CWMO 2006 Problem 1

Let $n$ be a positive integer with $n \geq 2$ , and $0<a_{1}, a_{2},...,a_{n}< 1$ . Find the maximum value of the sum $\sum_{i=1}^{n}(a_{i}(1-a_{i+1}))^{\frac{1}{6}}$ where $a_{n+1}=a_{1}$