Beauty Sum

Chef is given a tree with $N$ nodes numbered $1$ to $N$. The $i^{th}$ node has a value $A_i$ associated to it. For any pair $(x, y)$ of nodes where $x \neq y$, define: - $f(x, y)$ as the **maximum** value of $A_u$ over every node $u$ on the *simple path* from $x$ to $y$. - $g(x, y)$ as the **minimum** value of $A_u$ over every node $u$ on the *simple path* from $x$ to $y$. - $h(x, y)$ as the pro