You are given a set of $N distinct points P_{1}, P_{2}, P_{3}, \ldots, P_{N} on a 2-D$ plane.

A triplet (i, j, k) is called a holy triplet if
1 ≤ i < j < k ≤ N
P_{i}, P_{j} and P_{k} are non-collinear and
Any two of the points P_{i}, P_{j} and 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.

Find the total number of holy triplets.

------ Input Format ------

• The first line contains a single integer T - the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer N - the number of points.
• Each of the next N lines contains two space separated integers x_{i} and y_{i}, denoting the co-ordinates of i-th point P_{i}.

------ Output Format ------

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

------ Constraints ------

$1 ≤ T ≤ 10$
$3 ≤ N ≤ 2000$
- Sum of $N$ over all test cases does not exceed $2000$
$-10^{9} ≤ x_{i}, y_{i} ≤ 10^{9}$
- All points $P_{1}, P_{2}, \ldots, P_{N}$ in each test case are distinct.

----- Sample Input 1 ------
1
4
0 1
0 -1
1 0
-1 0
----- Sample Output 1 ------
4
----- explanation 1 ------
Test case 1: The holy triplets in this case are
$$ \begin{array}{|c|c|c|c|} \hline \textbf{Holy Triplet} & 1 ≤ i < j < k ≤ N & \textbf{Non collinear} & \textbf{Antipodal points} \\ \hline (1, 2, 3) & \checkmark & \checkmark & 1 \text{ and } 2 \\ \hline (1, 2, 4) & \checkmark & \checkmark & 1 \text{ and } 2 \\ \hline (1, 3, 4) & \checkmark & \checkmark & 3 \text{ and } 4 \\ \hline (2, 3, 4) & \checkmark & \checkmark & 3 \text{ and } 4 \\ \hline \end{array} $$

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