18481번 - Five Points 스페셜 저지다국어

문제

You have placed n distinct points on a plane. Then you will draw a half-line starting from each point in a direction chosen uniformly at random and independently from other points. Find the probability that no two half-lines will intersect.

입력

The first line of the input contains a single integer n (2 ≤ n ≤ 5), denoting the number of points.

The i-th of the following n lines contains two integers x_i and y_i (−100 ≤ x_i, y_i ≤ 100), denoting the coordinates of the i-th point.

No two points coincide.

출력

Display the probability that no two half-lines will have a common point. Your answer must be correct to within an absolute or relative error of 10⁻⁹.

제한

힌트