tetrahedron

Problem Description

Given four points ABCD, if ABCD is a tetrahedron, calculate the inscribed sphere of ABCD.

Input

Multiple test cases (test cases $\leq 100$). Each test cases contains a line of 12 integers $[-1e6, 1e6]$ indicate the coordinates of four vertices of ABCD. Input ends by EOF.

Output

Print the coordinate of the center of the sphere and the radius, rounded to 4 decimal places. If there is no such sphere, output "O O O O".

Sample Input

0 0 0 2 0 0 0 0 2 0 2 0
0 0 0 2 0 0 3 0 0 4 0 0

Sample Output

0.4226 0.4226 0.4226 0.4226
O O O O

Author

HIT

Source

2016 Multi-University Training Contest 1