Let A₁, A₂, A₃, …, A₈ 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 PAᵢ denote the distance between the points P and Aᵢ for i = 1, 2, …, 8. If P varies over the circle, then the maximum value of the product PA₁ · PA₂ · … · PA₈ is ___.