4. For the set $S=\{1,2,3, \cdots, 2009\}$, a 12-element subset $T=\left\{a_{1}, a_{2}, \cdots, a_{12}\right\}$ is such that the absolute difference between any two elements is not 1. The number of such 12-element subsets $T$ is $\qquad$
4. $C_{1998}^{12}$ Analysis: Let's assume $a_{1}<a_{2}<\cdots<a_{12}$, and construct the set $T^{\prime}=\left\{a_{1}, a_{2}-1, a_{3}-2, a_{4}-3, a_{5}-4, \cdots, a_{12}-\right.$ $11\}$. Then, $T$ and $T^{\prime}$ are in one-to-one correspondence, and $T^{\prime}$ is a 12-element subset of $S^{\prime}=\{1,2,3, \cdots, 1998\}$, the number of which is $C_{1998}^{12}$.