int n = 3;
    //2^n -> (1 << n)
    for(int bitmask = 0; bitmask < (1 << n); ++bitmask) {
        string mask = "";
        for(int bit = 0; bit < n; ++bit) {
            if((bitmask & (1 << bit)) != 0) {
                //bit is on
            }
            else {
                //bit is off
            }
        }
        cout << mask << "\n";
    }