Three computers A, B, and C communicate using a protocol that implements the idea of Lamport clocks (they include their clock timestamp in messages). For reference, if you need a reminder, recall that the three rules of Lamport's algorithm are: Rule 1: At process i, increment C; after every local event. Rule 2: To send message m at process i, include the current local time in the message, i.e., send(m, C), then apply apply Rule 1. Rule 3: To receive a message (m;t) at process j, process j updates its local clock C, to be C = max(C;;t + 1). At the beginning of time, all three computers begin with their logical clock set to zero (0). Later, the following sequence of events occurs: A sends message M1 to B: "hi". After sending M1, A sends message M2 to C: "hi" After receiving M1, B sends message M3 to C: "A said hi to me" After receiving M3 first and then M2, C sends message M4 to A: "B is boring" (a) Indicate the time included with the messages as they are sent at each step. Send (M1, ) ) ) ) (b) Maintaining all clock states from the previous question, three ADDITIONAL messages are sent: After receiving M4, A sends message M5 to B: "C is kind of random!" After receiving M5, B sends message M6 to A: "C is boring" A receives message M6 Send (M2, Send (M3, Send (M4, After all of these messages have been sent and received, what time does each computer think it is? (c) Is this a relatively or totally ordered system? (d) Write out the vector time representation with the following messages as they are sent at each step. Send (M1, [ Send (M2, [ Send (M3, [ Send (M4, [ ]) 1) ]) 1)