2010 AIME II Problem 8

Let N be the number of ordered pairs of nonempty sets \mathcal{A} and \mathcal{B} that have the following properties: \mathcal{A} \cup \mathcal{B {1,2,3,4,5,6,7,8,9,10,11,12\},\mathcal{A} \cap \mathcal{B}=\emptyset,
The number of elements of \mathcal{A} is not an element of \mathcal{A},
The number of elements of \mathcal{B} is not an element of \mathcal{B}.
Find N.