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: It is the empty string, or It can be written as AB (A concatenated with B), where A and B are valid strings, or It can be written as (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. Example 1: Input: "())" Output: 1 Example 2: Input: "(((" Output: 3 Example 3: Input: "()" Output: 0 Example 4: Input: "()))((" Output: 4 Note: S.length <= 1000 S only consists of '(' and ')' characters.