$(10$ points$)$ There are $100$ computers connected to each other. How many connections

required if they are connected to each other with a direct link? Given a set of $5$X$5$

switches $(5$ inputs and $5$ outputs in the switch$),$ what is the minimum number of switches

needed to provide connectivity between any two computers? Please show how these

switches are connected. Please note that we typically put one input port together with one

output port such that we can send and receive on the same port. A $5$X$5$ switch is a switch

with $5$ ports $($each port includes a connection for input and another for output$).$