





import math




def 		lowerCAmelCase_    (  __UpperCAmelCase:			Union[str, Any]      )      ->	List[str]:
    UpperCamelCase__							:				Any          =      [True] * n
    UpperCamelCase__							:				List[Any]          =      False
    UpperCamelCase__							:				Optional[int]          =      False
    UpperCamelCase__							:				Optional[int]          =      True

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

    UpperCamelCase__							:				Any          =      [2]

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

    return primes




def 		lowerCAmelCase_    (  __UpperCAmelCase:			Tuple = 9999_6666_3333      )      ->	Union[str, Any]:
    UpperCamelCase__							:				Tuple          =      math.floor(math.sqrt(lowercase__      )      ) + 100
    UpperCamelCase__							:				Optional[int]          =      prime_sieve(lowercase__      )

    UpperCamelCase__							:				List[Any]          =      0
    UpperCamelCase__							:				Optional[int]          =      0
    UpperCamelCase__							:				Tuple          =      primes[prime_index]

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

        UpperCamelCase__							:				Dict          =      last_prime**2
        UpperCamelCase__							:				int          =      next_prime**2

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

        # Remove the numbers divisible by both ups and lps
        UpperCamelCase__							:				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
        UpperCamelCase__							:				str          =      next_prime
        prime_index += 1

    return matches_sum


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







"""simple docstring"""






import functools
from typing import Any







def      _snake_case			(				lowercase__							,    lowercase__		):

				# Validation
				if not isinstance(lowercase__							,    lowercase__		) or len(lowercase__		) == 0:
								raise ValueError('the string should be not empty string'		)

				if not isinstance(lowercase__							,    lowercase__		) or not all(
				    isinstance(lowercase__							,    lowercase__		) and len(lowercase__		) > 0 for item in words		):
								raise ValueError('the words should be a list of non-empty strings'		)

				# Build trie
				_lowerCamelCase     :			dict[str, Any]    =    {}
				_lowerCamelCase     :			List[Any]    =    'WORD_KEEPER'

				for word in words:
								_lowerCamelCase     :			Dict    =    trie
								for c in word:
												if c not in trie_node:
																_lowerCamelCase     :			Any    =    {}

												_lowerCamelCase     :			str    =    trie_node[c]

								_lowerCamelCase     :			Optional[Any]    =    True

				_lowerCamelCase     :			Dict    =    len(lowercase__		)

				# Dynamic programming method
				@functools.cache
				def is_breakable(lowercase__		) -> bool:
								if index == len_string:
												return True

								_lowerCamelCase     :			List[Any]    =    trie
								for i in range(lowercase__							,    lowercase__		):
												_lowerCamelCase     :			Any    =    trie_node.get(string[i]							,    lowercase__		)

												if trie_node is None:
																return False

												if trie_node.get(lowercase__							,    lowercase__		) and is_breakable(i + 1		):
																return True

								return False

				return is_breakable(0		)


if __name__ == "__main__":
			import doctest

			doctest.testmod()