Min Max Paths

Chefland is an undirected, unweighted tree on $N$ nodes. The nodes are labeled from $1$ to $N$. Define: - $\text{pathmin}(u,v) = $ the minimum label of a node on the simple path from $u$ to $v$. - $\text{pathmax}(u,v) = $ the maximum label of a node on the simple path from $u$ to $v$. - $\text{cost}(u,v) = \text{pathmin}(u,v)\cdot\text{pathmax}(u,v)$ If Chef is currently at node $u$, he can mov