Antipodal Points April Long Solution | CodeChef Problem Solution 2022 | April Long Two

Antipodal Points Solution | CodeChef Problem Solution 2022 | April Long Two

You are given a set of N$N$ distinct points P1,P2,P3,…,PN$P_1,P_2,P_3,\dots ,P_N$ on a 2$2$-D plane.

A triplet (i,j,k)$(i,j,k)$ is called a holy triplet if

• 1≤i<j<k≤N$1\le i<j<k\le N$
• Pi$P_i$, Pj$P_j$ and Pk$P_k$ are non-collinear and
• Any two of the points Pi$P_i$, Pj$P_j$ and Pk$P_k$ are antipodal points of the circle that passes through all three of them.

Two points on a circle are said to be antipodal points of the circle if they are diametrically opposite to each other.

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Find the total number of holy triplets.

Solution Click Below:- 

Input Format

• The first line contains a single integer T$T$ - the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer N$N$ - the number of points.
• Each of the next N$N$ lines contains two space separated integers xi$x_i$ and yi$y_i$, denoting the co-ordinates of i$i$-th point Pi$P_i$.

Output Format

For each test case output a single line denoting the number of holy triplets.

Constraints

• 1≤T≤10$1\le T\le 10$
• 3≤N≤2000$3\le N\le 2000$
• Sum of N$N$ over all test cases does not exceed 2000$2000$
• −109≤xi,yi≤109$-{10}^9\le x_i,y_i\le {10}^9$
• All points P1,P2,…,PN$P_1,P_2,\dots ,P_N$ in each test case are distinct.

Sample Input 1 

1
4
0 1
0 -1
1 0
-1 0

Sample Output 1 

4

Explanation

Test case 1: The holy triplets in this case are :

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Holy Triplet(1,2,3)(1,2,4)(1,3,4)(2,3,4)1≤i<j<k≤N✓✓✓✓Non collinear✓✓✓✓Antipodal points1 and 21 and 23 and 43 and 4

Holy Triplet(1,2,3)(1,2,4)(1,3,4)(2,3,4)1≤i<j<k≤N✓✓✓✓Non collinear✓✓✓✓Antipodal points1 and 21 and 23 and 43 and 4