Suppose you place commands "turn left" or "turn right" in some points with integer coordinates (on a plane). Then, a robot is placed at $(0; 0)$. The robot begins to move in the positive direction of X-axis and when it gets into a point where a command is written it turns by $90^\circ$ and begins to move in the new direction. When it gets to a point with no command it just continues to move straight.
Suppose the commands are written so that the robot visits all points with integer coordinates.
Now, you can delete commands from points. The question is: can you always delete just one command so that the property "the robot visits all points" breaks? If not, what is the minimum number of points which should be tampered with to achieve this?
Any hints are welcome.