CF528E Triangles 3000

Description

You are given a set $ L={l_{1},l_{2},...,l_{n}} $ of $ n $ pairwise non-parallel lines on the Euclidean plane. The $ i $ -th line is given by an equation in the form of $ a_{i}x+b_{i}y=c_{i} $ . $ L $ doesn't contain three lines coming through the same point. A subset of three distinct lines is chosen equiprobably. Determine the expected value of the area of the triangle formed by the three lines.

Input Format

N/A

Output Format

N/A

Explanation/Hint

A sample from the statement is shown below. There are four triangles on the plane, their areas are $ 0.25,0.5,2,2.25 $ . ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF528E/450ecf6bf6b7d8bf32be30846155196ebe3c9f35.png)