Profitable Paths

You are given a tree with $N$ vertices (numbered $1$ through $N$) and a sequence of integers $A_1, A_2, \ldots, A_N$. You may choose an arbitrary permutation $p_1, p_2, \ldots, p_N$ of the integers $1$ through $N$. Then, for each vertex $i$, you should assign the value $A_{p_i}$ to this vertex. The *profit* of a path between two vertices $u$ and $v$ is the sum of the values assigned to the vert