The network uses a Distance Vector Routing protocol. Once the routes have stabilized, the distance vectors at different nodes will be N$1$: $(0,1,7,8,4),$ N$2$: $(1,0,6,7,3),$ N$3$: $(7,6,0,2,6),$ N$4$: $(8,7,2,0,4)$ and N$5$: $(4,3,6,4,0).$ Each distance vector is the distance of the best known path at that instance to nodes, N$1$ to N$5,$ where the distance to itself is $0.$ Also, all links are symmetric and the cost is identical in both directions. In each round, all nodes exchange their distance vectors with their respective neighbours. Then all nodes update their distance vectors. In between two rounds, any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors. The cost of link N$2-$N$3$ reduces to $2($in both directions$).$ For the above scenario solve the following: a$)$ After the next round of updates, what will be the new distance vector at node N$3.$ b$)$ After the update in the $4.$ a$),$ the link N$1-$N$2$ goes down. N$2$ will reflect this change immediately in its distance vector as cost to $.$ After the next round of update, what will be cost to N$1$ in the distance vector of N$3?$