


'''simple docstring'''


from math import isqrt






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

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






def  __lowerCAmelCase (__lowerCAmelCase = 10**8   ):
		_UpperCAmelCase		:       Optional[Any]								=      calculate_prime_numbers(max_number // 2   )

		_UpperCAmelCase		:       Tuple								=      0
		_UpperCAmelCase		:       List[Any]								=      0
		_UpperCAmelCase		:       List[str]								=      len(__lowerCAmelCase   ) - 1
		while left <= right:
				while prime_numbers[left] * prime_numbers[right] >= max_number:
						right -= 1
				semiprimes_count += right - left + 1
				left += 1

		return semiprimes_count


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







'''simple docstring'''


# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


lowerCamelCase__    	=     {'configuration_mra': ['MRA_PRETRAINED_CONFIG_ARCHIVE_MAP', 'MraConfig']}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__    	=     [
						    'MRA_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'MraForMaskedLM',
						    'MraForMultipleChoice',
						    'MraForQuestionAnswering',
						    'MraForSequenceClassification',
						    'MraForTokenClassification',
						    'MraLayer',
						    'MraModel',
						    'MraPreTrainedModel',
						]


if TYPE_CHECKING:
						from .configuration_mra import MRA_PRETRAINED_CONFIG_ARCHIVE_MAP, MraConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_mra import (
												    MRA_PRETRAINED_MODEL_ARCHIVE_LIST,
												    MraForMaskedLM,
												    MraForMultipleChoice,
												    MraForQuestionAnswering,
												    MraForSequenceClassification,
												    MraForTokenClassification,
												    MraLayer,
												    MraModel,
												    MraPreTrainedModel,
												)
else:
						import sys

						lowerCamelCase__    	=     _LazyModule(__name__, globals()['__file__'], _import_structure)



