Problem Description
Given n points which are in three-dimensional space(without repetition).
Please find out how many distinct Special Tetrahedron among them. A tetrahedron is called Special Tetrahedron if it has two following characters.
At least four edges have the same length.
If it has exactly four edges of the same length, the other two edges are not adjacent.
Input
Intput contains multiple test cases.
The first line is an integer T,1≤T≤20, the number of test cases.
Each case begins with an integer n(n≤200), indicating the number of the points.
The next n lines contains three integers xi,yi,zi, (−2000≤xi,yi,zi≤2000), representing the coordinates of the ith point.
Output
For each test case,output a line which contains"Case #x: y",x represents the xth test(starting from one),y is the number of Special Tetrahedron.
Sample Input
2
4
0 0 0
0 1 1
1 0 1
1 1 0
9
0 0 0
0 0 2
1 1 1
-1 -1 1
1 -1 1
-1 1 1
1 1 0
1 0 1
0 1 1
Sample Output
Case #1: 1
Case #2: 6
