HDU 5738 Eureka 2016多校合练contest2

传送门

Professor Zhang draws n points on the plane, which are conveniently labeled by 1,2,...,n. The i-th point is at (xi,yi). Professor Zhang wants to know the number of best sets. As the value could be very large, print it modulo 109+7.

A set P (P contains the label of the points) is called best set if and only if there are at least one best pair in P. Two numbers u and v (u,v∈P,u≠v) are called best pair, if for every w∈P, f(u,v)≥g(u,v,w), where f(u,v)=(xu−xv)2+(yu−yv)2−−−−−−−−−−−−−−−−−−√ and g(u,v,w)=f(u,v)+f(v,w)+f(w,u)2.

Input

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line contains an integer n (1≤n≤1000) -- then number of points.

Each of the following n lines contains two integers xi and yi (−109≤xi,yi≤109) -- coordinates of the i-th point.

Output

For each test case, output an integer denoting the answer.

 

Sample Input

3 3 1 1 1 1 1 1 3 0 0 0 1 1 0 1 0 0

 

Sample Output

4 3 0

题意：

满足题意的点集为共线点集和相同点集，一个集合至少两个点； 

额上面是搜到的题意，其实就是问任意多个在一条直线上点，构成一个集合。问集合数多少。例如，同一条直线有三个点，a,b,c。ab,bc,ac,abc共有四个点集合，这里有方向。

因为有方向，要排个序。因为有相同点的存在，求出相同点多少个，然后从相同点抽取i个点，2^i个，乘上其他在这条直线上的点个数的2^k个。自己单独集合单算。具体公式：(2 m −1−m)+sum((s m −1)∗(2 k −1)) 。公式摘自http://blog.csdn.net/lhfl911/article/details/52004755。

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