There are light bulbs $\ell_1,\dots, \ell_n$ controlled by the switches $s_1, \dots, s_n$. The $i$th switch flips the status of the $i$th light and possibly others as well. If $s_i$ flips the status of $\ell_j$, then $s_j$ flips the status of $\ell_i$. All lights are initially off. Prove that it is possible to turn all the lights on.