## Evan's Cube

Points: 12 (partial)
Time limit: 1.0s
Memory limit: 128M

Author:
Problem type
Allowed languages
Java

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 colous: 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 $$Q$$ rotations that was performed on it. Can you determine if the cube is "solved" after these series of rotations?

Online Rubik's Cube Simulator

#### Input Specification

The first $$3$$ lines will each contain $$3$$ 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 $$3$$ lines will follow a similar format as the first $$3$$ lines. These will denote face 2.

The next $$3$$ lines will denote the colours on face 3.
The next $$3$$ lines will denote the colours on face 4.
The next $$3$$ lines will denote the colours on face 5.
The next $$3$$ lines will denote the colours on face 6.

All faces are given as if you are facing it directly. For faces $$1-4$$, they are given with face $$5$$ facing down and face $$6$$ facing up. For faces $$5$$ and $$6$$, they are given with face $$1$$ facing up and face $$3$$ facing down.

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

The next line will contain the integer $$Q$$, the number of rotations that was performed. There will be at most $$50$$ operations performed on the cube.

The next $$Q$$ 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.

There will be no rotations. $$(Q = 0)$$

There will be at most one rotation. $$(Q \le 1)$$

No further constraints.

#### 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!