Let the line $\mathrm{L}: \sqrt{2} \mathrm{x}+\mathrm{y}=\alpha$ pass through the point of the intersection P (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2 y$. Let the line $L$ touch two circles $C_1$ and $C_2$ of equal radius $2 \sqrt{3}$. If the centres $Q_1$ and $Q_2$ of the circles $C_1$ and $C_2$ lie on the $y$-axis, then the square of the area of the triangle $\mathrm{PQ}_1 \mathrm{Q}_2$ is equal to