### Minimal Circle

Time Limit: 1000 ms Memory Limit: 65536 KiB

#### Problem Description

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 1.41

#### Source

1997-1998 Asia Regional