Winning Strategy for 5467500000-Cube Chocolate Bar Game

[ghostfirefox]

Consider the following game. Two players alternately break vertical or horizontal lines from a rectangular chocolate bar. In each move the player can break one or two lines, either vertical on the right or horizontal from below. The chocolate bar in the upper left corner of the plate is poisoned. The player forced to take her loses. How many different rectangular chocolate bars of 5467500000 cubes, for which the first player has a winning strategy (tablets of sizes n × m and m × n are considered the same)?