"""simple docstring"""






import math



def   a_						(					lowerCamelCase       ):
				UpperCAmelCase__             =							[True] * n
				UpperCAmelCase__             =							False
				UpperCAmelCase__             =							False
				UpperCAmelCase__             =							True

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

				UpperCAmelCase__             =							[2]

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

				return primes



def   a_						(					lowerCamelCase = 9_9_9_9_6_6_6_6_3_3_3_3       ):
				UpperCAmelCase__             =							math.floor(math.sqrt(lowerCamelCase       )       ) + 1_0_0
				UpperCAmelCase__             =							prime_sieve(lowerCamelCase       )

				UpperCAmelCase__             =							0
				UpperCAmelCase__             =							0
				UpperCAmelCase__             =							primes[prime_index]

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

								UpperCAmelCase__             =							last_prime**2
								UpperCAmelCase__             =							next_prime**2

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

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

				return matches_sum


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




"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


lowerCAmelCase__  :  Tuple						     =	{'configuration_vit_mae': ['VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ViTMAEConfig']}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__  :  List[Any]						     =	[
						    'VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'ViTMAEForPreTraining',
						    'ViTMAELayer',
						    'ViTMAEModel',
						    'ViTMAEPreTrainedModel',
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__  :  int						     =	[
						    'TFViTMAEForPreTraining',
						    'TFViTMAEModel',
						    'TFViTMAEPreTrainedModel',
						]

if TYPE_CHECKING:
						from .configuration_vit_mae import VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTMAEConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_vit_mae import (
												    VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST,
												    ViTMAEForPreTraining,
												    ViTMAELayer,
												    ViTMAEModel,
												    ViTMAEPreTrainedModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_vit_mae import TFViTMAEForPreTraining, TFViTMAEModel, TFViTMAEPreTrainedModel


else:
						import sys

						lowerCAmelCase__  :  int						     =	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



