MCOCIR  Cocircular Points
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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
Output for the sample input
5
3
2
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[Rampage] Blue.Mary:
20101221 02:33:45
My solution has time complexity O(n^3logn). 

David Gómez:
20101220 21:49:10
Can O(N^4) get AC? 

Mahesh Chandra Sharma:
20101215 21:43:36
What is the time limit for C++? 

Shaka Shadows:
20101108 19:32:58
Problem corrected fellows. :) 

.:: Pratik ::.:
20101108 19:26:35
Fortune cookie is correct, can this be corrected?


fortune cookie:
20101108 19:26:35
It seems that the judge input terminates with n=0 or EOF (no zero). 
Added by:  ~!(*(@*!@^& 
Date:  20101104 
Time limit:  1s1.419s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  ACM ICPC2010 – Latin American Regional 