In a \(6 \times 4\) grid (\(6\) rows, \(4\) columns), \(12\) of the \(24\) squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let \(N\) be the number of shadings with this property. Find the remainder when \(N\) is divided by \(1000\).

(第二十五届AIME1 2007 第10题)