






'''simple docstring'''



from math import pow, sqrt


def 				lowercase_					(     *__A			:							float      )							->   bool:



 """simple docstring"""




 lowercase       : Dict						=len(__A      ) > 0 and all(value > 0.0 for value in values      )
 return result


def 				lowercase_					(     __A			:							float       ,   __A			:							float      )							->   float | ValueError:



 """simple docstring"""




 return (
     round(sqrt(molar_mass_a / molar_mass_a      )       ,   6      )
     if validate(__A       ,   __A      )
     else ValueError('''Input Error: Molar mass values must greater than 0.'''      )
 )


def 				lowercase_					(     __A			:							float       ,   __A			:							float       ,   __A			:							float      )							->   float | ValueError:



 """simple docstring"""




 return (
     round(effusion_rate * sqrt(molar_mass_a / molar_mass_a      )       ,   6      )
     if validate(__A       ,   __A       ,   __A      )
     else ValueError(
         '''Input Error: Molar mass and effusion rate values must greater than 0.'''      )
 )


def 				lowercase_					(     __A			:							float       ,   __A			:							float       ,   __A			:							float      )							->   float | ValueError:



 """simple docstring"""




 return (
     round(effusion_rate / sqrt(molar_mass_a / molar_mass_a      )       ,   6      )
     if validate(__A       ,   __A       ,   __A      )
     else ValueError(
         '''Input Error: Molar mass and effusion rate values must greater than 0.'''      )
 )


def 				lowercase_					(     __A			:							float       ,   __A			:							float       ,   __A			:							float      )							->   float | ValueError:



 """simple docstring"""




 return (
     round(molar_mass / pow(effusion_rate_a / effusion_rate_a       ,   2      )       ,   6      )
     if validate(__A       ,   __A       ,   __A      )
     else ValueError(
         '''Input Error: Molar mass and effusion rate values must greater than 0.'''      )
 )





def 				lowercase_					(     __A			:							float       ,   __A			:							float       ,   __A			:							float      )							->   float | ValueError:



 """simple docstring"""




 return (
     round(pow(effusion_rate_a / effusion_rate_a       ,   2      ) / molar_mass       ,   6      )
     if validate(__A       ,   __A       ,   __A      )
     else ValueError(
         '''Input Error: Molar mass and effusion rate values must greater than 0.'''      )
 )











'''simple docstring'''



from math import isqrt


def 				lowercase_					(     __A			:							int      )							->   list[int]:



 """simple docstring"""




 lowercase       : Dict						=[True] * max_number
 for i in range(2       ,   isqrt(max_number - 1      ) + 1      ):
  if is_prime[i]:
   for j in range(i**2       ,   __A       ,   __A      ):
    lowercase       : str						=False

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


def 				lowercase_					(     __A			:							int = 1_0**8      )							->   int:



 """simple docstring"""




 lowercase       : Dict						=calculate_prime_numbers(max_number // 2      )

 lowercase       : str						=0
 lowercase       : Optional[Any]						=0
 lowercase       : Union[str, Any]						=len(__A      ) - 1
 while left <= right:
  while prime_numbers[left] * prime_numbers[right] >= max_number:
   right -= 1
  semiprimes_count += right - left + 1
  left += 1

 return semiprimes_count


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



