

import math

def 		UpperCamelCase   (lowercase_:					int   )	-> list:
	A__				:       List[Any]	  =						[True] * n
	A__				:       Tuple	  =						False
	A__				:       Dict	  =						False
	A__				:       Optional[int]	  =						True

	for i in range(3       , int(n**0.5 + 1   )       , 2   ):
		A__				:       Any	  =						i * 2
		while index < n:
			A__				:       int	  =						False
			A__				:       Dict	  =						index + i

	A__				:       Any	  =						[2]

	for i in range(3       , lowercase_       , 2   ):
		if is_prime[i]:
			primes.append(lowercase_   )

	return primes

def 		UpperCamelCase   (lowercase_:					int = 999966663333   )	-> int:
	A__				:       Optional[Any]	  =						math.floor(math.sqrt(lowercase_   )   ) + 100
	A__				:       Optional[Any]	  =						prime_sieve(lowercase_   )

	A__				:       List[Any]	  =						0
	A__				:       int	  =						0
	A__				:       Any	  =						primes[prime_index]

	while (last_prime**2) <= limit:
		A__				:       Tuple	  =						primes[prime_index + 1]

		A__				:       Optional[Any]	  =						last_prime**2
		A__				:       Optional[Any]	  =						next_prime**2

		# Get numbers divisible by lps(current)
		A__				:       Union[str, Any]	  =						lower_bound + last_prime
		while upper_bound > current <= limit:
			matches_sum += current
			current += last_prime

		# Reset the upper_bound
		while (upper_bound - next_prime) > limit:
			upper_bound -= next_prime

		# Add the numbers divisible by ups(current)
		A__				:       Tuple	  =						upper_bound - next_prime
		while current > lower_bound:
			matches_sum += current
			current -= next_prime

		# Remove the numbers divisible by both ups and lps
		A__				:       List[str]	  =						0
		while upper_bound > current <= limit:
			if current <= lower_bound:
				# Increment the current number
				current += last_prime * next_prime
				continue

			if current > limit:
				break

			# Remove twice since it was added by both ups and lps
			matches_sum -= current * 2

			# Increment the current number
			current += last_prime * next_prime

		# Setup for next pair
		A__				:       List[Any]	  =						next_prime
		prime_index += 1

	return matches_sum


if __name__ == "__main__":
	print(solution())






import os
import re
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


A_			:					Tuple    			=     logging.get_logger(__name__)

A_			:					Tuple    			=     {'vocab_file': 'spiece.model'}

A_			:					Optional[Any]    			=     {
    'vocab_file': {
        'google/bigbird-roberta-base': 'https://huggingface.co/google/bigbird-roberta-base/resolve/main/spiece.model',
        'google/bigbird-roberta-large': (
            'https://huggingface.co/google/bigbird-roberta-large/resolve/main/spiece.model'
        ),
        'google/bigbird-base-trivia-itc': (
            'https://huggingface.co/google/bigbird-base-trivia-itc/resolve/main/spiece.model'
        ),
    }
}

A_			:					Tuple    			=     {
    'google/bigbird-roberta-base': 4096,
    'google/bigbird-roberta-large': 4096,
    'google/bigbird-base-trivia-itc': 4096,
}



class        _a		(__magic_name__							):


					'''simple docstring'''






					UpperCAmelCase__:  Optional[int]    				=			VOCAB_FILES_NAMES
					UpperCAmelCase__:  str    				=			PRETRAINED_VOCAB_FILES_MAP
					UpperCAmelCase__:  List[str]    				=			PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
					UpperCAmelCase__:  str    				=			['''input_ids''', '''attention_mask''']
					UpperCAmelCase__:  List[int]    				=			[]






					def __init__(					self       ,			A__       ,			A__="<unk>"       ,			A__="<s>"       ,			A__="</s>"       ,			A__="<pad>"       ,			A__="[SEP]"       ,			A__="[MASK]"       ,			A__="[CLS]"       ,			A__ = None       ,			**A__       ,			):
						A__				:       Tuple	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else bos_token
						A__				:       int	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else eos_token
						A__				:       Tuple	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else unk_token
						A__				:       str	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else pad_token
						A__				:       Dict	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else cls_token
						A__				:       Any	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else sep_token

						# Mask token behave like a normal word, i.e. include the space before it
						A__				:       Optional[Any]	  =						AddedToken(A__       ,			lstrip=A__       ,			rstrip=A__     ) if isinstance(A__       ,			A__     ) else mask_token

						A__				:       Optional[Any]	  =						{} if sp_model_kwargs is None else sp_model_kwargs

