Even Distances

You are given a tree on $N$ vertices numbered $1$ to $N$, and a permutation $P$ of $\{1, 2, \ldots, N\}$. In one **operation** on a tree, you may: - Choose an edge of the tree and remove it, then - Add an edge between any two vertices. The graph must remain a tree after the operation. For a tree $G$, let $\text{dist}_G(u, v)$ denote the number of edges on the path between $u$ and $v$ in $G$. F