Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin $O$. In the first quadrant, $P_1$, $P_2, \ldots, P_{12}$ are 12 points on line $L_1$ and $Q_1, Q_2, \ldots, Q_9$ are 9 points on line $L_2$. Then the total number of triangles, that can be formed having vertices at three of the 22 points $\mathrm{O}, \mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{12}$, $Q_1, Q_2, \ldots, Q_9$, is: