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Score of Parentheses

code

Given a balanced parentheses string S, compute the score of the string based on the following rule:

() has score 1
AB has score A + B, where A and B are balanced parentheses strings.
(A) has score 2 * A, where A is a balanced parentheses string.


Example 1:

Input: "()"
Output: 1
Example 2:

Input: "(())"
Output: 2
Example 3:

Input: "()()"
Output: 2
Example 4:

Input: "(()(()))"
Output: 6


Note:

S is a balanced parentheses string, containing only ( and ).
2 <= S.length <= 50