Migrated from Lutece 227 2-Dimensional Rubik's Cube

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Description

Alex loves Rubik's Cube. The $3$-dimensional cubes are so difficult that Alex can only challenge the 2D ones, which have six colors: $W, Y, R, O, G, B$.

Alex names the six faces as $U$(upper), $D$(bottom), $L$(left), $R$(right), $F$(front), $B$(back). The expanded cube will appear like this:

Alex is able to rotate any face $90$ degrees in clockwise or counter-clockwise in a second. $U, D, L, R, F, B$ are used for rotating the corresponding face in clockwise, while $U', D', L', R', F', B'$ are for counter-clockwise.

Now Alex got a Cube, he wants to know the minimum number of steps required for making one state to the other.

Input

The input consists of multiple test cases. The first line of input contains an integer $T$, which is the number of test cases.

Each test case is on $12$ lines. The first $6$ lines indicate the initial state, while the next $6$ lines indicate the destination state, both according to the form of the sample input.

[Technical Specification]

$T$ is an integer, and $T \leq 10$.

You can assume that it is always possible to complete the task.

Output

For each test case, print the minimal steps required on a single line.

Samples

1 
G W
Y G
W G O Y R B O R
Y B R W G B O B
W O
R Y
B B
B B
O O W W R R Y Y
O O W W R R Y Y
G G
G G

10

Resources

The 4th Baidu Cup Central China Invitational