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)