Two capacitors $C_1$ and $C_2$ are charged to the same potential $V$, but with opposite polarity, as shown in the figure. The switches $S_1$ and $S_2$ are then closed.

Two capacitors of equal capacitance $\left(C_1=C_2\right)$ are as shown in the figure. Initially, while the switch is open (as shown) one of the capacitors is uncharged and the other carries charge $Q_0$. The energy stored in the charged capacitor is $U_0$. Sometime after the switch is closed, the capacitors $C_1$ and $C_2$ carry charges $Q_1$ and $Q_2$, respectively. The energies stored in the capacitors are $U_1$ and $U_2$ respectively. Which of the following expression is correct?