Migrated from Lutece 121 Guess the Dice

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Description

A regular dice is a cube with $6$ numbers ($1$ to $6$) on its $6$ faces. When you look at a corner of a dice you can see $3$ faces and of course the numbers on them. Now you're given $8$ views from $8$ corners of a dice, and your task is to tell what number is on the opposite side of a given number.

Input

One integer $T$ on the first line indicates the number of cases.

Then followed by $T$ cases, every case contains $8$ lines. Each line contains $3$ integers $A$, $B$, $C$ describing the view from one corner of the dice (look at the picture for details).

It's not guaranteed that the order of the $8$ views is given in the same way as the sample input.

Output

For each case, print $6$ integers separated by space on a line. The $i$-th number indicates the number on the opposite side of $i$.

Samples

1
1 2 3
1 3 4
1 4 5
1 5 2
6 3 2
6 4 3
6 5 4
6 2 5

6 4 5 2 3 1

Resources

The 8th UESTC Programming Contest Final