Consider three hypothetical companies with multiple class$-$C IP addresses. The following $52$ addresses are assigned to Company X: a block of $8$ addresses from $199\mathrm{.}86\mathrm{.}128\mathrm{.}0$ through $199\mathrm{.}86\mathrm{.}135\mathrm{.}0$ and a block of $28$ addresses from $199\mathrm{.}86\mathrm{.}144\mathrm{.}0$ through $199\mathrm{.}86\mathrm{.}171\mathrm{.}0$ and a block of $16$ addresses from $199\mathrm{.}86\mathrm{.}176\mathrm{.}0$ through $199\mathrm{.}86\mathrm{.}191\mathrm{.}0.$ Company Y is assigned a block of $8$ addresses from $199\mathrm{.}86\mathrm{.}136\mathrm{.}0$ through $199\mathrm{.}86\mathrm{.}143\mathrm{.}0.$ Company Z is assigned $4$ addresses from $199\mathrm{.}86\mathrm{.}172\mathrm{.}0$ through $199\mathrm{.}86\mathrm{.}175\mathrm{.}0.$ Each company has a single border router that is responsible for receiving all incoming traffic destined to any host in this company $($note: the block of $28$ addresses

violate the block size requirement being power of $2$ but works fine in this particular problem$).$

a$)$Design a supernetting CIDR addressing scheme that minimizes the total number of entries associated with the three companies in core internet routers. Indicate the destination IP address and the network mask used in the router entries for these three companies.

b$)$ Before obtaining the $52$ class$-$C addresses, Company X had a Class B address, say $133\mathrm{.}170\mathrm{.}0\mathrm{.}0.$ The company organized its network as a group of $52$ subnets corresponding to the class$-$C IP addresses. Design a subnetting scheme that maximizes the number of hosts in each subnet and indicate the subnet mask used in this scheme. Indicate the maximum number of hosts per subnet and list the contents of the entry $($or entries$)$ associated with this company in an outside router that uses CIDR addressing.