hackercupai/hackercup huggingface dataset:
While en route to the 295th annual Galactic Dance Party on Risa, you find
yourself unceremoniously yanked out of hyperspace and, according to your
sensors, surrounded by **N** space bombs. Apparently caught in a trap laid out
by some dastardly and unknown enemy, and unable to return to hyperspace, you
must find the safest place in the vicinity to weather the detonation of all
the space bombs. Your unseen opponent has constructed a cube-shaped space
anomaly that you are unable to leave, so your options are limited to points
within that cube.

Before the bombs explode (all simultaneously), you have just enough time to
travel to any integer point in the cube [0, 0, 0]-[1000, 1000, 1000], both
inclusive. You must find the point with the maximum distance to the nearest
bomb, which your captain's intuition tells you will be the safest point.

## Input

The first line of the input file consists of a single number **T**, the number
of test cases. Each test consists of single number **N**, the number of bombs,
followed by **3*N** integers describing the positions of the bombs.

## Output

Output **T** integers, one per test case each on its own line, representing
the square of distance to the nearest bomb from the safest point in the cube.

## Constraints

**T** = 50
1 ≤ **N** ≤ 200
All bombs coordinates will be in [0, 1000], both inclusive.