Putnam 1996 B3

Given that $\{x_1, x_2, \ldots, x_n\} = \{1, 2, \ldots, n\}$, find, with proof, the largest possible value, as a function of $n$ (with $n \geq 2$), of $$x_1x_2 + x_2x_3 + \cdots + x_{n-1}x_n + x_nx_1.$$