# Cocircular Points

Time Limit: 1 Second Memory Limit: 65536 KB

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 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.

## 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.

## Sample Input

7 -10 0 0 -10 10 0 0 10 -20 10 -10 20 -2 4 4 -10000 10000 10000 10000 10000 -10000 -10000 -9999 3 -1 0 0 0 1 0 0

## Sample Output

5 3 2Submit

Source: Latin American Regional Contest 2010