



"""simple docstring"""




from math import isqrt, loga

def 						__snake_case						(						SCREAMING_SNAKE_CASE__     :						int    )  ->       list[int]:





     '''simple docstring'''

     _UpperCAmelCase      :     Union[str, Any]        =   [True] * max_number
     for i in range(2						,  isqrt(max_number - 1    ) + 1    ):
          if is_prime[i]:
               for j in range(i**2						,  SCREAMING_SNAKE_CASE__						,  SCREAMING_SNAKE_CASE__    ):
                    _UpperCAmelCase      :     List[str]        =   False

     return [i for i in range(2						,  SCREAMING_SNAKE_CASE__    ) if is_prime[i]]

def 						__snake_case						(						SCREAMING_SNAKE_CASE__     :						int = 800_800						,  SCREAMING_SNAKE_CASE__     :						int = 800_800    )  ->       int:





     '''simple docstring'''

     _UpperCAmelCase      :     Tuple        =   degree * loga(SCREAMING_SNAKE_CASE__    )
     _UpperCAmelCase      :     List[str]        =   int(SCREAMING_SNAKE_CASE__    )
     _UpperCAmelCase      :     Any        =   calculate_prime_numbers(SCREAMING_SNAKE_CASE__    )

     _UpperCAmelCase      :     Optional[Any]        =   0
     _UpperCAmelCase      :     Union[str, Any]        =   0
     _UpperCAmelCase      :     Optional[Any]        =   len(SCREAMING_SNAKE_CASE__    ) - 1
     while left < right:
          while (
              prime_numbers[right] * loga(prime_numbers[left]    )
              + prime_numbers[left] * loga(prime_numbers[right]    )
              > upper_bound
          ):
               right -= 1
          hybrid_integers_count += right - left
          left += 1

     return hybrid_integers_count


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





"""simple docstring"""




import json
import os
from functools import lru_cache
from typing import List, Optional, Tuple

import regex as re

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


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


_lowerCAmelCase    : Dict							=							{"vocab_file": "vocab.json", "merges_file": "merges.txt"}

_lowerCAmelCase    : Tuple							=							{
    "vocab_file": {
        "allenai/longformer-base-4096": "https://huggingface.co/allenai/longformer-base-4096/resolve/main/vocab.json",
        "allenai/longformer-large-4096": (
            "https://huggingface.co/allenai/longformer-large-4096/resolve/main/vocab.json"
        ),
        "allenai/longformer-large-4096-finetuned-triviaqa": (
            "https://huggingface.co/allenai/longformer-large-4096-finetuned-triviaqa/resolve/main/vocab.json"
        ),
        "allenai/longformer-base-4096-extra.pos.embd.only": (
            "https://huggingface.co/allenai/longformer-base-4096-extra.pos.embd.only/resolve/main/vocab.json"
        ),
        "allenai/longformer-large-4096-extra.pos.embd.only": (
            "https://huggingface.co/allenai/longformer-large-4096-extra.pos.embd.only/resolve/main/vocab.json"
        ),
    },
    "merges_file": {
        "allenai/longformer-base-4096": "https://huggingface.co/allenai/longformer-base-4096/resolve/main/merges.txt",
        "allenai/longformer-large-4096": (
            "https://huggingface.co/allenai/longformer-large-4096/resolve/main/merges.txt"
        ),
        "allenai/longformer-large-4096-finetuned-triviaqa": (
            "https://huggingface.co/allenai/longformer-large-4096-finetuned-triviaqa/resolve/main/merges.txt"
        ),
        "allenai/longformer-base-4096-extra.pos.embd.only": (
            "https://huggingface.co/allenai/longformer-base-4096-extra.pos.embd.only/resolve/main/merges.txt"
        ),
        "allenai/longformer-large-4096-extra.pos.embd.only": (
            "https://huggingface.co/allenai/longformer-large-4096-extra.pos.embd.only/resolve/main/merges.txt"
        ),
    },
}

_lowerCAmelCase    : str							=							{
    "allenai/longformer-base-4096": 40_96,
    "allenai/longformer-large-4096": 40_96,
    "allenai/longformer-large-4096-finetuned-triviaqa": 40_96,
    "allenai/longformer-base-4096-extra.pos.embd.only": 40_96,
    "allenai/longformer-large-4096-extra.pos.embd.only": 40_96,
}

@lru_cache()
# Copied from transformers.models.roberta.tokenization_roberta.bytes_to_unicode
def 						__snake_case						(				)  ->       List[Any]:





     '''simple docstring'''

