Ellipse

Let E be the ellipse ‌

x2

16

+‌

y2

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 midpoint of the line segment joining P and Q′. Then the maximum possible value of the distance between M(P,Q) and M(P,Q′), as P,Q and Q′ vary on E, is