Farmer John is going to build a new rectangular barn. But the 4 corners of  
the barn mustn't be on soft soil. He examined the ground and found that  
there are only N (4 <= N <= 1,000) appropriate points for the corners. He
wants to know the number of possible ways to build the new barn.
 
Given the points, help him find the answer.
 
INPUT FORMAT:
 
Input exactly contains 10 test cases each of them as follows:
 
* Line 1: A single integer, N.
 
* Lines 2..N+1: Each line has two space-separated integers x, y which
        are the coordinates  of a point. The magnitude of the
        coordinates is not more than 16,000. All points will be
        distinct.
 
SAMPLE INPUT :
 
8
1 2
1 -2
2 1
2 -1
-1 2
-1 -2
-2 1
-2 -1
 
[and 9 more Test cases ....]
 
OUTPUT FORMAT:
 
For each Test case print one line contains:
 
* The number of possible ways to build the new barn.
 
SAMPLE OUTPUT :
 
6
 
[and 9 more Test cases ....]
 
OUTPUT DETAILS:
 
the answers are: {1,2,6,5}, {1,3,6,8}, {1,4,6,7}, {2,3,5,8}, {2,4,5,7},
{3,4,8,7}