hackercupai/hackercup huggingface dataset:
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
(**Xi**, **Yi**).

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 **Xi** and **Yi**.

### 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 ≤ **Xi**, **Yi** ≤ 10,000

### 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).