Let E be the ellipse $$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$$. For any three distinct points 𝑃,Q and $$Q^{'}$$ on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and $$M(P, Q^{'})$$ be the mid-point of the line segment joining P and $$Q^{'}$$. Then the maximum possible valu of the distance between M(P, Q) and $$M(P, Q^{'})$$ as P, Q and $$Q^{'}$$ vary on E, is