Consider the layer$-2$ network composed of $5$ Ethernet switches depicted in the figure below. The switches are running the Spanning Tree Protocol $($STP$)$ as described in the course. All links have a cost of $1.$ When equal$-$cost paths to the root are encountered, switches break the tie based on the sender ID $($lower is better$).$

$(2$ points$)$ Which links $($use the format $[$s$1,$ s$2])$ will end up deactivated in the steady state, once all the switches have converged on the final spanning tree? Which switch is the root?

$(2$ points$)$ Assume now that the root fails which triggers a new recomputation of the spanning tree $($including removing all links between the root switch and its neighbors completely$).$ Which links will now end up deactivated in the steady state, once all the switches have converged on the final spanning tree? Which switch is the root?