Separate Them All

In Chefland, there are $N$ cities numbered from $1$ to $N$. The cities are connected using $N-1$ roads such that there exists a path between all pairs of cities. In other words, the cities and roads forma a tree-structure The roads of Chefland are not in good condition. Therefore, all the roads need to be destroyed. The cost of destroying a road between cities $x$ and $y$ is $d_x \cdot d_y$, wher