Five Points
시간 제한2초메모리 제한512 MB
서로 다른 점이 최대 다섯 개 주어지고, 각 점에서 독립적으로 균등한 방향의 반직선을 그을 때 두 반직선이 만나지 않을 확률을 구한다.
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 xi and yi (−100 ≤ xi, yi ≤ 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.