$.$ Show that the count$-$to$-$infinity problem shown in Fig. $5-10($b$)$ can be solved by having routers add to their distance vectors the outgoing link for every destination and cost pair. For example, In Fig. $5-10($a$),$ node C not only advertises a route to A with distance $2,$ it also communicates that this path goes through node B$.$ Show the distances from all routers to A after every distance vector exchange, until all routers realize A is no longer reachable.