Sum of LCA

You are given a tree $T$ consisting of $N$ nodes, rooted at node $1$. The nodes are numbered $1, 2, \ldots, N$. $\text{dep}(x)$ is defined as the number of nodes on the path from the root node $1$ and the node $x$. Note that this means $\text{dep}(1) = 1$. $\text{lca}(x, y)$ is defined as the node $z$ with the largest value of $\text{dep}(z)$ that lies on both the paths $(1, x)$ and $(1, y)$. F