Mex Tree (Min)

**The problem is nearly identical to Mex Tree (Max Version) except here you must find the minimum possible score**. You have a tree with $N$ vertices. A tree is a connected undirected acyclic graph on $N$ vertices with $N - 1$ edges. You want to assign **distinct labels** to the vertices of the tree. You will choose a permutation $P$ of the integers $[0, N - 1]$ and then assign the vertex $X$ a