





'''simple docstring'''




import math





def 	__lowerCamelCase			(      __lowerCAmelCase       :							int		)		->  list:
   snake_case 						=   [True] * n
   snake_case 						=   False
   snake_case 						=   False
   snake_case 						=   True

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

   snake_case 						=   [2]

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

   return primes





def 	__lowerCamelCase			(      __lowerCAmelCase       :							int = 99_99_66_66_33_33		)		->  int:
   snake_case 						=   math.floor(math.sqrt(__lowerCAmelCase		)		) + 1_00
   snake_case 						=   prime_sieve(__lowerCAmelCase		)

   snake_case 						=   0
   snake_case 						=   0
   snake_case 						=   primes[prime_index]

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

      snake_case 						=   last_prime**2
      snake_case 						=   next_prime**2

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

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

   return matches_sum


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








'''simple docstring'''




from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 from ..utils.dummy_pt_objects import *  # noqa F403
else:
 from .scheduling_consistency_models import CMStochasticIterativeScheduler
 from .scheduling_ddim import DDIMScheduler
 from .scheduling_ddim_inverse import DDIMInverseScheduler
 from .scheduling_ddim_parallel import DDIMParallelScheduler
 from .scheduling_ddpm import DDPMScheduler
 from .scheduling_ddpm_parallel import DDPMParallelScheduler
 from .scheduling_deis_multistep import DEISMultistepScheduler
 from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
 from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
 from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
 from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
 from .scheduling_euler_discrete import EulerDiscreteScheduler
 from .scheduling_heun_discrete import HeunDiscreteScheduler
 from .scheduling_ipndm import IPNDMScheduler
 from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
 from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
 from .scheduling_karras_ve import KarrasVeScheduler
 from .scheduling_pndm import PNDMScheduler
 from .scheduling_repaint import RePaintScheduler
 from .scheduling_sde_ve import ScoreSdeVeScheduler
 from .scheduling_sde_vp import ScoreSdeVpScheduler
 from .scheduling_unclip import UnCLIPScheduler
 from .scheduling_unipc_multistep import UniPCMultistepScheduler
 from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
 from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 from ..utils.dummy_flax_objects import *  # noqa F403
else:
 from .scheduling_ddim_flax import FlaxDDIMScheduler
 from .scheduling_ddpm_flax import FlaxDDPMScheduler
 from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
 from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
 from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
 from .scheduling_pndm_flax import FlaxPNDMScheduler
 from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
 from .scheduling_utils_flax import (
     FlaxKarrasDiffusionSchedulers,
     FlaxSchedulerMixin,
     FlaxSchedulerOutput,
     broadcast_to_shape_from_left,
 )


try:
 if not (is_torch_available() and is_scipy_available()):
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 from ..utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
 from .scheduling_lms_discrete import LMSDiscreteScheduler

try:
 if not (is_torch_available() and is_torchsde_available()):
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 from ..utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
 from .scheduling_dpmsolver_sde import DPMSolverSDEScheduler

