A server S provides the service of testing if a client computer is located behind NATs or not. Server S has a public IP address s$1,$ and allocates two ports p$1$ and p$2($either UDP or TCP port$)$ for this purpose. Note that the s$1,$ p$1$ and p$2$ are known to every computer which wants to use the service. $($a$)$ Explain how a computer, say computer A$,$ can test if it is behind an NAT or not by exchanging packets with S$.($b$)$ Suppose we like to get additional information regarding if $.$ A is located behind a $$symmetric$$ NAT or not. Can this be done with the setting above? Explain your answer.