# [Usaco2016 Dec]Lots of Triangles

### 题目描述

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.

### 输入格式

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.

### 输出格式

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

```7
3 6
17 15
13 15
6 12
9 1
2 7
10 19```

```28
6
1
0
0```

### 题目来源

Platinum 鸣谢Firstlast提供译文