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# Cocircular Points

**Timelimit: 6**

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 (-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, 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 |