At Amazon, a user owns a unique tool called the"Parentheses Perfection Kit." This kit contains different types of parentheses, each with a specific efficiency rating. The goal is to create a balanced sequence of parentheses by adding zero or more parentheses from the kit to maximize the sequences total EfficiencyScore. The EfficiencyScore of a sequence is the sum of the efficiency ratings of the parentheses used from the kit.

A sequence is considered balanced if it has an equal number of opening '(' and closing )' parentheses, with each opening parentheses properly matched with a closing one in the correct order (i.e., circular balance). For instance, sequences like (()), (), and (()()) are balanced, while sequences like ), ((), and (()(())) are not.

You are given an initial parentheses sequence represented by the string s, along with a Parentheses Perfection Kit containing different types of parentheses in the form of the string kitParentheses and their respective efficiency ratings in the efficiencyRatings array (both of size m). The EfficiencyScore of the original strings is initially 0. You can use any number of unused parentheses from the kit to create the final sequence, as long as the final sequence remains balanced.

The task is to determine the maximum possible EfficiencyScore that can be achieved for the resulting balanced sequence

Note: It is guaranteed that the sequence can be made balanced by adding zero or more parentheses from the kit.

Sample Case 0

Sample Input 0

STDIN Function
() → s = "() "
(()) → kitParentheses = "(())"
4 → efficiencyRatings[] size m=4
4 → efficiencyRatings = [4, 2, -3, -3]
2
-3
-3

Explanation
If the user used the 0th indexed and 2nd indexed parentheses from the bag and add them to the start and end of the
string respectively, then the final balanced sequence will be "(0)" with a total EfficiencyScore of 4 + (-3) = 1. There are
no other combinations of adding parentheses that can yield a balanced sequence with total EfficiencyScore greater than 1, Hence return 1 as answer.

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