IL-GILLIS 2014 Problem 6

Let $n$ be a positive integer. Find the maximal real number $k$ , such that the following holds:

For any $n$ real numbers $x_1,x_2,...,x_n$ , we have $\sqrt{x_1^2+x_2^2+\dots+x_n^2}\geq k\cdot\min(|x_1-x_2|,|x_2-x_3|,...,|x_{n-1}-x_n|,|x_n-x_1|)$