| 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). | |