JBMO-SL 2002 Problem 13

Let $A_1,A_2,...,A_{2002}$ be arbitrary points in the plane. Prove that for every circle of radius $1$ and for every rectangle inscribed in this circle, there exist $3$ vertices $M,N,P$ of the rectangle such that $MA_1 + MA_2 + \cdots + MA_{2002} +$ $NA_1 + NA_2 + \cdots + NA_{2002} +$ $PA_1 + PA_2 + \cdots + PA_{2002}\ge 6006$ .