class Solution {
public:
    vector<string> result;
    string path;
    void backtracking(int left, int right, int n) {
        if(left > n || right > n) return;
        if(left == n && right == n) {
            result.push_back(path);
            return;
        }

        if(left >= right) {
            path.push_back('(');
            backtracking(left+1, right, n);
            path.pop_back();
        }
        if(left > right) {
            path.push_back(')');
            backtracking(left, right+1, n);
            path.pop_back();
        }
    }
    vector<string> generateParenthesis(int n) {
        path = "(";
        backtracking(1, 0, n);
        return result;
    }
};