MinPath Minimize

**This problem has the same setup and definitions as MINMEXSUM. However, they differ in what needs to be computed, as well as the constraint on $N$.** Consider a tree on $N$ vertices, with vertex $u$ having value $A_u$ written on it. We have the following definitions: - For two vertices $u, v$, define $P(u, v)$ to be the set of vertices on the unique simple path from $u$ to $v$ in the tree.