All sides of a polygonal billiard table are in one of two perpendicular directions. A tiny billiard ball rolls out of the vertex $A$ of an inner $90^o$ angle and moves inside the billiard table, bouncing off its sides according to the law “angle of reflection equals angle of incidence”. If the ball passes a vertex, it will drop in and srays there. Prove that the ball will never return to $A$.