


from __future__ import annotations






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		List[str]	):





   """simple docstring"""




   return len(set(__lowerCAmelCase	)	) == len(__lowerCAmelCase	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()








import math






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int	):





			"""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 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int = 999_966_663_333	):





			"""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())




