Three concentric, thin, spherical conducting shells have radii \(R\), \(2R\), and \(4R\). Initially, the innermost shell has a net charge of \(+Q\), the middle shell has a net charge of \(-6Q\), and the outermost shell has a net charge of \(+5Q\). A thin conducting wire with an open switch connects the innermost shell to the outermost shell, passing through a small insulated hole in the middle shell without touching it. After the switch is closed and electrostatic equilibrium is established, what is the final net charge on the innermost shell?