Problem:
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Circumscribed Circle of A Triangle.

Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.

Input

Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$

in a line. All the input are real numbers.

Output

For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.

Constraints

$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$

$ n \leq 20$

Sample Input

1
0.0 0.0 2.0 0.0 2.0 2.0

Output for the Sample Input

1.000 1.000 1.414

Solution in JavaScript (judge verdict: Accepted)

require("fs").readFileSync("/dev/stdin","utf8").split('\n').map(function(i){j=i.split(' ');if(j[1])a=j[0],b=j[1],c=j[2],d=j[3],e=j[4],f=j[5],g=a*a,h=b*b,k=c*c,l=d*d,m=e*e,n=f*f,o=a-c,r=b-d,s=b-f,t=a-e,p=(s*(h-l+g-k)-r*(h-n+g-m))/(2*s*o-2*r*t),q=(t*(g-k+h-l)-o*(g-m+h-n))/(2*t*r-2*o*s),console.log(p.toFixed(3),q.toFixed(3),Math.sqrt((a-p)*(a-p)+(b-q)*(b-q)).toFixed(3))})