Consider a distributed system with five processes: P$1,$ P$2,$ P$3,$ P$4,$ and P$5.$ Each

process maintains a Lamport vector clock with five components corresponding to

the processes. Initially, all vector clocks are set to $0,0,0,0,0$ for all processes.

Suppose the following events occur in the system:

P$1$ sends a message to P$3.$

P$2$ sends a message to P$4.$

P$3$ receives the message from P$1.$

P$4$ receives the message from P$2.$

P$5$ sends a message to P$3.$

P$3$ sends a reply message to P$5.$

P$4$ sends a message to P$1.$

P$1$ receives the message from P$4.$

P$2$ receives the reply message from P$3.$

P$5$ receives the message from P$3.$

Provide the Lamport vector clock timestamps for each of these events.

After the above events, if $P3$ sends another message to $P2,$ and $P2$ receives the

message from P$3,$ provide the updated Lamport vector clock timestamps for

these new events.