A multi-loop circuit consists of three vertical parallel branches connected between a top horizontal wire containing node \(X\) and a bottom horizontal wire containing node \(Y\). The left branch contains an ideal battery of emf \(\mathcal{E}\) in series with a resistor of resistance \(R\), with the positive battery terminal connected toward node \(X\). The middle branch contains only a single resistor of resistance \(R\). The right branch contains an ideal battery of emf \(3\mathcal{E}\) in series with a resistor of resistance \(R\), with its positive battery terminal also connected toward node \(X\). What is the electric potential difference \(V_X - V_Y\) between node \(X\) and node \(Y\)?