Rectangle in an Ellipse

Geometry Level 3

A,B,C,DA,B,C,D are consecutive vertices of a rectangle whose area is 20062006 square units. An ellipse with area 2006π2006\pi, which passes through AA and CC has its foci at BB and DD.

If the perimeter of the rectangle can be expressed as pqp\sqrt{q} where pp is a positive integer and qq is a square-free positive integer, find p+qp+q.

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