4741 - [Usaco2016 Dec]Lots of Triangles

Farmer John is thinking of selling some of his land to earn a bit of extra income. His property cont ains n trees (3≤N≤300), each described by a point in the 2D plane, no three of which are collinear . FJ is thinking about selling triangular lots of land defined by having trees at their vertices; th ere are of course L =C(n,3)such lots he can consider, based on all possible triples of trees on his property.A triangular lot has value v if it contains exactly v trees in its interior (the tr ees on the corners do not count, and note that there are no trees on the boundaries since no three t rees are collinear). For every v = 0 \ldots N-3, please help FJ determine how many of his L potentia l lots have value v. 农夫约翰打算卖掉一些土地来获得额外的收入。他的土地上有N颗树(3 ≤ N ≤ 300)，可以看做一个平面上的点， 并且没有三点在一条直线上。约翰打算出售一块由三棵树构成的三角形土地，当然这样一共有L =C(n,3)种 可能性。如果一个三角形内部有v个点（不含边界），那么这块土地的价值为v。请帮助约翰统计当v = 0 ... N-3 时，分别有多少块三角形土地价值为v。

The first line of input contains N. The following N lines contain the x and y coordinates of a single tree; these are both integers in the range 0 \ldots 1,000,000.

Output N-2 lines, where output line i contains a count of the number of lots having value i-1.