Alice is at a computer behind a NAT gateway that has the private IP address $10\mathrm{.}23\mathrm{.}44\mathrm{.}55.$ The gateway has the first IP address in the range; she has the fifty$-$fifth. She opens a connection to a file transfer server at $74\mathrm{.}125\mathrm{.}224\mathrm{.}80.$

a$)$ Choose a five$-$digit source port number to be used by Alice$$s protocol stack.

b$)$ Given the port number chosen for Alice$$s protocol stack above, give the full socket address as seen on the private side of the gateway.

c$)$ Choose another five$-$digit port number to be assigned by the NAT to this connection.

d$)$ Assume that the NAT gateway has a global IP address of $11\mathrm{.}22\mathrm{.}33\mathrm{.}44.$ Using the NAT port number chosen above, give the full socket address as seen on the internet side of the gateway.