4. (10 points) Suppose that an n-node undirected graph G contains two nodes S and t such that the distance between S and t is strictly greater than n/2. Show that there must exist some node v not equal to either S or t, such that deleting V from G destroys all paths between s and t In other words, in the graph Gv obtained by deleting V from G, the vertices s and t are in different components. Give a linear-time algorithm to find such a nodeV