A surveyor places n distinct markers at integer coordinates. Determine the largest number of markers that lie on one straight line. A single marker counts as 1, and any two distinct markers always share a line (count 2).
Input format
Line 1: an integer n, the number of markers.
Next n lines: two integers x y, the position of a marker. All positions are distinct.
Output format
A single integer: the maximum number of markers on any one line.
Constraints
- 1 <= n <= 2000
- -1000000 <= x, y <= 1000000
- All marker positions are distinct.