12 Let the planar point set be
$$
G_{n}=\{(i, j) \mid i=1,2, \cdots, n ; j=1,2, \cdots, n\} .
$$

It is easy to see that $G_{2}$ can be covered by 1 triangle, and $G_{3}$ can be covered by 2 triangles, as shown in the figure. To cover $G_{2008}$, at least $\qquad$ triangles are needed.
（Question 12）
(12) 1338 .