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# Cocircular Points

By Pablo Ariel Heiber Argentina

Timelimit: 6

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.

## 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 (-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.

## Output

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 -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 5 3 2