Let P={(x,y)∣x,y∈{0,1,2,...,2015}} be a set of points on the plane. Straight wires of unit length are placed to connect points in P so that each piece of wire connects exactly two points in P, and each point in P is an endpoint of exactly one wire. Prove that no matter how the wires are placed, it is always possible to draw a straight line parallel to either the horizontal or vertical axis passing through midpoints of at least 506 pieces of wire. combinatoricscombinatorial geometry