Facebook Hacker Cup 2016 Qualification Round
Problem A: Boomerang Constellations

The night sky can be modeled as an infinite 2D plane. There are N stars at 
distinct positions on this plane, the i-th of which is at coordinates (X[i], 
Y[i]).

A boomerang constellation is a pair of distinct equal-length line segments 
which share a single endpoint, such that both endpoints of each segment 
coincide with a star's location.

Two boomerang constellations are distinct if they're not made up of the same 
unordered pair of line segments. How many distinct boomerang constellations can 
you spot?

INPUT

Input begins with an integer T, the number of nights on which you look out at 
the sky. For each night, there is first a line containing the integer N. Then, 
N lines follow, the i-th of which contains the space-separated integers X[i] 
and Y[i].

OUTPUT

For the i-th night, print a line containing "Case #i: " followed by the number 
of boomerang constellations in the night sky.

CONSTRAINTS

1 ≤ T ≤ 50 
1 ≤ N ≤ 2,000 
-10,000 ≤ X[i], Y[i] ≤ 10,000 

EXAMPLE INPUT

5
3
0 0
0 1
0 3
5
0 0
0 1
0 2
0 3
0 4
4
0 0
0 100
100 0
100 100
4
0 0
-3 4
0 5
-5 0
6
5 6
6 5
7 6
6 7
7 8
8 7

EXAMPLE OUTPUT

Case #1: 0
Case #2: 4
Case #3: 4
Case #4: 3
Case #5: 12

EXPLANATION OF SAMPLE

On the first night, every pair of stars is a unique distance apart, so there 
are no boomerang constellations. On the second night, there are 4 boomerang 
constellations. One of them consists of the line segments (0,0)-(0,2) and 
(0,2)-(0,4).