JEE Math Practice Question

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 what is the maximum value of the product $P A_{1} \cdot P A_{2} \cdots P A_{8}?