






'''simple docstring'''

import math
def     __lowercase  (_lowercase     )   ->     list:


     """simple docstring"""
     __lowerCamelCase						:       Any				   =				[True] * n
     __lowerCamelCase						:       Optional[Any]				   =				False
     __lowerCamelCase						:       List[str]				   =				False
     __lowerCamelCase						:       List[Any]				   =				True

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

     __lowerCamelCase						:       List[str]				   =				[2]

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

     return primes
def     __lowercase  (_lowercase = 999_966_663_333     )   ->     int:


     """simple docstring"""
     __lowerCamelCase						:       int				   =				math.floor(math.sqrt(_lowercase     )     ) + 100
     __lowerCamelCase						:       Optional[Any]				   =				prime_sieve(_lowercase     )

     __lowerCamelCase						:       List[str]				   =				0
     __lowerCamelCase						:       Optional[Any]				   =				0
     __lowerCamelCase						:       Dict				   =				primes[prime_index]

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

          __lowerCamelCase						:       Any				   =				last_prime**2
          __lowerCamelCase						:       List[Any]				   =				next_prime**2

          # Get numbers divisible by lps(current)
          __lowerCamelCase						:       List[str]				   =				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)
          __lowerCamelCase						:       Tuple				   =				upper_bound - next_prime
          while current > lower_bound:
               matches_sum += current
               current -= next_prime

          # Remove the numbers divisible by both ups and lps
          __lowerCamelCase						:       List[Any]				   =				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
          __lowerCamelCase						:       List[str]				   =				next_prime
          prime_index += 1

     return matches_sum


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











'''simple docstring'''

import shutil
import tempfile
import unittest

from transformers import ClapFeatureExtractor, ClapProcessor, RobertaTokenizer, RobertaTokenizerFast
from transformers.testing_utils import require_sentencepiece, require_torchaudio

from .test_feature_extraction_clap import floats_list







@require_torchaudio
@require_sentencepiece
class 	SCREAMING_SNAKE_CASE	(      unittest.TestCase  ):




       def 					a_					(					self      : str					):


            """simple docstring"""







            __lowerCamelCase						:       Any				   =				"""laion/clap-htsat-unfused"""
            __lowerCamelCase						:       List[Any]				   =				tempfile.mkdtemp()




       def 					a_					(					self      : Optional[int]	,    **A__      : Union[str, Any]					):


            """simple docstring"""







            return RobertaTokenizer.from_pretrained(self.checkpoint	,    **A__					)




       def 					a_					(					self      : str	,    **A__      : Any					):


            """simple docstring"""







            return ClapFeatureExtractor.from_pretrained(self.checkpoint	,    **A__					)




       def 					a_					(					self      : List[str]					):


            """simple docstring"""







            shutil.rmtree(self.tmpdirname					)




       def 					a_					(					self      : str					):


            """simple docstring"""







            __lowerCamelCase						:       Dict				   =				self.get_tokenizer()
            __lowerCamelCase						:       Union[str, Any]				   =				self.get_feature_extractor()

            __lowerCamelCase						:       Dict				   =				ClapProcessor(tokenizer=A__	,    feature_extractor=A__					)

            processor.save_pretrained(self.tmpdirname					)
            __lowerCamelCase						:       Optional[Any]				   =				ClapProcessor.from_pretrained(self.tmpdirname					)

            self.assertEqual(processor.tokenizer.get_vocab()	,    tokenizer.get_vocab()					)
            self.assertIsInstance(processor.tokenizer	,    A__					)

            self.assertEqual(processor.feature_extractor.to_json_string()	,    feature_extractor.to_json_string()					)
            self.assertIsInstance(processor.feature_extractor	,    A__					)




       def 					a_					(					self      : str					):


            """simple docstring"""







            __lowerCamelCase						:       str				   =				ClapProcessor(tokenizer=self.get_tokenizer()	,    feature_extractor=self.get_feature_extractor()					)
            processor.save_pretrained(self.tmpdirname					)

