A Rubik's Cube is a 3-D combination puzzle. The cube consists of six faces, each of which is covered by nine stickers. The stickers are one of six solid colours: white, red, blue, orange, green, and yellow. Initially, the cube is "scrambled", meaning that each of the nine stickers on each face are a random colour. The goal of the Rubik's cube is to "solve" it, making each face of the cube one specific colour, through a series of rotations.

There are exactly six faces to a Rubik's Cube. Each face can be "rotated" clockwise or counter-clockwise. We will denote each face a number between one and six, and `C`

for a clockwise rotation and `W`

for a counter-clockwise rotation. If we imagine a cube facing directly towards us, face `1`

denotes the face facing towards us, face `2`

the one facing to the left, face `3`

the one facing away, face `4`

the one facing to the right, face `5`

the one facing down, and face `6`

the one facing up. When we rotate a face clockwise, we are imagining as if we are looking directly at the face, and rotating the face to the right. The opposite is true for a counter-clockwise rotation.

You are given a scrambled Rubik's Cube, and a series of rotations that was performed on it. Can you determine if the cube is "solved" after these series of rotations?

#### Input Specification

The first lines will each contain characters. These will denote the colours of the nine stickers on face `1`

. The characters will be one of `W`

,`R`

,`B`

,`O`

,`G`

,`Y`

, denoting white, red, blue, orange, green, and yellow, respectively.

The next lines will follow a similar format as the first lines. These will denote face `2`

.

The next lines will denote the colours on face `3`

.

The next lines will denote the colours on face `4`

.

The next lines will denote the colours on face `5`

.

The next lines will denote the colours on face `6`

.

All faces are given as if you are facing it directly. For faces , they are given with face facing down and face facing up. For faces and , they are given with face facing up and face facing down.

*It is guaranteed that there will be exactly nine of each of the six colours.*

The next line will contain the integer , the number of rotations that was performed. There will be at most operations performed on the cube.

The next lines will each contain a string of the form `FD`

. `F`

is the face that is being rotated, and `D`

is either `C`

for a clockwise rotation or `W`

for a counter-clockwise rotation.

**Note that in this problem, the middle section cannot be rotated directly, only the faces.**

#### Output Specification

Output `Solved!`

if the Rubik's Cube is solved after the rotations, or `Boo!`

if it is not solved.

#### Subtasks

##### Subtask 1 [10%]

There will be no rotations.

##### Subtask 2 [20%]

There will be at most one rotation.

##### Subtask 3 [70%]

No further constraints.

##### Note: you do NOT need to pass the sample test cases to pass some of the subtasks.

#### Sample Input 1

```
WWW
WWW
WWW
RRR
RRR
RRR
BBB
BBB
BBB
OOO
OOO
OOO
GGG
GGG
GGG
YYY
YYY
YYY
1
1C
```

#### Sample Output 1

`Boo!`

#### Explanation For Sample 1

The cube was initially solved, but the one clockwise rotation on face `1`

unsolved it. Boo!

#### Sample Input 2

```
RRB
WWW
RRB
YYY
RRB
YYY
GOO
YYY
GOO
WWW
GOO
WWW
BBO
BBO
BBO
RGG
RGG
RGG
3
6C
5W
1W
```

#### Sample Output 2

`Solved!`

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