I. Fruit Ninja
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are playing a 3D version of Fruit Ninja. A strange fruit appears — it is shaped like a tetrahedron, defined by $$$4$$$ points in 3d-space that do not lie on the same plane.

To get a perfect score, you must slice the fruit with a single plane so that the two pieces have exactly equal volume.

The fruit's vertices are:

$$$$$$P_1(x_1,y_1,z_1), P_2(x_2,y_2,z_2), P_3(x_3,y_3,z_3), P_4(x_4,y_4,z_4)$$$$$$

Your task is to output any plane that cuts the tetrahedron into two equal-volume parts.

A plane is written as: $$$ax + by + cz + d = 0$$$

A correct answer is guaranteed to exist, and if there are multiple such slicing planes, you may output any.

Input

The first line contains a single integer $$$T~(T \le 10^4)$$$ — the number of test cases.

For each test case, the input contains four lines. Each line has three integers $$$x_i, y_i, z_i ~(|x_i|, |y_i|, |z_i| \le 10^4)$$$ — the coordinates of the tetrahedron's vertices $$$(P_1, P_2, P_3, P_4)$$$.

Output

For each test case, print four real numbers $$$a, b, c, d$$$ — defining a plane $$$(ax + by + cz + d = 0)$$$ that splits the tetrahedron into two equal volumes. Any of $$$|a|,|b|,|c|,|d|$$$ are bounded by $$$10^{9}$$$.

Your answer is accepted if the absolute or relative error is less than or equal to $$$10^{-6}$$$.

Example
Input
2
0 0 0
0 0 2
0 2 0
2 1 1
1 2 6
2 4 3
2 5 9
1 7 9
Output
0.47778 -3.00000 -2.40000 4.00000
-11.01667 -2.88333 -0.19444 31.45000