2. In the plane $\alpha$ there is $\triangle A B C, \angle A B C=60^{\circ}, A C=\sqrt{3}$. On both sides of the plane $\alpha$ there are points $S$ and $T$, satisfying $S A=S B=S C$ $=2, T A=T B=T C=3$. Then the length of $S T$ is $\qquad$
$2 \cdot \sqrt{3}+2 \sqrt{2}$