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Ural SU contest. Petrozavodsk training camp. Summer 2008

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C. Droid flies

Time limit: 3.0 second
Memory limit: 64 MB
Soon after the peace on Naboo planet had been restored, a gungan Dao-Dao decided to go hunting. However, he found a strange metal container with an emblem of the Trade Federation on it. Dao-Dao regarded it as trash and threw it into the forest. But the very next moment poor gungan was attacked by the whistling hive of droid flies — the modern weapon constructed by the Federation. He had to immediately alarm all gungans! But Dao-Dao decided to defeat the flies himself and create an indestructible power field around them. For the maximal stability the power field created by Dao-Dao must have a cubic shape, moreover, there must be at least one droid fly on each of the faces of the field. Help gungan to position this power field in space.


The first line contains an integer N (2 ≤ N ≤ 100) — the number of droid flies. The following N lines contain the coordinates of the flies Xi, Yi, Zi— integers with absolute values not exceeding 100. No two flies are located at the same point.


Output the coordinates of three normalized vectors collinear to the edges of the required cube. Output the answer as precisely as possible. You can assume that the required power field always exists.


0 1 1
1 0 1
1 1 0
1 1 2
1 2 1
2 1 1
1 0 0
0 1 0
0 0 1
1 0 0
-1 0 0
0.577350269 0.211324865 -0.788675135
0.577350269 0.577350269 0.577350269
0.577350269 -0.788675135 0.211324865
Problem Author: Dmitry Ivankov
Problem Source: Ural SU Contest. Petrozavodsk Summer Session, August 2008
To submit the solution for this problem go to the Problem set: 1672. Droid flies