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 \(1000\).

(第二十届AIME2 2002 第4题)