2002 AIME II Problem 4

Patio blocks that are 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\left(\sqrt3/2\right) square units, where m is a positive integer. Find the remainder when m is divided by 1000.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.