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class Solution {
public:
    void dfs(string s, int left, int u, int n, vector<string>& res) {
        if (u == n && left == 0) {
            res.push_back(s);
            return;
        } else if (u == n) {
            return;
        }

        dfs(s + "(", left + 1, u + 1, n, res);

        if (left > 0) {
            dfs(s + ")", left - 1, u + 1, n, res);
        }
    }

    vector<string> generateParenthesis(int n) {
        vector<string> res;
        dfs("", 0, 0, 2 * n, res);
        return res;
    }
};