            __lowerCamelCase						:       Tuple				   =				self.get_tokenizer(bos_token="""(BOS)"""	,    eos_token="""(EOS)"""					)
            __lowerCamelCase						:       Any				   =				self.get_feature_extractor(do_normalize=A__	,    padding_value=1.0					)

            __lowerCamelCase						:       List[Any]				   =				ClapProcessor.from_pretrained(
                self.tmpdirname	,    bos_token="""(BOS)"""	,    eos_token="""(EOS)"""	,    do_normalize=A__	,    padding_value=1.0					)

            self.assertEqual(processor.tokenizer.get_vocab()	,    tokenizer_add_kwargs.get_vocab()					)
            self.assertIsInstance(processor.tokenizer	,    A__					)

            self.assertEqual(processor.feature_extractor.to_json_string()	,    feature_extractor_add_kwargs.to_json_string()					)
            self.assertIsInstance(processor.feature_extractor	,    A__					)




       def 					a_					(					self      : Optional[int]					):


            """simple docstring"""







            __lowerCamelCase						:       Dict				   =				self.get_feature_extractor()
            __lowerCamelCase						:       Tuple				   =				self.get_tokenizer()

            __lowerCamelCase						:       Optional[int]				   =				ClapProcessor(tokenizer=A__	,    feature_extractor=A__					)

            __lowerCamelCase						:       Dict				   =				floats_list((3, 1000)					)

            __lowerCamelCase						:       str				   =				feature_extractor(A__	,    return_tensors="""np"""					)
            __lowerCamelCase						:       Any				   =				processor(audios=A__	,    return_tensors="""np"""					)

            for key in input_feat_extract.keys():
                 self.assertAlmostEqual(input_feat_extract[key].sum()	,    input_processor[key].sum()	,    delta=1e-2					)




       def 					a_					(					self      : Any					):


            """simple docstring"""







            __lowerCamelCase						:       Optional[Any]				   =				self.get_feature_extractor()
            __lowerCamelCase						:       int				   =				self.get_tokenizer()

            __lowerCamelCase						:       str				   =				ClapProcessor(tokenizer=A__	,    feature_extractor=A__					)

            __lowerCamelCase						:       int				   =				"""This is a test string"""

            __lowerCamelCase						:       Any				   =				processor(text=A__					)

            __lowerCamelCase						:       Any				   =				tokenizer(A__					)

            for key in encoded_tok.keys():
                 self.assertListEqual(encoded_tok[key]	,    encoded_processor[key]					)




       def 					a_					(					self      : List[Any]					):


            """simple docstring"""







            __lowerCamelCase						:       Optional[int]				   =				self.get_feature_extractor()
            __lowerCamelCase						:       List[str]				   =				self.get_tokenizer()

            __lowerCamelCase						:       int				   =				ClapProcessor(tokenizer=A__	,    feature_extractor=A__					)

            __lowerCamelCase						:       Union[str, Any]				   =				[[1, 4, 5, 8, 1, 0, 8], [3, 4, 3, 1, 1, 8, 9]]

            __lowerCamelCase						:       int				   =				processor.batch_decode(A__					)
            __lowerCamelCase						:       List[Any]				   =				tokenizer.batch_decode(A__					)

            self.assertListEqual(A__	,    A__					)




       def 					a_					(					self      : str					):


            """simple docstring"""







            __lowerCamelCase						:       Any				   =				self.get_feature_extractor()
            __lowerCamelCase						:       List[Any]				   =				self.get_tokenizer()

            __lowerCamelCase						:       Any				   =				ClapProcessor(tokenizer=A__	,    feature_extractor=A__					)

            self.assertListEqual(
                processor.model_input_names[2:]	,    feature_extractor.model_input_names	,    msg="""`processor` and `feature_extractor` model input names do not match"""	,    )



