Line \(L_{1}\) of slope 2 and line \(L_{2}\) of slope \(\frac{1}{2}\) intersect at the origin O . In the first quadrant, \(\mathrm{P}_{1}, \mathrm{P}_{2}, \ldots . \mathrm{P}_{12}\) are 12 points on line \(L_{1}\) and \(\mathrm{Q}_{1}, \mathrm{Q}_{2}, \ldots . . \mathrm{Q}_{9}\) 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:
(1) 1080
(2) 1134
(3) 1026
(4) 1188
