/**
knakul853
**/
class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string>ans;

        backtrack(n , ans , 0 , 0 , "");

        return ans;
    }

    void backtrack(int n, vector<string>& ans , int open , int close , string res)
    {
        if(res.size()==n*2)
        {
            ans.push_back(res);
        }

        if(open < n) backtrack( n , ans , open+1 , close , res+"(");   // u can have at max n opening brackets.
        if(close < open)backtrack(n , ans , open , close+1 , res+")" ); // u must close after opening the brackets.

    }
};