An observatory logs n distinct star positions on an integer sky chart. A trio of stars is called aligned when all three lie on a single straight line. Count how many unordered triples of stars are aligned.
Input format
Line 1: an integer n, the number of stars.
Next n lines: two integers x y, the position of a star. All positions are distinct.
Output format
A single integer: the number of aligned (collinear) triples.
Constraints
- 1 <= n <= 2000
- -1000000 <= x, y <= 1000000
- All star positions are distinct.