Suppose that an n$-$node undirected graph G $=($V$,$ E$)$ 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 u$,$ not equal to either s or t$,$ such that deleting v from G destroys all s$-$t paths. $($In other words, the graph obtained from G by deleting v contains no path from s to t$.)$ Give an algorithm with runnin~ time O$($m $+$ n$)$ to find such a node v$.$