OBM 2000 Problem 5

Let $X$ the set of all sequences $\{a_1, a_2,\ldots , a_{2000}\}$ , such that each of the first 1000 terms is 0, 1 or 2, and each of the remaining terms is 0 or 1. The distance between two members $a$ and $b$ of $X$ is defined as the number of $i$ for which $a_i$ and $b_i$ are different.

Find the number of functions $f : X \to X$ which preserve the distance.