[Usaco2016 Dec]Lots of Triangles

时间限制:10s      空间限制:128MB

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.
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。


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.


样例输入

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

样例输出

28
6
1
0
0

提示

没有写明提示


题目来源

Platinum 鸣谢Firstlast提供译文