[unsolved] Gooood but more difficult!

Let
$x_1,x_2,\cdots,x_n$ $(n\geq2)$ be a nondecreasing monotonous sequence of positive numbers such that$x_1,\frac{x_2}{2},\cdots,\frac{x_n}{n}$ is a nonincreasing monotonous sequence .Prove that
$\frac{\sum_{i=1}^{n} x_i }{n\left (\prod_{i=1}^{n}x_i \right )^{\frac{1}{n}}}\le \frac{n+1}{2\sqrt[n]{n!}}$