Question 142
Let $S = \{(a, b) \mid 1 \le a, b \le 5,\ a, b \in \mathbb{Z}\}$. Let $T$ be the set of integer points in the plane such that for any point $P$ in $S$, there exists a different point $Q$ in $T$ such that $PQ$ does not contain integer points except $P$ and $Q$. Find the minimum value of $|T|$, where $|T|$ denotes the number of elements of the finite set $T$.