Let A and B be the endpoints of a semicircular arc of radius 2 . The arc is divided into seven congruent arcs by six equally spaced points C_{1}, C_{2}, \ldots, C_{6}. All chords of the form \overline{A C_{i}} or \overline{B C_{i}} are drawn. Let n be the product of the lengths of these twelve chords. Find the remainder when n is divided by 1000 .