CN-TST 2011 Problem 13

Let $n\geq 3$ be an integer. Find the largest real number $M$ such that for any positive real numbers $x_1,x_2,\cdots,x_n$ , there exists an arrangement $y_1,y_2,\cdots,y_n$ of real numbers satisfying $$\sum_{i=1}^n \frac{y_i^2}{y_{i+1}^2-y_{i+1}y_{i+2}+y_{i+2}^2}\geq M,$$ where $y_{n+1}=y_1,y_{n+2}=y_2$ .