Line \( L_1 \) of slope \( 2 \) and \( L_2 \) 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 \( O, P_1, P_2, \ldots, P_{12}, Q_1, Q_2, \ldots, Q_9 \), is:
