Minimum Add to Make Parentheses Valid

Description

A parentheses string is valid if and only if:

- It is the empty string,

- 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.

You are given a parentheses string s. In one move, you can insert a parenthesis at any position of the string.

- For example, if s = "()))", you can insert an opening parenthesis to be "(()))" or a closing parenthesis to be "())))".

Return the minimum number of moves required to make s valid.