CN-SMO 2014 Problem 8

Define a figure which is constructed by unit squares "cross star" if it satisfies the following conditions: $(1)$ Square bar $AB$ is bisected by square bar $CD$ $(2)$ At least one square of $AB$ lay on both sides of $CD$ $(3)$ At least one square of $CD$ lay on both sides of $AB$ There is a rectangular grid sheet composed of $38\times 53=2014$ squares,find the number of such cross star in this rectangle sheet