Triangles

$n$ pairwise distinct points in the plane are given ($n \ge 3$). Among them, the number of triangles whose vertices are three distinct points is $\frac{n(n-1)(n-2)}{6}$ (including degenerate triangles, i.e. ones whose three vertices are collinear).

We want to compute the sum of the areas of all such triangles. A region that belongs to several triangles is counted once for each triangle it belongs to. The area of a degenerate triangle (with collinear vertices) is taken to be $0$.

Write a program that reads the coordinates of the points from standard input, computes the sum of the areas of all triangles whose vertices are among the given points, and prints the result to standard output.

The first line contains one integer $n$ ($3 \le n \le 3{,}000$), the number of points. Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ($0 \le x_i, y_i \le 10{,}000$) separated by a single space, the coordinates of the $i$-th point. No coordinate pair $(x_i, y_i)$ appears more than once.

Print the sum of the areas of all the triangles, with exactly one digit after the decimal point. (Because all coordinates are integers, this sum is always a multiple of $0.5$ and is represented exactly with one decimal digit.)