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1021. Remove Outermost Parentheses

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Description

A valid parentheses string is either empty (""), "(" + A + ")", or A + B, where A and B are valid parentheses strings, and + represents string concatenation.  For example, "", "()", "(())()", and "(()(()))" are all valid parentheses strings.

A valid parentheses string S is primitive if it is nonempty, and there does not exist a way to split it into S = A+B, with A and B nonempty valid parentheses strings.

Given a valid parentheses string S, consider its primitive decomposition: S = P_1 + P_2 + ... + P_k, where P_i are primitive valid parentheses strings.

Return S after removing the outermost parentheses of every primitive string in the primitive decomposition of S.

 

Example 1:

Input: "(()())(())"

Output: "()()()"

Explanation: 

The input string is "(()())(())", with primitive decomposition "(()())" + "(())".

After removing outer parentheses of each part, this is "()()" + "()" = "()()()".

Example 2:

Input: "(()())(())(()(()))"

Output: "()()()()(())"

Explanation: 

The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".

After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".

Example 3:

Input: "()()"

Output: ""

Explanation: 

The input string is "()()", with primitive decomposition "()" + "()".

After removing outer parentheses of each part, this is "" + "" = "".

 

Note:

1. S.length <= 10000
2. S[i] is "(" or ")"
3. S is a valid parentheses string

 

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