Droid Flies
"'markdown After peace was restored on the planet Naboo, a Gungan named Dao-Dao went hunting. Near a lake, he stumbled upon a peculiar metal container marked with the Trade Federation's emblem. Mistaking it for trash, Dao-Dao threw it deeper into the forest. Moments later, a swarm of droid flies, the Federation's latest military innovation, emerged from the forest with a metallic screech, attacking Dao-Dao. It was crucial to alert the other Gungans! However, Dao-Dao chose to confront the flies alone by trapping the entire swarm within an impenetrable force field. For optimal stability, Dao-Dao's force field must be cubic, with at least one droid fly touching each face of the cube. Assist the Gungan in determining how to position the force field in space.
Input
The first line contains an integer N (2 ≤ N ≤ 100) — the number of droid flies. The next N lines provide the coordinates of the flies X_i, Y_i, Z_{i } — integers with absolute values not exceeding 100. No two flies share the same coordinates.
Output
Output the coordinates of three normalized vectors that are collinear with the sides of the desired cube. The numbers should be presented with the highest possible precision. It is guaranteed that any swarm of droid flies can be enclosed in a force field meeting the problem's conditions. "'