Given a string s consisting only of the characters '(' and ')', determine the minimum number of parentheses you must add to s so that the resulting string is a valid parentheses string.

A valid parentheses string is one where parentheses are properly matched and correctly nested.

Constraints:

• $1 \leq$ s.length $\leq 1000$

• s[i] is either '(' or ')'

Input: s = "()()"-str
Output: 0-int
Explanation: The string is already properly matched and nested, so no additions are needed.

Input: s = ")()("-str
Output: 2-int
Explanation: The first ) needs a matching ( added before it, and the last ( needs a matching ) added after it, for a total of 2 additions.

Input: s = "(()))(()"-str
Output: 2-int
Explanation: One extra ) appears in the middle (needing one ( added), and the final ( is left unmatched (needing one ) added), for a total of 2 additions.

Input: s = "))))((("-str
Output: 7-int
Explanation: The four leading ) each require an added ( (4 additions), and the three trailing ( each require an added ) (3 additions), for a total of 4 + 3 = 7 additions.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.