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.

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 (−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.

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.

Latin American Regional 2010