




import math





def 						UpperCAmelCase				(			A__:    int     )  ->     Optional[Any]:
			__lowerCamelCase					:	Optional[int]	       =				[True] * n
			__lowerCamelCase					:	Union[str, Any]	       =				False
			__lowerCamelCase					:	Optional[int]	       =				False
			__lowerCamelCase					:	Union[str, Any]	       =				True

			for i in range(3							,				int(n**0.5 + 1     )							,				2     ):
						__lowerCamelCase					:	Optional[Any]	       =				i * 2
						while index < n:
									__lowerCamelCase					:	Optional[int]	       =				False
									__lowerCamelCase					:	Optional[Any]	       =				index + i

			__lowerCamelCase					:	Any	       =				[2]

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

			return primes





def 						UpperCAmelCase				(			A__:    Union[str, Any] = 999966663333     )  ->     str:
			__lowerCamelCase					:	str	       =				math.floor(math.sqrt(lowercase__     )     ) + 100
			__lowerCamelCase					:	Any	       =				prime_sieve(lowercase__     )

			__lowerCamelCase					:	int	       =				0
			__lowerCamelCase					:	int	       =				0
			__lowerCamelCase					:	Dict	       =				primes[prime_index]

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

						__lowerCamelCase					:	Tuple	       =				last_prime**2
						__lowerCamelCase					:	List[Any]	       =				next_prime**2

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

						# Remove the numbers divisible by both ups and lps
						__lowerCamelCase					:	Optional[int]	       =				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
						__lowerCamelCase					:	List[str]	       =				next_prime
						prime_index += 1

			return matches_sum


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









"""simple docstring"""
import math





def 						UpperCAmelCase				(			A__:    int = 100     )  ->     int:
			__lowerCamelCase					:	Optional[Any]	       =				sum(i * i for i in range(1							,				n + 1     )     )
			__lowerCamelCase					:	Union[str, Any]	       =				int(math.pow(sum(range(1							,				n + 1     )     )							,				2     )     )
			return square_of_sum - sum_of_squares


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



