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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:

  • 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: s = "())"
Output: 1

Example 2:

Input: s = "((("
Output: 3

Example 3:

Input: s = "()"
Output: 0

Example 4:

Input: s = "()))(("
Output: 4

 

Note:

  1. s.length <= 1000
  2. s only consists of '(' and ')' characters.
 

class Solution { public int minAddToMakeValid(String s) { } }