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2 초 512 MB 1 1 1 100.000%

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.

예제 입력 1

2
0 0
1 1

예제 출력 1

0.7500000000000

예제 입력 2

3
7 8
7 7
8 8

예제 출력 2

0.4303385416667