






'''simple docstring'''







import math
def     A__      (					__lowerCAmelCase		:      int    ):
						lowerCamelCase__								=	[True] * n
						lowerCamelCase__								=	False
						lowerCamelCase__								=	False
						lowerCamelCase__								=	True

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

						lowerCamelCase__								=	[2]

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

						return primes
def     A__      (					__lowerCAmelCase		:      int = 9999_6666_3333    ):
						lowerCamelCase__								=	math.floor(math.sqrt(__lowerCAmelCase    )    ) + 100
						lowerCamelCase__								=	prime_sieve(__lowerCAmelCase    )

						lowerCamelCase__								=	0
						lowerCamelCase__								=	0
						lowerCamelCase__								=	primes[prime_index]

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

												lowerCamelCase__								=	last_prime**2
												lowerCamelCase__								=	next_prime**2

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

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

						return matches_sum


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








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


A       :   Optional[int]					= {
    '''configuration_pix2struct''': [
        '''PIX2STRUCT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''Pix2StructConfig''',
        '''Pix2StructTextConfig''',
        '''Pix2StructVisionConfig''',
    ],
    '''processing_pix2struct''': ['''Pix2StructProcessor'''],
}

try:
					if not is_vision_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					A       :   Optional[int]					= ['''Pix2StructImageProcessor''']


try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					A       :   Dict					= [
					    '''PIX2STRUCT_PRETRAINED_MODEL_ARCHIVE_LIST''',
					    '''Pix2StructPreTrainedModel''',
					    '''Pix2StructForConditionalGeneration''',
					    '''Pix2StructVisionModel''',
					    '''Pix2StructTextModel''',
					]

if TYPE_CHECKING:
					from .configuration_pixastruct import (
					    PIX2STRUCT_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    PixaStructConfig,
					    PixaStructTextConfig,
					    PixaStructVisionConfig,
					)
					from .processing_pixastruct import PixaStructProcessor

					try:
										if not is_vision_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .image_processing_pixastruct import PixaStructImageProcessor

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_pixastruct import (
										    PIX2STRUCT_PRETRAINED_MODEL_ARCHIVE_LIST,
										    PixaStructForConditionalGeneration,
										    PixaStructPreTrainedModel,
										    PixaStructTextModel,
										    PixaStructVisionModel,
										)

else:
					import sys

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



