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.