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Given a string S of '(' and ')' parentheses, we add the minimum number of parentheses ( '(' or ')', and in any positions ) so that the resulting parentheses string is valid.
Formally, a parentheses string is valid if and only if:
AB (A concatenated with B), where A and B are valid strings, or(A), where A is a valid string.Given a parentheses string, return the minimum number of parentheses we must add to make the resulting string valid.
The given string can be balanced to "((()))(())", requiring 4 more paranthesis minimum.
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