You're still doing well physically and emotionally in this long trip, mostly because you were trained well at Illinois. You're about halfway through the trip to Saturn. As you're retiring to your room to sleep, you see both your cat Doraemon and dog Einstein walking together in the spaceship corridor. You call out to them, but they run away again. Trippy, Dude! Before you can chase them, you notice the spacecraft wobbling quite a bit, and you need to fix this. You trace the wobbling problem to the on-board storage system, and the fact that there is no leader election algorithm in there! Quick, you need to design one! The datacenter onboard (with hundreds of machines) uses a ring-based DHT (among the machines) with a Chord-like routing algorithm with each peer maintaining 3 ring successors and 3 ring predecessors, and Chord finger tables. This system needs to elect a leader that has the second-highest DHT Id in the system. i. ii. iii. iv. Design a leader election protocol that is efficient in that it uses very few messages (O(1) Chord DHT routing messages per participant). The only messages you can use are the Chord DHT routing messages (e.g., "route to ID X"). Argue briefly why your algorithm satisfies safety and liveness when finger tables are all correct and there are no failures during execution (formal proof not needed). What is the completion time and number of messages in your leader election protocol (both asymptotic)? Discuss briefly what might happen if failures occur during the election run, while finger tables stay inconsistent.