Given a string s consisting only of parentheses, where s is a valid parentheses string, split s into a concatenation of one or more primitive valid parentheses substrings. For each primitive substring, remove its outermost pair of parentheses, then concatenate the results in the original order. Return the resulting string.

Note: A primitive valid parentheses string is a nonempty valid parentheses string that cannot be written as the concatenation of two nonempty valid parentheses strings.

Constraints:

• $1 \leq$ s.length $\leq 10^5$

• s[i] is either '(' or ')'

• s is a valid parentheses string

Input: s = "()"-str
Output: ""-str
Explanation: The string is one primitive "()". Removing its outermost parentheses removes the entire primitive, leaving an empty string.

Input: s = "((()))"-str
Output: "(())"-str
Explanation: The string is one primitive "((()))". Removing the outermost pair yields "(())".

Input: s = "()(())(()(()))"-str
Output: "()()(())"-str
Explanation: Splitting into primitives gives "()" + "(())" + "(()(()))". Removing the outermost parentheses from each gives "", "()", and "()(())", which concatenate to "()()(())".

Input: s = "(()(()))((()()))(())"-str
Output: "()(())(()())()"-str
Explanation: Splitting into primitives gives "(()(()))" + "((()()))" + "(())". Removing the outermost parentheses from each gives "()(())", "(()())", and "()", which concatenate to "()(())(()())()".

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.