     _UpperCAmelCase      :     str        =   (
         list(range(ord("!"    )						,  ord("~"    ) + 1    )    ) + list(range(ord("¡"    )						,  ord("¬"    ) + 1    )    ) + list(range(ord("®"    )						,  ord("ÿ"    ) + 1    )    )
     )
     _UpperCAmelCase      :     Any        =   bs[:]
     _UpperCAmelCase      :     Tuple        =   0
     for b in range(2**8    ):
          if b not in bs:
               bs.append(SCREAMING_SNAKE_CASE__    )
               cs.append(2**8 + n    )
               n += 1
     _UpperCAmelCase      :     Union[str, Any]        =   [chr(SCREAMING_SNAKE_CASE__    ) for n in cs]
     return dict(zip(SCREAMING_SNAKE_CASE__						,  SCREAMING_SNAKE_CASE__    )    )

def 						__snake_case						(				SCREAMING_SNAKE_CASE__     :						Optional[Any]    )  ->       int:





     '''simple docstring'''

     _UpperCAmelCase      :     int        =   set()
     _UpperCAmelCase      :     int        =   word[0]
     for char in word[1:]:
          pairs.add((prev_char, char)    )
          _UpperCAmelCase      :     Optional[int]        =   char
     return pairs






class      UpperCAmelCase_  (    _UpperCamelCase						):
      __SCREAMING_SNAKE_CASE						:       List[str]								=			VOCAB_FILES_NAMES
      __SCREAMING_SNAKE_CASE						:       List[str]								=			PRETRAINED_VOCAB_FILES_MAP
      __SCREAMING_SNAKE_CASE						:       str								=			PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
      __SCREAMING_SNAKE_CASE						:       Union[str, Any]								=			['input_ids', 'attention_mask']



      def __init__(					self					:     Optional[Any]					,     A					:     int					,     A					:     Any					,     A					:     List[str]="replace"					,     A					:     List[Any]="<s>"					,     A					:     int="</s>"					,     A					:     Union[str, Any]="</s>"					,     A					:     Tuple="<s>"					,     A					:     str="<unk>"					,     A					:     Dict="<pad>"					,     A					:     Optional[Any]="<mask>"					,     A					:     Tuple=False					,     **A					:     Dict					,     ):
           _UpperCAmelCase      :     Tuple        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else bos_token
           _UpperCAmelCase      :     int        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else eos_token
           _UpperCAmelCase      :     int        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else sep_token
           _UpperCAmelCase      :     Dict        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else cls_token
           _UpperCAmelCase      :     Optional[int]        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else unk_token
           _UpperCAmelCase      :     Dict        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else pad_token

           # Mask token behave like a normal word, i.e. include the space before it
           _UpperCAmelCase      :     Dict        =   AddedToken(A					,     lstrip=A					,     rstrip=A						) if isinstance(A					,     A						) else mask_token

           super().__init__(
               errors=A					,     bos_token=A					,     eos_token=A					,     unk_token=A					,     sep_token=A					,     cls_token=A					,     pad_token=A					,     mask_token=A					,     add_prefix_space=A					,     **A					,     )

           with open(A					,     encoding="utf-8"						) as vocab_handle:
                _UpperCAmelCase      :     Union[str, Any]        =   json.load(A						)
           _UpperCAmelCase      :     List[str]        =   {v: k for k, v in self.encoder.items()}
           _UpperCAmelCase      :     Dict        =   errors  # how to handle errors in decoding
           _UpperCAmelCase      :     List[str]        =   bytes_to_unicode()
           _UpperCAmelCase      :     Dict        =   {v: k for k, v in self.byte_encoder.items()}
           with open(A					,     encoding="utf-8"						) as merges_handle:
                _UpperCAmelCase      :     Union[str, Any]        =   merges_handle.read().split("\n"						)[1:-1]
           _UpperCAmelCase      :     Union[str, Any]        =   [tuple(merge.split()						) for merge in bpe_merges]
           _UpperCAmelCase      :     List[str]        =   dict(zip(A					,     range(len(A						)						)						)						)
           _UpperCAmelCase      :     Tuple        =   {}
           _UpperCAmelCase      :     Optional[Any]        =   add_prefix_space

           # Should have added re.IGNORECASE so BPE merges can happen for capitalized versions of contractions
           _UpperCAmelCase      :     Optional[int]        =   re.compile(R"'s|'t|'re|'ve|'m|'ll|'d| ?\p{L}+| ?\p{N}+| ?[^\s\p{L}\p{N}]+|\s+(?!\S)|\s+"						)



