Super Line Segments

All submissions for this problem are available.
You are given n points in 2 D plane. Let us represent the n points by p[1],p[2],....p[n]. No two points have same coordinates and no three points are colinear.
Consider the set of lines L = {L : L is a line segment made by connecting (p[i],p[j]) for all 1 ≤ i,j ≤ n and i!=j}
Two line segments L1 and L2 are said to be related if they intersect at a point which is not an end point of either of segments.
A set of lines L is said to be a ”super” set if it does not contain any two line segments which are related.
Now you wonder what could be the maximum possible size of a "super set" which belongs to L
Input Format
 The first line contains an integer T, representing the number of test cases.
 For each test case, first line will contain a single integer N. Then the next N lines, will contain two space separated integer x[i] and y[i].
Output Format
 The output consists of T lines, each line corresponding to a test case. For each test case, output the maximum possible size of a "super set".
Constraints
1 ≤ N ≤ 10^{5}
10^9 ≤ x[i],y[i] ≤ 10^{9}
Sum of N over all test cases would be ≤ 2*(10^{5})
Sample Input
2
3
0 0
1 0
0 1
4
0 0
0 1
1 0
1 1
Sample Output
3
5
Author:  iopc_admin 
Tags  iopc_admin 
Date Added:  2022014 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP 4.3.2, CPP 4.9.2, GO, JAVA 
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