10 Let non-negative real numbers $a_{1}, a_{2}, \cdots, a_{2008}$ have a sum of 1, then the maximum value of $a_{1} a_{2}+a_{2} a_{3}+\cdots+$ $a_{2007} a_{2008}+a_{2008} a_{1}$ is $\qquad$.
(10) $\frac{1}{4}$.