Cocircular Points
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 larger subset of cocircular points.
Input
Each test case is given using several lines. The first line contains an integer n (1 ≤ n ≤ 100) representing the number of points in the set. Each of the next n lines contains two integers x and y representing the coordinates of a point of the set (−10^4 ≤ x, y ≤ 10^4). Within each test case, no two points have the same location.
The last test case is followed by a line containing one zero.
Output
For each test case output a single line with a single integer representing the number of points in one of the largest subsets of the input that are cocircular.