Consider sending a message of $6$MB over a path with a number of intermediate nodes in a circuit$-$switched network and in a $($lightly$-$loaded$)$ datagram packet$-$switched network. The circuit setup time is $2,700$ milli$-$seconds and the propagation delay is $15$ milli$-$seconds per hop. The data rate at each node is $40$Mb$/$s $($Mega bits per second$)$ and the packet size is $15$ KB$.$

Assume that the packet headers can be ignored in the packet$-$switched network and it is lightly loaded $($in other words, the queueing delays in each intermediate node are zero$).$

If the Packet Switching delay is to be no more than one third of the Circuit Switching delay, what is the maximum number of intermediate nodes possible?