

import math
def       __magic_name__(  __UpperCAmelCase		)						->    list:



      '''simple docstring'''

      _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 ,						__UpperCAmelCase ,						2		):
            if is_prime[i]:
                  primes.append(__UpperCAmelCase		)

      return primes
def       __magic_name__(  __UpperCAmelCase = 9999_6666_3333		)						->    int:



      '''simple docstring'''

      _lowerCamelCase			    =				math.floor(math.sqrt(__UpperCAmelCase		)		) + 100
      _lowerCamelCase			    =				prime_sieve(__UpperCAmelCase		)

      _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


snake_case__				= {
    'configuration_trajectory_transformer': [
        'TRAJECTORY_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'TrajectoryTransformerConfig',
    ],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     snake_case__				= [
         'TRAJECTORY_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
         'TrajectoryTransformerModel',
         'TrajectoryTransformerPreTrainedModel',
         'load_tf_weights_in_trajectory_transformer',
     ]


if TYPE_CHECKING:
     from .configuration_trajectory_transformer import (
         TRAJECTORY_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
         TrajectoryTransformerConfig,
     )

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_trajectory_transformer import (
              TRAJECTORY_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
              TrajectoryTransformerModel,
              TrajectoryTransformerPreTrainedModel,
              load_tf_weights_in_trajectory_transformer,
          )


else:
     import sys

     snake_case__				= _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)