RO-TST 2008 Problem 6

Let $n \geq 3$ be an odd integer. Determine the maximum value of $$\sqrt{|x_{1}-x_{2}|}+\sqrt{|x_{2}-x_{3}|}+\ldots+\sqrt{|x_{n-1}-x_{n}|}+\sqrt{|x_{n}-x_{1}|},$$ where $x_{i}$ are positive real numbers from the interval $[0,1]$ .