






import math
def 						_a    (      a :int )							->			list:
 a		  =      [True] * n
 a		  =      False
 a		  =      False
 a		  =      True

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

 a		  =      [2]

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

 return primes
def 						_a    (      a :int = 999_966_663_333 )							->			int:
 a		  =      math.floor(math.sqrt(a ) ) + 100
 a		  =      prime_sieve(a )

 a		  =      0
 a		  =      0
 a		  =      primes[prime_index]

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

  a		  =      last_prime**2
  a		  =      next_prime**2

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

  # Remove the numbers divisible by both ups and lps
  a		  =      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
  a		  =      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


UpperCAmelCase__				   =		{
    "configuration_nllb_moe": [
        "NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "NllbMoeConfig",
    ]
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__				   =		[
         "NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST",
         "NllbMoeForConditionalGeneration",
         "NllbMoeModel",
         "NllbMoePreTrainedModel",
         "NllbMoeTop2Router",
         "NllbMoeSparseMLP",
     ]


if TYPE_CHECKING:
     from .configuration_nllb_moe import (
         NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP,
         NllbMoeConfig,
     )

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_nllb_moe import (
              NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST,
              NllbMoeForConditionalGeneration,
              NllbMoeModel,
              NllbMoePreTrainedModel,
              NllbMoeSparseMLP,
              NllbMoeTopaRouter,
          )


else:
     import sys

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


