Soon after the peace on Naboo planet had been restored, a gungan DaoDao decided to go hunting. However, he found a strange metal container with an emblem of the Trade Federation on it. DaoDao 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 DaoDao decided to defeat the flies himself and create an indestructible power field around them. For the maximal stability the power field created by DaoDao 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.
Input
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 X_{i}, Y_{i}, Z_{i}— integers with absolute values not exceeding 100. No two flies are located at the same point.
Output
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.
Samples
input  output 

6
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

2
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