$.$ Compare Go$-$Back$-$N$,$ Selective Repeat and TCP ARQ mechanisms. Assume that the timeout values for all the protocols are sufficiently long such that $5$ consecutive data segments and their corresponding ACKs can be received $($if not lost in the channel$)$ by the receiving host $($Host B$)$ and the sending host $($Host A$)$ respectively before the timeout. Suppose Host A sends $5$ data segments to Host B$,$ and the $2$nd segment $($sent from A$)$ is lost. In the end, all $5$ segments have been correctly received by Host B$.$

a$)$ How many segments has Host A sent in total and how many ACKs has Host B sent in total? What are their sequence numbers? Answer this question for all the protocols.

b$)$ If the timeout values for all the protocols are much longer than $5$ RTTs$,$ then which protocol successfully delivers all five data segments in shortest time interval and why?