IL-GILLIS 2013 Problem 6

Let $x_1,...,x_n$ be positive real numbers, satisfying $x_1+\dots+x_n=n$ . Prove that $\frac{x_1}{x_2}+\frac{x_2}{x_3}+\dots+\frac{x_{n-1}}{x_n}+\frac{x_n}{x_1}\leq\frac{4}{x_1\cdot x_2\cdot\dots\cdot x_n}+n-4$ .