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 Python3 (judge verdict: Wrong Answer)

import math

n = int(input())
for i in range(n):
    x1, y1, x2, y2, x3, y3 = map(float, input().split())
    a1 = x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2
    a2 = y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2
    px = ((y1 - y3) * a1 - (y1 - y2) * a2) / \
        (2 * (y1 - y3) * (x1 - x2) - 2 * (y1 - y2) * (x1 - x3))
    py = ((x1 - x3) * a1 - (x1 - x2) * a2) / \
        (2 * (x1 - x3) * (y1 - y2) - 2 * (x1 - x2) * (y1 - y3))
    r = math.sqrt(px ** 2 + py ** 2)
    print("{0:.3f} {1:.3f} {2:.3f}".format(px, py, r))