Alignment of the Planets

Actually, this problem is about the alignment of $N$ ($1 \le N \le 770$) cows numbered $1$ to $N$ who are grazing in a field that is about $15000 \times 15000$ units. Every grazing location is on an integer coordinate in a standard $x, y$ grid, with coordinates in the range $0$ to $15000$.

Bessie looks up and notices that she is exactly lined up with Sara and Julie. She wonders how many groups of three aligned cows exist in the field.

Given the locations of all the cows (no two cows occupy the same location), find every set of three cows that are exactly collinear. Sort the cows in each set by ID number, lowest first. Then sort the sets by their three ID numbers, lowest first, breaking ties by the second and third ID numbers.

The first line contains a single integer $N$.

Each of the next $N$ lines contains two space-separated integers, the $x$ and $y$ coordinates of cow $i$ on line $i+1$.

The first line contains the number of sets of three cows that are exactly collinear. If four cows are collinear, they form four such sets.

Each following line contains three space-separated cow ID numbers of a collinear set. The lines are sorted as described above. If no collinear sets exist, nothing is printed after the first line.