tetrahedron

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

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

Hint

wange2014

Source

2016 Multi-University Training Contest 1

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