class CoordinateSystem implements Serializable {

	public short at(int r, int c) {
		assert isValidOneDimensionalCoordinate(r) : "Invalid row: " + r;
		assert isValidOneDimensionalCoordinate(c) : "Invalid column: " + c;
		return (short) ((r + 1) * south + (c + 1) * EAST);
	}

	private  CoordinateSystem(int width);

}