A message of size $10000$ bits is sent from sender A to receiver B passing through two routers R$1$ and R$2.$ All three links on the path have a propagation delay of $10$ms$.$ A has a transmission rate of $100$ bits$/$sec$,$ R$1$ and R$2$ have a transmission rate of $1000$ bits$/$sec$.$ All the routers obey the store$-$and$-$forward protocol. Assume there is no queuing and processing delay. a$.$ find the end$-$to$-$end latency of the message when the entire message is sent in one packet as a whole.

b$.$ find the end$-$to$-$end latency of the message when the message is broken into $10$ packets each of size $1000$ bits and then transmitted to the destination.