2. Given that $q$ is a positive rational number. There are two ants starting from a point $X$ on a plane at the same time. Each ant chooses one of the four directions (east, south, west, north) and moves $q^{n}$ meters in the $n$-th minute $(n=1,2, \cdots)$. Suppose they meet again after some integer minutes, but their paths are not identical. Find all possible values of $q$.