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Problem 1076. -- Color Hash

## Color Hash

Time Limit: 1 Sec  Memory Limit: 64 MB
Submit: 1  Solved: 0
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## Description

This puzzle consists of two wheels. Both wheels can rotate clockwise and counterclockwise. They contain 21 colored pieces, 10 of which are rounded triangles and 11 of which are separators. The left panel in figure shows the final puzzle position. Note that to perform a one-step rotation you must turn the wheel until you have advanced a triangle and a separator. Figure: Final puzzle configuration (l), with the puzzle after rotating the left wheel on step clockwise from the final configuration (r). Your job is to write a program that reads the puzzle configuration and prints the minimum sequence of movements required to reach the final position. We will use the following integer values to encode each type of piece: 0 gray separator 1 yellow triangle 2 yellow separator 3 cyan triangle 4 cyan separator 5 violet triangle 6 violet separator 7 green triangle 8 green separator 9 red triangle 10 red separator A puzzle configuration will be described using 24 integers; the first 12 describe the left wheel configuration; the last 12, the right wheel. The first integer represents the bottom right separator of the left wheel and the next 11 integers describe the left wheel clockwise. The 13th integer represents the bottom left separator of the right wheel and the next 11 integers describe the right wheel counterclockwise. The final position is therefore encoded 0 3 4 3 0 5 6 5 0 1 2 1 0 7 8 7 0 9 10 9 0 1 2 1 If we rotate the left wheel clockwise one position from the final configuration (as shown in the right-hand figure) the puzzle configuration would be encoded 2 1 0 3 4 3 0 5 6 5 0 1 0 7 8 7 0 9 10 9 0 5 0 1

## Input

Input for your program consists of several puzzles. The first line of the input will contain an integer n specifying the number of puzzles. There will then be n lines, each containing 24 integers separated with one white space, describing the initial puzzle configuration as explained above.

## Output

For each configuration, your program should output one line with just one number representing the solution. Each movement is encoded using one digit from 1 to 4 in the following way: 1 Left Wheel Clockwise rotation 2 Right Wheel Clockwise rotation 3 Left Wheel Counterclockwise rotation 4 Right Wheel Counterclockwise rotation No space should be printed between each digit. Since multiple solutions could be found, you should print the solution that is encoded as the smallest number. The solution will never require more than 16 movements. If no solution is found you should print, ``NO SOLUTION WAS FOUND IN 16 STEPS". If you are given the final position you should print, ``PUZZLE ALREADY SOLVED".

## Sample Input

```3
0 3 4 3 0 5 6 5 0 1 2 1 0 7 8 7 0 9 10 9 0 1 2 1
0 3 4 5 0 3 6 5 0 1 2 1 0 7 8 7 0 9 10 9 0 1 2 1
0 9 4 3 0 5 6 5 0 1 2 1 0 7 8 7 0 9 10 3 0 1 2 1

```

## Sample Output

```PUZZLE ALREADY SOLVED
1434332334332323
NO SOLUTION WAS FOUND IN 16 STEPS```

## Source

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