$2.$ Easy Warm$-$up #$2$: A boolean circuit is called a formula if its directed graph is a tree. In Lecture $13\mathrm{.}4$ we proved that any polynomial$-$size formula is equivalent to some NC$1$ circuit. Here we ask you to prove that any NC$1$ circuit is equivalent to a polynomial$-$size formula, which also has O$($log n$)$ depth.