Three thin, concentric conducting spherical shells have radii \(R\), \(2R\), and \(3R\). The innermost shell of radius \(R\) and the outermost shell of radius \(3R\) are connected to each other by a thin conducting wire. A battery maintaining a potential difference \(V_0\) is connected between the middle shell of radius \(2R\) and the wire connecting the inner and outer shells. If the system is initially uncharged, what is the total work done by the battery to fully charge the system?