Maximum Number of Colinear Points

Input contains several test cases. Each test case begins with an integer $n$ ($1 \leq n \leq 1000$). Then follow a list of n points, one per line, each of the form $x\ y$. Coordinates are integer with absolute value bounded by 10000. The given points are all distinct. The input is terminated by a case beginning with 0.

For each test case, output the maximum number of simultaneously colinear points in the given set of points.

Sample Input 1 | Sample Output 1 |
---|---|

3 0 0 10 0 0 10 1 20 20 6 50 50 60 55 70 60 80 65 50 40 50 30 0 |
2 1 4 |