Hamiltonian Tree

You are given a tree $T$ with $N$ vertices. Recall that a tree is a connected graph with $N-1$ edges. Determine the **minimum** number of edges you must add to $T$ to get a new graph $G$ such that $G$ has a Hamiltonian path. Note: A graph $G$ is said to have a hamiltonian path if and only if there exists a simple path in $G$ that includes every vertex exactly once. ### Input - The first line of