CN-LEAGUE 2016 Problem 1

Let $a_1, a_2, \ldots, a_{2016}$ be real numbers such that $9a_i\ge 11a^2_{i+1}$ $(i=,2,\cdots,2015)$ . Find the maximum value of $(a_1-a^2_2)(a_2-a^2_3)\cdots (a_{2015}-a^2_{2016})(a_{2016}-a^2_{1}).$