



"""simple docstring"""
import os
import sys
from contextlib import contextmanager


# Windows only
if os.name == "nt":
      import ctypes
      import msvcrt  # noqa



      class       SCREAMING_SNAKE_CASE__  (					ctypes.Structure ):
         __lowerCAmelCase  :   List[Any]						=						[('''size''', ctypes.c_int), ('''visible''', ctypes.c_byte)]

def       _snake_case						(						):
 if os.name == "nt":
  UpperCAmelCase	:					Optional[int]	=	CursorInfo()
  UpperCAmelCase	:					List[Any]	=	ctypes.windll.kernelaa.GetStdHandle(-11						)
  ctypes.windll.kernelaa.GetConsoleCursorInfo(snake_case__			,		ctypes.byref(snake_case__						)						)
  UpperCAmelCase	:					Optional[int]	=	False
  ctypes.windll.kernelaa.SetConsoleCursorInfo(snake_case__			,		ctypes.byref(snake_case__						)						)
 elif os.name == "posix":
  sys.stdout.write("""\033[?25l"""						)
  sys.stdout.flush()

def       _snake_case						(						):
 if os.name == "nt":
  UpperCAmelCase	:					int	=	CursorInfo()
  UpperCAmelCase	:					Any	=	ctypes.windll.kernelaa.GetStdHandle(-11						)
  ctypes.windll.kernelaa.GetConsoleCursorInfo(snake_case__			,		ctypes.byref(snake_case__						)						)
  UpperCAmelCase	:					str	=	True
  ctypes.windll.kernelaa.SetConsoleCursorInfo(snake_case__			,		ctypes.byref(snake_case__						)						)
 elif os.name == "posix":
  sys.stdout.write("""\033[?25h"""						)
  sys.stdout.flush()

@contextmanager
def       _snake_case						(						):
 try:
  hide_cursor()
  yield
 finally:
  show_cursor()

from math import isqrt, loga






def  snake_case  (       snake_case__			:int)						->   list[int]:
       _A        =  [True] * max_number
       for i in range(2   ,	isqrt(max_number - 1) + 1):
              if is_prime[i]:
                     for j in range(i**2   ,	snake_case__   ,	snake_case__):
                            _A        =  False

       return [i for i in range(2   ,	snake_case__) if is_prime[i]]






def  snake_case  (       snake_case__			:int = 800_800   ,	snake_case__			:int = 800_800)						->   int:
       _A        =  degree * loga(snake_case__)
       _A        =  int(snake_case__)
       _A        =  calculate_prime_numbers(snake_case__)

       _A        =  0
       _A        =  0
       _A        =  len(snake_case__) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left])
                  + prime_numbers[left] * loga(prime_numbers[right])
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


if __name__ == "__main__":
    print(F'''{solution() = }''')




