


'''simple docstring'''



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_speech_available,
    is_torch_available,
)


__lowercase	:						Tuple       =	{
    'configuration_trocr': ['TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP', 'TrOCRConfig'],
    'processing_trocr': ['TrOCRProcessor'],
}


try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowercase	:						Optional[int]       =	[
	    'TROCR_PRETRAINED_MODEL_ARCHIVE_LIST',
	    'TrOCRForCausalLM',
	    'TrOCRPreTrainedModel',
	]


if TYPE_CHECKING:
	from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
	from .processing_trocr import TrOCRProcessor

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
	import sys

	__lowercase	:						Optional[Any]       =	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)







from math import isqrt
def 				UpperCAmelCase_					(							__snake_case						)     ->			list[int]:







 """simple docstring"""


 _lowercase							      =[True] * max_number
 for i in range(2     ,						isqrt(max_number - 1						) + 1						):
  if is_prime[i]:
   for j in range(i**2     ,						__snake_case     ,						__snake_case						):
    _lowercase							      =False

 return [i for i in range(2     ,						__snake_case						) if is_prime[i]]
def 				UpperCAmelCase_					(							__snake_case = 10**8						)     ->			int:







 """simple docstring"""


 _lowercase							      =calculate_prime_numbers(max_number // 2						)

 _lowercase							      =0
 _lowercase							      =0
 _lowercase							      =len(__snake_case						) - 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() = }''')

