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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

Problem Statement