In geometry, collinearity is a property of a set of points, specifically, the property of lying on a single line. A set of points with this property is said to be collinear (often misspelled as colinear).
---Wikipedia
Today, Collinearity takes revenge on you. Given a set of N points in two-dimensional coordinate system, you have to find how many set of <P
i, P
j, P
k> from these N points are collinear. Note that <P
i, P
j,
P
k> cannot contains same point, and <P
i, P
j, P
k> and <P
i, P
k, P
j> are considered as the same set, i.e. the order in the set doesn’t matter.
The first line contains a single integer T, indicating the number of test cases.
Each test case begins with an integer N, following N lines, each line contains two integers Xi and Yi, describing a point.
[Technical Specification]
1. 1 <= T <= 33
2. 3 <= N <= 1 000
3. -1 000 000 000 <= Xi, Yi <= 1 000 000 000, and no two points are identical.
4. The ratio of test cases with N > 100 is less than 25%.
For each query, output the number of three points set which are collinear.
2
3
1 1
2 2
3 3
4
0 0
1 0
0 1
1 1
