CGMO 2006 Problem 5

The set $S = \{ (a,b) \mid 1 \leq a, b \leq 5, a,b \in \mathbb{Z}\}$ be a set of points in the plane with integeral coordinates. $T$ is another set of points with integeral coordinates in the plane. If for any point $P \in S$ , there is always another point $Q \in T$ , $P \neq Q$ , such that there is no other integeral points on segment $PQ$ . Find the least value of the number of elements of $T$ .