwargs is None else sp_model_kwargs

       super().__init__(
           bos_token=_A				,						eos_token=_A				,						unk_token=_A				,						sep_token=_A				,						cls_token=_A				,						pad_token=_A				,						mask_token=_A				,						sp_model_kwargs=self.sp_model_kwargs				,						**_A				,						)

       lowercase :       Any       =			vocab_file
       lowercase :       Any       =			spm.SentencePieceProcessor(**self.sp_model_kwargs				)
       self.sp_model.Load(str(_A				)				)

       lowercase :       Optional[Any]       =			{'''<s>''': 0, '''<pad>''': 1, '''</s>''': 2, '''<unk>''': 3}

       lowercase :       Tuple       =			len(self.sp_model				) - 1
       lowercase :       Any       =			{v: k for k, v in self.fairseq_tokens_to_ids.items()}






  def  __a      (  self		:     Tuple				,						_A		:     List[int]				,						_A		:     Optional[List[int]] = None				)		->   List[int]:






       """simple docstring"""







       if token_ids_a is None:
            return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
       lowercase :       Any       =			[self.cls_token_id]
       lowercase :       int       =			[self.sep_token_id]
       return cls + token_ids_a + sep + sep + token_ids_a + sep






  def  __a      (  self		:     Optional[int]				,						_A		:     List[int]				,						_A		:     Optional[List[int]] = None				,						_A		:     bool = False				)		->   List[int]:






       """simple docstring"""







       if already_has_special_tokens:
            return super().get_special_tokens_mask(
                token_ids_a=_A				,						token_ids_a=_A				,						already_has_special_tokens=_A				)

       if token_ids_a is None:
            return [1] + ([0] * len(_A				)) + [1]
       return [1] + ([0] * len(_A				)) + [1, 1] + ([0] * len(_A				)) + [1]






  def  __a      (  self		:     Optional[int]				,						_A		:     List[int]				,						_A		:     Optional[List[int]] = None				)		->   List[int]:






       """simple docstring"""







       lowercase :       List[str]       =			[self.sep_token_id]
       lowercase :       List[str]       =			[self.cls_token_id]

       if token_ids_a is None:
            return len(cls + token_ids_a + sep				) * [0]
       return len(cls + token_ids_a + sep + sep + token_ids_a + sep				) * [0]






  @property
  def  __a      (  self		:     List[Any]				)		->   Optional[Any]:






       """simple docstring"""







       return len(self.sp_model				)






  def  __a      (  self		:     List[Any]				)		->   int:






       """simple docstring"""







       lowercase :       int       =			{self.convert_ids_to_tokens(_A				): i for i in range(self.vocab_size				)}
       vocab.update(self.added_tokens_encoder				)
       return vocab






  def  __a      (  self		:     Union[str, Any]				,						_A		:     str				)		->   List[str]:






       """simple docstring"""







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






  def  __a      (  self		:     Optional[int]				,						_A		:     str				)		->   Dict:






       """simple docstring"""







       if token in self.fairseq_tokens_to_ids:
            return self.fairseq_tokens_to_ids[token]
       lowercase :       Optional[int]       =			self.sp_model.PieceToId(_A				)

       return spm_id if spm_id else self.unk_token_id






  def  __a      (  self		:     Any				,						_A		:     List[str]				)		->   List[str]:






       """simple docstring"""







       if index in self.fairseq_ids_to_tokens:
            return self.fairseq_ids_to_tokens[index]
       return self.sp_model.IdToPiece(_A				)






  def  __a      (  self		:     Any				,						_A		:     Tuple				)		->   Tuple:






       """simple docstring"""







       lowercase :       Dict       =			[]
       lowercase :       Any       =			''''''
       lowercase :       str       =			False
       for token in tokens:
            # make sure that special tokens are not decoded using sentencepiece model
            if token in self.all_special_tokens:
                 if not prev_is_special:
                      out_string += " "
                 out_string += self.sp_model.decode(_A				) + token
                 lowercase :       int       =			True
                 lowercase :       Optional[Any]       =			[]
            else:
                 current_sub_tokens.append(_A				)
                 lowercase :       List[str]       =			False
       out_string += self.sp_model.decode(_A				)
       return out_string.strip()






  def __getstate__(  self		:     int				)		->   Optional[Any]:






       """simple docstring"""







       lowercase :       str       =			self.__dict__.copy()
       lowercase :       Any       =			None
       return state






  def __setstate__(  self		:     Optional[int]				,						_A		:     Tuple				)		->   str:






       """simple docstring"""







       lowercase :       List[str]       =			d

       # for backward compatibility
       if not hasattr(self				,						'''sp_model_kwargs'''				):
            lowercase :       Union[str, Any]       =			{}

       lowercase :       List[Any]       =			spm.SentencePieceProcessor(**self.sp_model_kwargs				)
       self.sp_model.Load(self.vocab_file				)






  def  __a      (  self		:     str				,						_A		:     str				,						_A		:     Optional[str] = None				)		->   Tuple[str]:






       """simple docstring"""







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

       if os.path.abspath(self.vocab_file				) != os.path.abspath(_A				) and os.path.isfile(self.vocab_file				):
            copyfile(self.vocab_file				,						_A				)
       elif not os.path.isfile(self.vocab_file				):
            with open(_A				,						'''wb'''				) as fi:
                 lowercase :       Optional[Any]       =			self.sp_model.serialized_model_proto()
                 fi.write(_A				)

       return (out_vocab_file,)