n pairwise disjoint points in the plane are given (n ≥ 3). There are n*(n−1)*(n−2)/6 triangles whose vertices
are some pairwise different points among them (including degenerate triangles, i.e. ones whose vertices are
collinear).
We want to calculate the sum of areas of all the triangles with vertices in the given points.
Those parts of the plane that belong to many triangles are to be calculated multiple times. We assume that
the area of degenerate triangles (i.e. those with collinear vertices) is zero.
Write a program that:
There are multiple test cases in the input file. For each test case:
In the first line of the standard input there is one integer n (3 ≤ n ≤ 3000) denoting the number of selected
points. Each of the following n lines contains two integers xi and yi (0 ≤ xi,yi ≤ 10000) separated by a
single space and denoting the coordinates of the i-th point (for i= 1,2, ..., n). No pair (ordered) of coordinates
appears more than once.
For each test case please output one real number equal to the sum of the areas of all the triangles with vertices in the given points. The outcome should be printed out with exactly one digit after dot. There is no need to print any blank lines between test cases.
5 0 0 1 2 0 2 1 0 1 1 3 0 0 2 2 0 2
7.0 2.0
Migrated from old NTUJ.
POI 15th Stage III
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