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ZOJ Problem Set - 2821
Cubic Eight-Puzzle

Time Limit: 5 Seconds      Memory Limit: 32768 KB

Let��s play a puzzle using eight cubes placed on a 3 �� 3 board leaving one empty square.

Faces of cubes are painted with three colors. As a puzzle step, you can roll one of the cubes to a adjacent empty square. Your goal is to make the specified color pattern visible from above by a number of such steps.

The rules of this puzzle are as follows.

  1. Coloring of Cubes: All the cubes area colored in the same way as shown in Figure 1. The opposite faces have the same color.

    Figure 1: Coloring of a cube

  2. Initial Board State: Eight cubes are placed on the 3 �� 3 board leaving one empty square. All the cubes have the same orientation as shown in Figure 2. As shown in the figure, squares on the board are given x and y coordinates, (1, 1), (1, 2), ��, and (3, 3). The position of the initially empty square may vary.

    Figure 2: Initial board state

  3. Rolling Cubes: At each step, we can choose one of the cubes adjacent to the empty square and roll it into the empty square, leaving the original position empty. Figure 3 shows an example.

    Figure 3: Rolling a cube

  4. Goal: The goal of this puzzle is to arrange the cubes so that their top faces form the specified color pattern by a number of cube rolling steps described above.

Your task is to write a program that finds the minimum number of steps required to make the specified color pattern from the given initial state.

Input

The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets is less than 16. Each dataset is formatted as follows.

x y
F11 F21 F31
F12 F22 F32
F13 F23 F33

The first line contains two integers x and y separated by a space, indicating the position (x, y) of the initially empty square. The values of x and y are 1, 2, or 3.

The following three lines specify the color pattern to make. Each line contains three characters F1j, F2j, and F3j, separated by a space. Character Fij indicates the top color of the cube, if any, at the position (i, j) as follows:

B: Blue,

W: White,

R: Red,

E: the square is Empty.

There is exactly one ��E�� character in each dataset.

Output

For each dataset, output the minimum number of steps to achieve the goal, when the goal can be reached within 30 steps. Otherwise, output ��-1�� for the dataset.

Sample Input

1 2 
W W W 
E W W 
W W W 
2 1 
R B W 
R W W 
E W W 
3 3 
W B W 
B R E 
R B R 
3 3 
B W R 
B W R 
B E R 
2 1 
B B B 
B R B 
B R E 
1 1 
R R R 
W W W 
R R E 
2 1 
R R R 
B W B 
R R E 
3 2 
R R R 
W E W 
R R R
0 0

Sample Output

0 
3 
13 
23 
29 
30 
-1 
-1

Source: Asia Regional Contest, Yokohama, 2006
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