vector<string> gray(int n) {
    vector<string> ans = {"0", "1"};
    for (int bit = 2; bit <= n; ++bit) {
        int oldSize = ans.size();
        for (int i = oldSize - 1; i >= 0; --i)
            ans.push_back(__________________________);
        for (int i = 0; i < oldSize; ++i)
            ans[i] = "0" + ans[i];
    }
    return ans;
}