



"""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


_lowerCAmelCase       :List[str]	=   '▁'

_lowerCAmelCase       :List[str]	=   {'vocab_file': 'spiece.model'}

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

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


_lowerCAmelCase       :Optional[int]	=   logging.get_logger(__name__)
class 				_UpperCAmelCase				(					lowerCAmelCase__ ):





     '''simple docstring'''



     a__   							=VOCAB_FILES_NAMES

     a__   							=VOCAB_FILES_NAMES
     a__   							=PRETRAINED_VOCAB_FILES_MAP
     a__   							=PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
     a__   							=['''input_ids''', '''attention_mask''']





     def __init__(   self			,      A			,      A="<pad>"			,      A="</s>"			,      A="<unk>"			,      A="<mask_2>"			,      A="<mask_1>"			,      A=None			,      A=1_0_3			,      A = None			,      **A			,      )				->   Tuple:
         _UpperCAmelCase				:    List[str]											=       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						)}'						)

             _UpperCAmelCase				:    List[Any]											=       (
                 ([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}.'						)
             _UpperCAmelCase				:    int											=       additional_special_tokens_extended
         else:
             _UpperCAmelCase				:    Union[str, Any]											=       [mask_token_sent] if mask_token_sent is not None else []
             additional_special_tokens += [f'<unk_{i}>' for i in range(2			,      self.offset						)]

         _UpperCAmelCase				:    Optional[Any]											=       {} 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			,      )
         _UpperCAmelCase				:    str											=       mask_token_sent
         _UpperCAmelCase				:    Dict											=       vocab_file
         _UpperCAmelCase				:    int											=       spm.SentencePieceProcessor(**self.sp_model_kwargs						)
         self.sp_model.Load(__UpperCAmelCase						)

         # add special tokens to encoder dict
         _UpperCAmelCase				:    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						)}						)

         _UpperCAmelCase				:    str											=       {v: k for k, v in self.encoder.items()}





     @property
     def 					__lowerCAmelCase      (   self						)				->   int:
         return len(self.sp_model						) + self.offset





     def 					__lowerCAmelCase      (   self						)				->   List[str]:
         _UpperCAmelCase				:    Optional[int]											=       {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						)				->   Optional[int]:
         _UpperCAmelCase				:    List[Any]											=       self.__dict__.copy()
         _UpperCAmelCase				:    List[Any]											=       None
         return state





     def __setstate__(   self			,      A						)				->   str:
         _UpperCAmelCase				:    Union[str, Any]											=       d

         # for backward compatibility
         if not hasattr(self			,      '''sp_model_kwargs'''						):
             _UpperCAmelCase				:    Optional[int]											=       {}

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





     def 					__lowerCAmelCase      (   self			,      A						)				->   List[Any]:
         return self.sp_model.encode(__UpperCAmelCase			,      out_type=__UpperCAmelCase						)





     def 					__lowerCAmelCase      (   self			,      A						)				->   int:
         if token in self.decoder:
             return self.decoder[token]
         elif token in self.added_tokens_decoder:
             return self.added_tokens_decoder[token]
         _UpperCAmelCase				:    Any											=       self.sp_model.piece_to_id(__UpperCAmelCase						)
         return sp_id + self.offset





     def 					__lowerCAmelCase      (   self			,      A						)				->   Optional[int]:
         if index in self.encoder:
             return self.encoder[index]
         elif index in self.added_tokens_encoder:
             return self.added_tokens_encoder[index]
         else:
             _UpperCAmelCase				:    Dict											=       self.sp_model.IdToPiece(index - self.offset						)
         return token





     def 					__lowerCAmelCase      (   self			,      A						)				->   Optional[Any]:
         _UpperCAmelCase				:    Optional[Any]											=       []
         _UpperCAmelCase				:    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
                 _UpperCAmelCase				:    str											=       []
             else:
                 current_sub_tokens.append(__UpperCAmelCase						)
         out_string += self.sp_model.decode(__UpperCAmelCase						)
         return out_string.strip()





     def 					__lowerCAmelCase      (   self			,      A=False						)				->   Optional[int]:
         return 1





     def 					__lowerCAmelCase      (   self			,      A						)				->   Union[str, Any]:
         _UpperCAmelCase				:    Optional[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			,      A			,      A = None			,      A = False						)				->   Optional[int]:
         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			,      A			,      A=None						)				->   List[str]:
         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			,      A			,      A = None						)				->   Optional[int]:
         if not os.path.isdir(__UpperCAmelCase						):
             logger.error(f'Vocabulary path ({save_directory}) should be a directory'						)
             return
         _UpperCAmelCase				:    Union[str, 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:
                 _UpperCAmelCase				:    int											=       self.sp_model.serialized_model_proto()
                 fi.write(__UpperCAmelCase						)

         return (out_vocab_file,)







from __future__ import annotations

from math import ceil, floor, sqrt





def 		a__      (		_UpperCamelCase      :			int = 2_00_00_00				):
   __lowerCamelCase    				=     [0]
   __lowerCamelCase    				=     42

   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
   __lowerCamelCase    				=     0
   # the area corresponding to the grid that gives the product closest to target
   __lowerCamelCase    				=     0
   # an estimate of b, using the quadratic formula
   __lowerCamelCase    				=     42
   # the largest integer less than b_estimate
   __lowerCamelCase    				=     42
   # the largest integer less than b_estimate
   __lowerCamelCase    				=     42
   # the triangle number corresponding to b_floor
   __lowerCamelCase    				=     42
   # the triangle number corresponding to b_ceil
   __lowerCamelCase    				=     42

   for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,1				):
      __lowerCamelCase    				=     (-1 + sqrt(1 + 8 * target / triangle_a				)) / 2
      __lowerCamelCase    				=     floor(_UpperCamelCase				)
      __lowerCamelCase    				=     ceil(_UpperCamelCase				)
      __lowerCamelCase    				=     triangle_numbers[b_floor]
      __lowerCamelCase    				=     triangle_numbers[b_ceil]

      if abs(target - triangle_b_first_guess * triangle_a				) < abs(
          target - best_product				):
         __lowerCamelCase    				=     triangle_b_first_guess * triangle_a
         __lowerCamelCase    				=     idx_a * b_floor

      if abs(target - triangle_b_second_guess * triangle_a				) < abs(
          target - best_product				):
         __lowerCamelCase    				=     triangle_b_second_guess * triangle_a
         __lowerCamelCase    				=     idx_a * b_ceil

   return area


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






