How to save/retrieve mt19937 so that the sequence is repeated?

Here is my attempt

using namespace std;

int main()
{
    mt19937 mt(time(0));

    cout << mt() << endl;
    cout << "----" << endl;

    std::ofstream ofs;
    ofs.open("/path/save", ios_base::app | ifstream::binary);
    ofs << mt;

    cout << mt() << endl;
    cout << "----" << endl;

    std::ifstream ifs;
    ifs.open("/path/save", ios::in | ifstream::binary);
    ifs >> mt;

    cout << mt() << endl;

    return 0;
}

Here is a possible output

1442642936
----
1503923883
----
3268552048

I expected the two last number to be the same. Obviously, I have failed to write and/or read my mt19937. Can you help fixing this code?