# Minimal Circle

Time Limit: 5 Seconds Memory Limit: 32768 KB

You are to write a program to find a circle which covers a set of points and has the minimal area. There will be no more than 100 points in one problem.## Input

The input contains several problems. The first line of each problem is a line containing only one integer N which indicates the number of points to be covered. The next N lines contain N points. Each point is represented by x and y coordinates separated by a space. After the last problem, there will be a line contains only a zero.

## Output

For each input problem, you should give a one-line answer which contains three numbers separated by spaces. The first two numbers indicate the x and y coordinates of the result circle, and the third number is the radius of the circle. (use escape sequence %.2f)

## Sample Input

2 0.0 0.0 3 0 5 0 0 0 1 1 0 1 1 2 2 0

## Sample Output

1.50 0.00 1.50 1.00 1.00 1.41Submit

Source: Asia 1997, Shanghai (Mainland China)