1021. Remove Outermost Parentheses

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1021. Remove Outermost Parentheses
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:
S.length <= 10000
S[i] is "(" or ")"
S is a valid parentheses string
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class Solution {
    public String removeOuterParentheses(String S) {
        int len = S.length();
        int count = 0;
        int begin = 0;
        int end = 0;
        StringBuilder s = new StringBuilder();
        
        for (int i = 0; i < len; i ++) {
            char c = S.charAt(i);
            if (c == '(') {
                count ++;
            }
            else {
                count --;
            }
            if (count == 0) {
                end = i;
                s.append(S.substring(begin + 1, end));
                begin = end + 1;
            }
        }
        
        return s.toString();
    }
}