## Magic Squares

Following the success of the magic cube, Mr. Rubik invented its planar version, called magic squares. This is a sheet composed of 8 equal-sized squares:

 1 2 3 4 8 7 6 5

In this task we consider the version where each square has a different color. Colors are denoted by the first 8 positive integers. A sheet configuration is given by the sequence of colors obtained by reading the colors of the squares starting at the upper left corner and going in clockwise direction. For instance, the configuration above is given by the sequence (1,2,3,4,5,6,7,8). This configuration is the initial configuration.

Three basic transformations, identified by the letters 'A', 'B' and 'C', can be applied to a sheet:

• 'A': exchange the top and bottom row,
• 'B': single right circular shifting of the rectangle,
• 'C': single clockwise rotation of the middle four squares.

Below is a demonstration of applying the transformations to the initial squares given above:

A:
 8 7 6 5 1 2 3 4
B:
 4 1 2 3 5 8 7 6
C:
 1 7 2 4 8 6 3 5

All possible configurations are available using the three basic transformations.

You are to write a program that computes a minimal sequence of basic transformations that transforms the initial configuration above to a specific target configuration.

### Input Format

A single line with 8 space-separated integers (a permutation of (1..8)) that describe the target configuration.

### Output Format

On the first line of output, your program must write the length L of the transformation sequence. On the following L lines it must write the sequence of identifiers of basic transformations, one letter in the first position of each line.

### Sample Input

`2 6 8 4 5 7 3 1`

### Sample Output

```7
B
C
A
B
C
C
B```

Point Value: 15 (partial)
Time Limit: 2.00s
Memory Limit: 32M