$[$Analytical Question$]$ Assume we have a VL$2$ implementation in our DCN$.$

$(1)$ Using location address $($LA$)$ space $20\mathrm{.}20\mathrm{.}0\mathrm{.}0/16,$ and application address $($AA$)$ space $15\mathrm{.}15\mathrm{.}0\mathrm{.}0/16$ provide example address assignments for applications X and Y$,$ and all relevant TOR interfaces for two example TOR switches A and B$,$ and two intermediate switches we name IS$1$ and IS$2.(2$ points$)$

$(2)$ Using the IP addresses you have chosen, explain in detail how the Directory Service helps in sending packets from application X to application Y$.(0\mathrm{.}5$ points$)$

$(3)$ Using the IP addresses you have chosen, explain the implications of changing application Y$\text{'}$s location. $(0\mathrm{.}5$ points$)$

$(4)$ Using the details discussed in your example, discuss the benefits and shortcomings of a Layer $2$ versus Layer $3$ implementation of a DCN$,$ and compare that with what is achieved in VL$2.(1$ points$)$