SDZ is very bored at home recently. He always watches videos of animals such as violent elephants at station B. Just last week, SDZ found a game called "Windmill".The following describes what a "windmill" is.
There are some point (at least two) in the plane. Assume that no three points are collinear. A windmill is a process that starts with a line l going through a single point P in the plane. The line rotated clockwise about the point P until the first time that the line meets some other point in the plane.This point, Q, takes over as the new pivot, and the line now rotates clockwise about Q, until it next meets point.
SDZ found that sometimes the windmill can hit all the points, but sometimes it can't. For example, the windmill has been rotating outside the point, so you can't touch the point inside. SDZ thinks it's amazing, so let it be.
He wants to know which point on the line is when the line L rotates α. We guarantee that there is only one point on the line at the beginning and end.