Cocircular Points
By Pablo Ariel Heiber 
Argentina
By Pablo Ariel Heiber Argentina
You probably know what a set of collinear points is: a set of points such that there exists a straight line that passes through all of them. A set of cocircular points is defined in the same fashion, but instead of a straight line, we ask that there is a circle such that every point of the set lies over its perimeter.
The International Collinear Points Centre (ICPC) has assigned you the following task: given a set of points, calculate the size of the largest subset of cocircular points.
Each test case is given using several lines. The first line contains an integer N representing the number of points in the set(1 ≤ N ≤ 100). Each of the next N lines contains two integers X and Y representing the coordinates of a point of the set (-104 ≤ X,Y≤104). Within each test case, no two points have the same location.
The last test case is followed by a line containing one zero.
For each test case, print a single line with a single integer representing the number of points in one of the largest subsets of the input that are cocircular.
| Input Sample | Output Sample |
|
7 |
5 |