Minimal Circle

Input

The input consists of several test cases. Each test case begins with an integer $N$, the number of points. The next $N$ lines each contain two numbers representing the $x$ and $y$ coordinates of a point, separated by a space. The end of input is marked by a line containing a single $0$.

Output

For each test case, output one line with the $x$ and $y$ coordinates of the center and the radius of the minimal covering circle, separated by spaces. Print all values with exactly $2$ digits after the decimal point.

Examples