If we want to find a path from S$1$ to destination B$,$ we will look$-$up the forwarding table on S$1$ first, where the next hop is suggested to be S$2$ based on $($B$,$ S$2).$ Then S$2$s forwarding table is looked up$,$ and $($B$,$ S$5)$ reveals the next hop $($S$5)$ of the packet. Finally, S$5$s forwarding table give the final hop $($B$,$ S$11).$ So the path of the packet is S$1-$S$2-$S$5-$S$11.$

Suppose two packets are sent from S$1$ to destination A and from S$1$ to destination E$,$ respectively. Please list the switches that each packet will pass through, including the initial switch S$1,$ up until the final switch $($S$10,$ S$11,$ and S$12).$