Prime Cut 4

Waahahaha, I'm a Wario!

I need your help to win a game. I have steak that is in the shape of a rectangular prism with an arbitrary position, rotation and scale. I want to cut the steak into $2$ pieces with a flat cut such that the volume of the pieces are equal. But, the Laser-cutter-$3000$ I got Penny to make cannot rotate, and always cuts the steak on the YZ plane.

I can define an $x_i$ value for the laser cutter such that the steak is cut by the plane $x = x_i$.

Can you find the value of $x_i$ such that the plane $x = x_i$ will bisect the steak?

Input

There are $8$ lines, one for each vertex of the steak.

Each line has $3$ integers, $x y z$, giving the $3$-dimensional coordinate of the vertex.

It is guaranteed these $8$ coordinates form the vertices of a rectangular prism.

Output

Give me the x-value of the plane that divides the steak in $2$. Answers with a relative or absolute error less than $10^{-3}$ will be accepted.

Constraints

• $-10^4 \le x, y, z \le 10^4$

Example 1

0 0 0
0 0 1
0 1 0
1 0 0
0 1 1
1 0 1
1 1 0
1 1 1

0.5

Here is a diagram of the prism and the plane that bisects it.

Example 2

0 4 0
3 0 0
3 0 6
7 3 6
7 3 0
4 7 0
0 4 6
4 7 6

3.5

Here is a diagram of the rotated prism and the plane that bisects it.