Tree Distance Sum

You are given a tree consisting of $N$ nodes. The nodes are numbered from $1$ to $N$. The tree is rooted at the node $1$. A tree is a connected undirected graph with $N − 1$ edges. Find the sum of the distance between nodes $x$ and $y$ over all tuples ($u, v, x, y$) satisfying the following conditions: $1)$ $u \lt v$ $2)$ $u$ is the ancestor of node $x$ and $v$ is the ancestor of node $y$. $