Patio blocks that are regular hexagons 1 unit on a side are used to outline a garden by placing the blocks edge to edge with n on each side. The diagram indicates the path of blocks around the garden when n=5.
If n=202, then the area of the garden enclosed by the path, not including the path itself, is m(\sqrt{3} / 2) square units, where m is a positive integer. Find the remainder when m is divided by 1000 .
