At least how many elements does the set which contains all of the midpoints of segments connecting 2003 different points in a plane have? <spanclass=′latex−bold′>(A)</span>2006<spanclass=′latex−bold′>(B)</span>4001<spanclass=′latex−bold′>(C)</span>4003<spanclass=′latex−bold′>(D)</span>4006<spanclass=′latex−bold′>(E)</span>None of the preceeding