Consider the multi-loop circuit shown in the figure, consisting of two ideal batteries with electromotive forces \(\varepsilon_1 = 2\varepsilon_0\) and \(\varepsilon_2 = \varepsilon_0\), and three resistors with resistances \(R_1 = R\), \(R_2 = 2R\), and \(R_3 = R\). All components are connected by ideal wires. The currents in the left, middle, and right branches are \(I_1\), \(I_2\), and \(I_3\), respectively, with defined directions indicated by the arrows.