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 "" + "" = "".