$2$N computers have been connected in a network as illustrated. The length of each link is written in meters. Let k be the last three digits of your student number. Each computer generates $1000$ packets per second with each packet being $500$ bytes. The maximum rate of all links is $1$ Gbps$.$ The propagation speed in the medium is $2\mathrm{.}0\backslash$times $108$ meters$/$second$.$

$(1)$ What is the maximum number of nodes supported in the network if CSMA$-$CD is used on the shared medium?

$(2)$ Assume that hub$1$ is replaced with a switch. Find the maximum number of nodes supported in the network if CSMA$-$CD is used on the shared medium. Assume that $3/4$ of the traffic is kept in its own side and $1/4$ of the traffic goes to the other side.