| 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. | |