Green triangle
Due to a shortage of volunteers at the olympiad, the jury members were also tasked with decorating the hall for the closing ceremony. As part of this effort, the zebra named Hippo was given the job of drawing a green triangle.
Hippo's plan is as follows: On a plane, there are N distinct points, none of which are collinear. Hippo will randomly select three different points, form a triangle using these points as vertices, and paint it green. The amount of green paint needed to paint a triangle with an area of s is exactly s milliliters. Your task is to calculate the expected amount of paint that Hippo will use.
Input
The first line of the input contains an integer N (3 ≤ N ≤ 2000), representing the number of points. Each of the following N lines contains two integers x_i and y_i (0 ≤ x_i, y_i ≤ 10^9), separated by a space, which are the coordinates of the i-th point. It is guaranteed that no three points are collinear.
Output
Output the expected amount of paint that Hippo will use to paint the triangle, with an absolute or relative precision of at least 10^{-9}.