Let A B C D E F be a convex hexagon with area S such that A B\|D E, B C\| E F, C D \| F A holds, and whose all angles are obtuse and opposite sides are not the same length. Prove that the following inequality holds: A_{A B C}+A_{B C D}+A_{C D E}+A_{D E F}+A_{E F A}+A_{F A B}<S, where A_{X Y Z} is the area of triangle X Y Z.