CWMO 2014 Problem 6

Let $n\ge 2$ is a given integer , $x_1,x_2,\ldots,x_n$ be real numbers such that $(1) x_1+x_2+\ldots+x_n=0$ , $(2) |x_i|\le 1$ $(i=1,2,\cdots,n)$ . Find the maximum of Min $\{|x_1-x_2|,|x_2-x_3|,\cdots,|x_{n-1}-x_n|\}$ .