Circle

Let $A_1, A_2, A_3, \ldots, A_8$ be the vertices of a regular octagon that lie on a circle of radius 2 . Let $P$ be a point on the circle and let $P A_i$ denote the distance between the points $P$ and $A_i$ for $i=1,2, \ldots, 8$. If $P$ varies over the circle, then the maximum value of the product $P A_1 \times P A_2 \times \cdots \cdots \times P A_8$, is :