Drawing Lines

There is an infinite sheet of paper and a pen. At any time, the pen may be placed above a point $(x, y)$ on the paper or touching it at a point $(x, y)$; in both cases, we call the point $(x, y)$ the *position* of the pen. The initial position of the pen is $(0, 0)$. You may perform the following types of actions: - move the pen down until it touches the paper - lift the pen (if it was touching t