





import math


def       UpperCamelCase__(			UpperCamelCase__     :			int    )->list:
       A__		   =		[True] * n
       A__		   =		False
       A__		   =		False
       A__		   =		True

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

       A__		   =		[2]

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

       return primes


def       UpperCamelCase__(			UpperCamelCase__     :			int = 99_99_66_66_33_33    )->int:
       A__		   =		math.floor(math.sqrt(UpperCamelCase__    )    ) + 1_00
       A__		   =		prime_sieve(UpperCamelCase__    )

       A__		   =		0
       A__		   =		0
       A__		   =		primes[prime_index]

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

              A__		   =		last_prime**2
              A__		   =		next_prime**2

              # Get numbers divisible by lps(current)
              A__		   =		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__		   =		upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              A__		   =		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__		   =		next_prime
              prime_index += 1

       return matches_sum


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












import pytest

import datasets


# Import fixture modules as plugins
a__: Dict							   =						['tests.fixtures.files', 'tests.fixtures.hub', 'tests.fixtures.fsspec']


def       UpperCamelCase__(			UpperCamelCase__     :			List[Any]					,	UpperCamelCase__     :			Tuple    )->List[str]:
       # Mark tests as "unit" by default if not marked as "integration" (or already marked as "unit")
       for item in items:
              if any(marker in item.keywords for marker in ['''integration''', '''unit''']    ):
                     continue
              item.add_marker(pytest.mark.unit    )


def       UpperCamelCase__(			UpperCamelCase__     :			Dict    )->List[Any]:
       config.addinivalue_line('''markers'''					,	'''torchaudio_latest: mark test to run with torchaudio>=0.12'''    )


@pytest.fixture(autouse=UpperCamelCase__    )
def       UpperCamelCase__(			UpperCamelCase__     :			Optional[int]					,	UpperCamelCase__     :			int    )->Union[str, Any]:
       # test_hf_cache_home = tmp_path_factory.mktemp("cache")  # TODO: why a cache dir per test function does not work?
       A__		   =		tmp_path_factory.getbasetemp() / '''cache'''
       A__		   =		test_hf_cache_home / '''datasets'''
       A__		   =		test_hf_cache_home / '''metrics'''
       A__		   =		test_hf_cache_home / '''modules'''
       monkeypatch.setattr('''datasets.config.HF_DATASETS_CACHE'''					,	str(UpperCamelCase__    )    )
       monkeypatch.setattr('''datasets.config.HF_METRICS_CACHE'''					,	str(UpperCamelCase__    )    )
       monkeypatch.setattr('''datasets.config.HF_MODULES_CACHE'''					,	str(UpperCamelCase__    )    )
       A__		   =		test_hf_datasets_cache / '''downloads'''
       monkeypatch.setattr('''datasets.config.DOWNLOADED_DATASETS_PATH'''					,	str(UpperCamelCase__    )    )
       A__		   =		test_hf_datasets_cache / '''downloads''' / '''extracted'''
       monkeypatch.setattr('''datasets.config.EXTRACTED_DATASETS_PATH'''					,	str(UpperCamelCase__    )    )


@pytest.fixture(autouse=UpperCamelCase__					,	scope='''session'''    )
def       UpperCamelCase__(			)->int:
       datasets.disable_progress_bar()


@pytest.fixture(autouse=UpperCamelCase__    )
def       UpperCamelCase__(			UpperCamelCase__     :			str    )->Tuple:
       # don't take tests into account when counting downloads
       monkeypatch.setattr('''datasets.config.HF_UPDATE_DOWNLOAD_COUNTS'''					,	UpperCamelCase__    )


@pytest.fixture
def       UpperCamelCase__(			UpperCamelCase__     :			List[Any]    )->Optional[Any]:
       # Required to suppress RemovedIn20Warning when feature(s) are not compatible with SQLAlchemy 2.0
       # To be removed once SQLAlchemy 2.0 supported
       monkeypatch.setattr('''sqlalchemy.util.deprecations.SILENCE_UBER_WARNING'''					,	UpperCamelCase__    )





