





"""simple docstring"""






import math

def       __lowerCamelCase    (       SCREAMING_SNAKE_CASE							)		->       list:






       """simple docstring"""




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

       return primes

def       __lowerCamelCase    (       SCREAMING_SNAKE_CASE = 999966663333							)		->       int:






       """simple docstring"""




       _UpperCAmelCase     =     math.floor(math.sqrt(SCREAMING_SNAKE_CASE							)							) + 100
       _UpperCAmelCase     =     prime_sieve(SCREAMING_SNAKE_CASE							)

       _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 dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL

from ...utils import BaseOutput, OptionalDependencyNotAvailable, is_torch_available, is_transformers_available
from .timesteps import (
    fastaa_timesteps,
    smartaa_timesteps,
    smartaa_timesteps,
    smartaaa_timesteps,
    smartaaa_timesteps,
    superaa_timesteps,
    superaa_timesteps,
    superaaa_timesteps,
)



@dataclass
class 	lowerCAmelCase					(      snake_case							):
       lowerCAmelCase__						 =  42
       lowerCAmelCase__						 =  42
       lowerCAmelCase__						 =  42


try:
    if not (is_transformers_available() and is_torch_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
    from .pipeline_if import IFPipeline
    from .pipeline_if_imgaimg import IFImgaImgPipeline
    from .pipeline_if_imgaimg_superresolution import IFImgaImgSuperResolutionPipeline
    from .pipeline_if_inpainting import IFInpaintingPipeline
    from .pipeline_if_inpainting_superresolution import IFInpaintingSuperResolutionPipeline
    from .pipeline_if_superresolution import IFSuperResolutionPipeline
    from .safety_checker import IFSafetyChecker
    from .watermark import IFWatermarker






