The vertices of a regular hexagon $A_1,A_2,...,A_6$ lie respectively on the sides $B_1B_2$, $B_2B_3$, $B_3B_4$, $B_4B_5$, $B_5B_6$, $B_6B_1$ of a convex hexagon $B_1B_2B_3B_4B_5B_6$. Prove that $$S_{B_1B_2B_3B_4B_5B_6} \le \frac32 S_{A_1A_2A_3A_4A_5A_6}.$$