You are given four points in space (i.e. $\mathbb {R}^3$). The points are not coplanar. In other words, there is no plane in space that contains all four points.

It is guaranteed that under such assumption, there exists a (unique) sphere whose surface touches all four points. Find the coordinates of the centre of the sphere.

-----Input-----
The input consists of four lines. Line $i$ consists of three integers $x_ i$, $y_ i$, $z_ i$, representing the coordinates $(x_ i, y_ i, z_ i)$ of point $i$.

For all test cases, $-100 \leq x_ i, y_ i, z_ i \leq 100$.

-----Output-----
Output three numbers (not necessarily integers) $x_ c$, $y_ c$, $z_ c$, representing the coordinates $(x_ c, y_ c, z_ c)$ of the centre of the sphere that touches all four points.

Let the jury’s answer be $(x_ j, y_ j, z_ j)$. Your answer will be considered as correct if and only if\[ \sqrt {(x_ j - x_ c)^2 + (y_ j - y_ c)^2 + (z_ j - z_ c)^2} < 10^{-4}. \]

-----Examples-----
Sample Input 1:
0 0 0
1 0 0
0 1 0
0 0 1
Sample Output 1:
0.5 0.5 0.5

Sample Input 2:
-1 0 0
1 0 0
0 1 0
0 0 1
Sample Output 2:
0.0 0.0 -0.0

Source: kattis | Difficulty: HARD


Solutions: