





import math



def      __lowercase     (   _SCREAMING_SNAKE_CASE			)				->     list:


						'''simple docstring'''


						SCREAMING_SNAKE_CASE	=		[True] * n
						SCREAMING_SNAKE_CASE	=		False
						SCREAMING_SNAKE_CASE	=		False
						SCREAMING_SNAKE_CASE	=		True

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

						SCREAMING_SNAKE_CASE	=		[2]

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

						return primes



def      __lowercase     (   _SCREAMING_SNAKE_CASE = 99_99_66_66_33_33			)				->     int:


						'''simple docstring'''


						SCREAMING_SNAKE_CASE	=		math.floor(math.sqrt(_SCREAMING_SNAKE_CASE			)			) + 1_00
						SCREAMING_SNAKE_CASE	=		prime_sieve(_SCREAMING_SNAKE_CASE			)

						SCREAMING_SNAKE_CASE	=		0
						SCREAMING_SNAKE_CASE	=		0
						SCREAMING_SNAKE_CASE	=		primes[prime_index]

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

												SCREAMING_SNAKE_CASE	=		last_prime**2
												SCREAMING_SNAKE_CASE	=		next_prime**2

												# Get numbers divisible by lps(current)
												SCREAMING_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)
												SCREAMING_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
												SCREAMING_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
												SCREAMING_SNAKE_CASE	=		next_prime
												prime_index += 1

						return matches_sum


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









def      __lowercase     (   _SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE			)				->     float:


      '''simple docstring'''


      _validate_point(_SCREAMING_SNAKE_CASE			)
      _validate_point(_SCREAMING_SNAKE_CASE			)
      if len(_SCREAMING_SNAKE_CASE			) != len(_SCREAMING_SNAKE_CASE			):
            raise ValueError("""Both points must be in the same n-dimensional space"""			)

      return float(sum(abs(a - b			) for a, b in zip(_SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE			)			)			)



def      __lowercase     (   _SCREAMING_SNAKE_CASE			)				->     None:


      '''simple docstring'''


      if point:
            if isinstance(_SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE			):
                  for item in point:
                        if not isinstance(_SCREAMING_SNAKE_CASE				,		(int, float)			):
                              SCREAMING_SNAKE_CASE	=		(
                                  """Expected a list of numbers as input, found """
                                  F"""{type(_SCREAMING_SNAKE_CASE			).__name__}"""
                              )
                              raise TypeError(_SCREAMING_SNAKE_CASE			)
            else:
                  SCREAMING_SNAKE_CASE	=		F"""Expected a list of numbers as input, found {type(_SCREAMING_SNAKE_CASE			).__name__}"""
                  raise TypeError(_SCREAMING_SNAKE_CASE			)
      else:
            raise ValueError("""Missing an input"""			)



def      __lowercase     (   _SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE			)				->     float:


      '''simple docstring'''


      _validate_point(_SCREAMING_SNAKE_CASE			)
      _validate_point(_SCREAMING_SNAKE_CASE			)
      if len(_SCREAMING_SNAKE_CASE			) != len(_SCREAMING_SNAKE_CASE			):
            raise ValueError("""Both points must be in the same n-dimensional space"""			)

      return float(sum(abs(x - y			) for x, y in zip(_SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE			)			)			)


if __name__ == "__main__":
      import doctest

      doctest.testmod()


