Groundhog is very good at depth first search algorithm because of his excellent pruning skills and a pair of big scissors. When there is nothing to do, Groundhog often practices how to use his big scissors.

Today, Groundhog gets a piece of paper. This piece of paper can be seen as a polygon on a two-dimensional plane. The shape of this piece of paper is very peculiar, which satisfies that for any two points on the piece of paper, any point on their line is inside the piece of paper. The piece of paper is fixed by a pushpin with coordinates , which can be rotated freely around the pushpin, but cannot be translated. Groundhog is going to use his big scissors to cut this piece of paper. He chooses a straight line and cuts the paper along this line.

Groundhog's scissors are limited in length, and can only cut one line segment with a length less than or equal to each time. Groundhog wants to show his proficiency in using scissors, so he hopes to cut pieces of paper with one stroke. In order to make this task more exciting and challenging, he would make the paper rotate a random angle around the pushpin. To avoid being embarrassed, Groundhog wanted to calculate the probability that he would not be able to cut a piece of paper at one time. Now he has left the question to you.

Ensure that the line selected by Groundhog does not cross the pushpin. Ensure that no matter how the paper is rotated, the scissors can always cut the paper, that is, the polygon and the straight line intersect.