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

						A__				:       Any	  =						vocab_file

						A__				:       Optional[int]	  =						spm.SentencePieceProcessor(**self.sp_model_kwargs     )
						self.sp_model.Load(A__     )






					@property
					def     __A     (					self     ):
						return self.sp_model.get_piece_size()






					def     __A     (					self     ):
						A__				:       List[str]	  =						{self.convert_ids_to_tokens(A__     ): i for i in range(self.vocab_size     )}
						vocab.update(self.added_tokens_encoder     )
						return vocab






					def __getstate__(					self     ):
						A__				:       Optional[Any]	  =						self.__dict__.copy()
						A__				:       Optional[Any]	  =						None
						return state






					def __setstate__(					self       ,			A__     ):
						A__				:       Dict	  =						d

						# for backward compatibility
						if not hasattr(self       ,			"""sp_model_kwargs"""     ):
							A__				:       str	  =						{}

						A__				:       Tuple	  =						spm.SentencePieceProcessor(**self.sp_model_kwargs     )
						self.sp_model.Load(self.vocab_file     )






					def     __A     (					self       ,			A__     ):
						return self.sp_model.encode(A__       ,			out_type=A__     )






					def     __A     (					self       ,			A__     ):
						return self.sp_model.piece_to_id(A__     )






					def     __A     (					self       ,			A__     ):
						A__				:       Dict	  =						self.sp_model.IdToPiece(A__     )
						return token






					def     __A     (					self       ,			A__     ):
						A__				:       str	  =						[]
						A__				:       Optional[int]	  =						""""""
						A__				:       Any	  =						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
								A__				:       Union[str, Any]	  =						True
								A__				:       Union[str, Any]	  =						[]
							else:
								current_sub_tokens.append(A__     )
								A__				:       Any	  =						False
						out_string += self.sp_model.decode(A__     )
						return out_string.strip()






					def     __A     (					self       ,			A__       ,			A__ = False       ,			A__ = None       ,			A__ = True       ,			**A__       ,			):
						A__				:       List[str]	  =						kwargs.pop("""use_source_tokenizer"""       ,			A__     )

						A__				:       Union[str, Any]	  =						self.convert_ids_to_tokens(A__       ,			skip_special_tokens=A__     )

						# To avoid mixing byte-level and unicode for byte-level BPT
						# we need to build string separately for added tokens and byte-level tokens
						# cf. https://github.com/huggingface/transformers/issues/1133
						A__				:       Dict	  =						[]
						A__				:       List[Any]	  =						[]
						for token in filtered_tokens:
							if skip_special_tokens and token in self.all_special_ids:
								continue
							if token in self.added_tokens_encoder:
								if current_sub_text:
									sub_texts.append(self.convert_tokens_to_string(A__     )     )
									A__				:       Optional[Any]	  =						[]
								sub_texts.append(A__     )
							else:
								current_sub_text.append(A__     )
						if current_sub_text:
							sub_texts.append(self.convert_tokens_to_string(A__     )     )

						# Mimic the behavior of the Rust tokenizer:
						# No space before [MASK] and [SEP]
						if spaces_between_special_tokens:
							A__				:       List[Any]	  =						re.sub(r""" (\[(MASK|SEP)\])"""       ,			r"""\1"""       ,			""" """.join(A__     )     )
						else:
							A__				:       Optional[Any]	  =						"""""".join(A__     )

						A__				:       Union[str, Any]	  =						(
						    clean_up_tokenization_spaces
						    if clean_up_tokenization_spaces is not None
						    else self.clean_up_tokenization_spaces
						)
						if clean_up_tokenization_spaces:
							A__				:       Union[str, Any]	  =						self.clean_up_tokenization(A__     )
							return clean_text
						else:
							return text






					def     __A     (					self       ,			A__       ,			A__ = None     ):
						if not os.path.isdir(A__     ):
							logger.error(F"""Vocabulary path ({save_directory}) should be a directory"""     )
							return
						A__				:       str	  =						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:
								A__				:       Dict	  =						self.sp_model.serialized_model_proto()
								fi.write(A__     )

						return (out_vocab_file,)






					def     __A     (					self       ,			A__       ,			A__ = None     ):
						if token_ids_a is None:
							return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
						A__				:       List[Any]	  =						[self.cls_token_id]
						A__				:       List[Any]	  =						[self.sep_token_id]
						return cls + token_ids_a + sep + token_ids_a + sep






					def     __A     (					self       ,			A__       ,			A__ = None       ,			A__ = 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] + ([0] * len(A__     )) + [1]






					def     __A     (					self       ,			A__       ,			A__ = None     ):
						A__				:       Any	  =						[self.sep_token_id]
						A__				:       List[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     ) * [0] + len(token_ids_a + sep     ) * [1]



