You are given a tree with $|$V$|$ vertices and $|$E$|$ edges. Remember for a tree we have: $|$E$|=|$V$|-1$

By removing one vertex and all the edges that go from that vertex to some other vertices, the tree will become disconnected and you end up with two or more connected components. Design an algorithm to return the largest number of components you can get by removing a single vertex of the tree. Develop the pseudocode and analyze the time complexity of your algorithm.

Example: The first one is a tree with four vertices and the second one is a tree with five vertices.