The Morning Star

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 2 \cdot 10^5$$$) — the number of points.

Then $$$n$$$ lines follow, each line containing two integers $$$x_i$$$, $$$y_i$$$ ($$$-10^9 \leq x_i, y_i \leq 10^9$$$) — the coordinates of each point, all points have distinct coordinates.

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output a single integer — the number of pairs of points that don't break the compass.

Sample Input:

5
3
0 0
-1 -1
1 1
4
4 5
5 7
6 9
10 13
3
-1000000000 1000000000
0 0
1000000000 -1000000000
5
0 0
2 2
-1 5
-1 10
2 11
3
0 0
-1 2
1 -2

Sample Output:

6
2
6
8
0

Note:

In the first test case, any pair of points won't break the compass:

• The compass is at $$$(0,0)$$$, the morning star is at $$$(-1,-1)$$$: the compass will point $$$\text{SW}$$$.
• The compass is at $$$(0,0)$$$, the morning star is at $$$(1,1)$$$: the compass will point $$$\text{NE}$$$.
• The compass is at $$$(-1,-1)$$$, the morning star is at $$$(0,0)$$$: the compass will point $$$\text{NE}$$$.
• The compass is at $$$(-1,-1)$$$, the morning star is at $$$(1,1)$$$: the compass will point $$$\text{NE}$$$.
• The compass is at $$$(1,1)$$$, the morning star is at $$$(0,0)$$$: the compass will point $$$\text{SW}$$$.
• The compass is at $$$(1,1)$$$, the morning star is at $$$(-1,-1)$$$: the compass will point $$$\text{SW}$$$.

In the second test case, only two pairs of points won't break the compass:

• The compass is at $$$(6,9)$$$, the morning star is at $$$(10,13)$$$: the compass will point $$$\text{NE}$$$.
• The compass is at $$$(10,13)$$$, the morning star is at $$$(6,9)$$$: the compass will point $$$\text{SW}$$$.