


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

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
 from .tokenization_pegasus import PegasusTokenizer
else:
 SCREAMING_SNAKE_CASE       :      Any												= None


SCREAMING_SNAKE_CASE       :      Union[str, Any]												= logging.get_logger(__name__)


SCREAMING_SNAKE_CASE       :      Union[str, Any]												= "▁"

SCREAMING_SNAKE_CASE       :      Union[str, Any]												= {"vocab_file": "spiece.model", "tokenizer_file": "tokenizer.json"}

SCREAMING_SNAKE_CASE       :      int												= {
    "vocab_file": {"google/pegasus-xsum": "https://huggingface.co/google/pegasus-xsum/resolve/main/spiece.model"},
    "tokenizer_file": {
        "google/pegasus-xsum": "https://huggingface.co/google/pegasus-xsum/resolve/main/tokenizer.json"
    },
}

SCREAMING_SNAKE_CASE       :      str												= {
    "google/pegasus-xsum": 512,
}






class _lowerCamelCase(						_a   ):
       lowercase_ :	Optional[Any]     =			VOCAB_FILES_NAMES
       lowercase_ :	Any     =			PRETRAINED_VOCAB_FILES_MAP
       lowercase_ :	List[Any]     =			PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
       lowercase_ :	List[Any]     =			PegasusTokenizer
       lowercase_ :	Optional[Any]     =			["""input_ids""", """attention_mask"""]
       def __init__(					self,      lowerCamelCase=None,      lowerCamelCase=None,      lowerCamelCase="<pad>",      lowerCamelCase="</s>",      lowerCamelCase="<unk>",      lowerCamelCase="<mask_2>",      lowerCamelCase="<mask_1>",      lowerCamelCase=None,      lowerCamelCase=1_03,      **lowerCamelCase,      )       ->   List[str]:




           """simple docstring"""

           _lowercase       :							str      		=		offset

           if additional_special_tokens is not None:
               if not isinstance(lowerCamelCase,      lowerCamelCase):
                   raise TypeError(
                       F'''additional_special_tokens should be of type {type(lowerCamelCase)}, but is'''
                       F''' {type(lowerCamelCase)}''')

               _lowercase       :							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(lowerCamelCase),      self.offset - 1)
               ]

               if len(set(lowerCamelCase)) != len(lowerCamelCase):
                   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       :							Any      		=		additional_special_tokens_extended
           else:
               _lowercase       :							Optional[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)]

           super().__init__(
               lowerCamelCase,      tokenizer_file=lowerCamelCase,      pad_token=lowerCamelCase,      eos_token=lowerCamelCase,      unk_token=lowerCamelCase,      mask_token=lowerCamelCase,      mask_token_sent=lowerCamelCase,      offset=lowerCamelCase,      additional_special_tokens=lowerCamelCase,      **lowerCamelCase,      )
           _lowercase       :							Optional[Any]      		=		vocab_file
           _lowercase       :							List[str]      		=		False if not self.vocab_file else True
       def 			UpperCamelCase     (					self,      lowerCamelCase)       ->   Any:




           """simple docstring"""

           _lowercase       :							str      		=		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

           if all_special_ids != set(range(len(self.additional_special_tokens) + 3)):
               raise ValueError(
                   'There should be 3 special tokens: mask_token, pad_token, and eos_token +'
                   F''' {len(self.additional_special_tokens)} additional_special_tokens, but got {all_special_ids}''')

           return [1 if x in all_special_ids else 0 for x in seq]
       def 			UpperCamelCase     (					self,      lowerCamelCase,      lowerCamelCase = None,      lowerCamelCase = False)       ->   List[int]:




           """simple docstring"""

           if already_has_special_tokens:
               return self._special_token_mask(lowerCamelCase)
           elif token_ids_a is None:
               return self._special_token_mask(lowerCamelCase) + [1]
           else:
               return self._special_token_mask(token_ids_a + token_ids_a) + [1]
       def 			UpperCamelCase     (					self,      lowerCamelCase,      lowerCamelCase=None)       ->   List[int]:




           """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 			UpperCamelCase     (					self,      lowerCamelCase,      lowerCamelCase = None)       ->   Tuple[str]:




           """simple docstring"""

           if not self.can_save_slow_tokenizer:
               raise ValueError(
                   'Your fast tokenizer does not have the necessary information to save the vocabulary for a slow '
                   'tokenizer.')

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

           if os.path.abspath(self.vocab_file) != os.path.abspath(lowerCamelCase):
               copyfile(self.vocab_file,      lowerCamelCase)

           return (out_vocab_file,)






from __future__ import annotations

from math import ceil, floor, sqrt



def 				UpperCamelCase_(      lowerCamelCase_ = 200_0000 )    ->						int:
    _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       :							Optional[int]      		=		(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
        _lowercase       :							List[str]      		=		floor(lowerCamelCase_ )
        _lowercase       :							Dict      		=		ceil(lowerCamelCase_ )
        _lowercase       :							List[str]      		=		triangle_numbers[b_floor]
        _lowercase       :							List[str]      		=		triangle_numbers[b_ceil]

        if abs(target - triangle_b_first_guess * triangle_a ) < abs(
            target - best_product ):
            _lowercase       :							Union[str, Any]      		=		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       :							Any      		=		triangle_b_second_guess * triangle_a
            _lowercase       :							Optional[Any]      		=		idx_a * b_ceil

    return area


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


