




'''simple docstring'''


from math import isqrt, loga
def 						lowerCamelCase__   (				a							):
						__snake_case						 =   [True] * max_number
						for i in range(2    ,	isqrt(max_number - 1							) + 1							):
												if is_prime[i]:
																		for j in range(i**2    ,	a    ,	a							):
																								__snake_case						 =   False

						return [i for i in range(2    ,	a							) if is_prime[i]]
def 						lowerCamelCase__   (				a = 800800    ,	a = 800800							):
						__snake_case						 =   degree * loga(a							)
						__snake_case						 =   int(a							)
						__snake_case						 =   calculate_prime_numbers(a							)

						__snake_case						 =   0
						__snake_case						 =   0
						__snake_case						 =   len(a							) - 1
						while left < right:
												while (
												    prime_numbers[right] * loga(prime_numbers[left]							)
												    + prime_numbers[left] * loga(prime_numbers[right]							)
												    > upper_bound
												):
																		right -= 1
												hybrid_integers_count += right - left
												left += 1

						return hybrid_integers_count


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







'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowercase  =			{
    """configuration_pegasus_x""": ["""PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP""", """PegasusXConfig"""],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_lowercase  =			[
	    """PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """PegasusXForConditionalGeneration""",
	    """PegasusXModel""",
	    """PegasusXPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_pegasus_x import (
		    PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
		    PegasusXForConditionalGeneration,
		    PegasusXModel,
		    PegasusXPreTrainedModel,
		)


else:
	import sys

	_lowercase  =			_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