      @property
      def 						snake_case_ (					self					:     Optional[Any]						):
           return len(self.encoder						)



      def 						snake_case_ (					self					:     List[str]						):
           return dict(self.encoder					,     **self.added_tokens_encoder						)



      def 						snake_case_ (					self					:     Tuple					,     A					:     Union[str, Any]						):
           if token in self.cache:
                return self.cache[token]
           _UpperCAmelCase      :     Optional[int]        =   tuple(A						)
           _UpperCAmelCase      :     Optional[Any]        =   get_pairs(A						)

           if not pairs:
                return token

           while True:
                _UpperCAmelCase      :     Optional[int]        =   min(A					,     key=lambda A						: self.bpe_ranks.get(A					,     float("inf"						)						)						)
                if bigram not in self.bpe_ranks:
                     break
                _UpperCAmelCase    ,	_UpperCAmelCase      :     str        =   bigram
                _UpperCAmelCase      :     Dict        =   []
                _UpperCAmelCase      :     Union[str, Any]        =   0
                while i < len(A						):
                     try:
                          _UpperCAmelCase      :     int        =   word.index(A					,     A						)
                     except ValueError:
                          new_word.extend(word[i:]						)
                          break
                     else:
                          new_word.extend(word[i:j]						)
                          _UpperCAmelCase      :     Dict        =   j

                     if word[i] == first and i < len(A						) - 1 and word[i + 1] == second:
                          new_word.append(first + second						)
                          i += 2
                     else:
                          new_word.append(word[i]						)
                          i += 1
                _UpperCAmelCase      :     Optional[Any]        =   tuple(A						)
                _UpperCAmelCase      :     Dict        =   new_word
                if len(A						) == 1:
                     break
                else:
                     _UpperCAmelCase      :     Optional[int]        =   get_pairs(A						)
           _UpperCAmelCase      :     Any        =   " ".join(A						)
           _UpperCAmelCase      :     int        =   word
           return word



      def 						snake_case_ (					self					:     Optional[int]					,     A					:     List[str]						):
           _UpperCAmelCase      :     str        =   []
           for token in re.findall(self.pat					,     A						):
                _UpperCAmelCase      :     Optional[Any]        =   "".join(
                    self.byte_encoder[b] for b in token.encode("utf-8"						)						)  # Maps all our bytes to unicode strings, avoiding control tokens of the BPE (spaces in our case)
                bpe_tokens.extend(bpe_token for bpe_token in self.bpe(A						).split(" "						)						)
           return bpe_tokens



      def 						snake_case_ (					self					:     Optional[int]					,     A					:     Union[str, Any]						):
           return self.encoder.get(A					,     self.encoder.get(self.unk_token						)						)



      def 						snake_case_ (					self					:     Union[str, Any]					,     A					:     List[str]						):
           return self.decoder.get(A						)



      def 						snake_case_ (					self					:     Dict					,     A					:     int						):
           _UpperCAmelCase      :     Tuple        =   "".join(A						)
           _UpperCAmelCase      :     Dict        =   bytearray([self.byte_decoder[c] for c in text]						).decode("utf-8"					,     errors=self.errors						)
           return text



      def 						snake_case_ (					self					:     int					,     A					:     str					,     A					:     Optional[str] = None						):
           if not os.path.isdir(A						):
                logger.error(f'Vocabulary path ({save_directory}) should be a directory'						)
                return
           _UpperCAmelCase      :     List[Any]        =   os.path.join(
               A					,     (filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["vocab_file"]						)
           _UpperCAmelCase      :     Any        =   os.path.join(
               A					,     (filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["merges_file"]						)

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

           _UpperCAmelCase      :     Optional[Any]        =   0
           with open(A					,     "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 A						: 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!"						)
                          _UpperCAmelCase      :     Any        =   token_index
                     writer.write(" ".join(A						) + "\n"						)
                     index += 1

           return vocab_file, merge_file



      def 						snake_case_ (					self					:     int					,     A					:     List[int]					,     A					:     Optional[List[int]] = None						):
           if token_ids_a is None:
                return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
           _UpperCAmelCase      :     List[Any]        =   [self.cls_token_id]
           _UpperCAmelCase      :     List[Any]        =   [self.sep_token_id]
           return cls + token_ids_a + sep + sep + token_ids_a + sep



      def 						snake_case_ (					self					:     Optional[Any]					,     A					:     List[int]					,     A					:     Optional[List[int]] = None					,     A					:     bool = False						):
           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 						snake_case_ (					self					:     str					,     A					:     List[int]					,     A					:     Optional[List[int]] = None						):
           _UpperCAmelCase      :     Optional[Any]        =   [self.sep_token_id]
           _UpperCAmelCase      :     Any        =   [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]



      def 						snake_case_ (					self					:     str					,     A					:     List[str]					,     A					:     List[str]=False					,     **A					:     List[str]						):
           _UpperCAmelCase      :     Optional[Any]        =   kwargs.pop("add_prefix_space"					,     self.add_prefix_space						)
           if (is_split_into_words or add_prefix_space) and (len(A						) > 0 and not text[0].isspace()):
                _UpperCAmelCase      :     List[Any]        =   " " + text
           return (text, kwargs)
