$(2)(12$ pts$)$ Twenty$-$five students are seated in twenty$-$five desks arranged in a $55$ array. Each student is then told to move to another desk; however, they can only move to a desk exactly two desks in front of$,$ two desks behind, or one desk to the left of$,$ or one desk to the right of the desk they are in$.$ Prove that this is not possible. Use the Pigeon Hole Principle. Clearly state what is playing the role of the pigeons and how many there are. Clearly state what is playing the role of the holes $($describe them completely$)$ and how many there are.