Lots of Triangles#10565
Farmer John is thinking about selling some of his land to earn some extra income. His property contains trees, each represented by a point in the 2D plane, with no three trees being collinear. FJ is considering selling triangular plots of land whose vertices are trees. There are, of course, L = n \cdot (n - 1) \cdot (n - 2) / 6 such plots to consider, corresponding to all possible triples of trees on his property.
A triangular plot has value if it contains exactly trees in its interior. Trees at the vertices are not counted, and there are no trees on the boundary since no three trees are collinear.
For every from to n - 3, please help FJ determine how many of his possible plots have value .
The first line contains an integer n~(3 \le n \le 300). The following lines each contain the and coordinates of a single tree. Both coordinates are integers in the range from to 10^6.
Print n - 2 lines. The -th line should contain the number of plots having value i - 1.
Example 1