The university of Algoland is located in a single huge building. It is great. It is the best building in the world. It only uses the best angles: the right angle! But the building is so huge that it is also very confusing to new students, because it is very easy to get lost.

The rector of Algoland's university, a former professor in physics, had a great idea to prevent students from getting lost in the future: He bought an incredibly strong magnet with the intention of placing it somewhere inside the building and using it as an emergency meeting point. On the first day of the semester, every student gets a free compass. With that compass the student can always tell the direction towards the magnet (the magnet is so strong that it completely dominates the earth's magnetic field). If a student gets lost, she can follow the following simple procedure to get to the emergency meeting point at the magnet's location:

• Move straight into the direction towards the magnet until you either reach the magnet, or bump into a wall.
• If your path is blocked by a wall, follow the direction alongside the wall that brings you closer towards the magnet, until you either reach the end of the wall or your path becomes orthogonal to the compass direction.
• If the wall is perfectly orthogonal to the compass direction, or you end up in a corner, you are stuck. Scream as loud as you can!

In the corner case where you want to walk parallel to a wall at the exact coordinate of a wall, you are not stopped by the wall. We assume here that you are infinitesimally small (which is true in proportion to the size of the building).

The rector now wants your help to place the magnet inside the building in such a way that every student can reach it (following the procedure above) no matter where inside the building the student gets lost. Actually, you just have to decide if this is possible or not.