ANARC08A  Tobo or not Tobo
The game of Tobo is played on a plastic board designed into a 3X3 grid with cells numbered from 1 to 9 as shown in figure (a). The grid has four dials (labeled 'A' to 'D' in the figure.) Each dial can be rotated in 90 degrees increment in either direction. Rotating a dial causes the four cells currently adjacent to it to rotate along. For example, figure (b) shows the Tobo after rotating dial 'A' once in a clockwise direction. Figure (c) shows the Tobo in figure (b) after rotating dial 'D' once in a counterclockwise direction.
Kids love to challenge each other playing the Tobo. Starting with the arrangement shown in figure (a), (which we'll call the standard arrangement,) one kid would randomly rotate the dials, X number of times, in order to shuffle the board. Another kid then tries to bring the board back to its standard arrangement, taking no more than X rotations to do so. The less rotations are needed to restore it, the better. This is where you see a business opportunity. You would like to sell these kids a program to advise them on the minimum number of steps needed to bring a Tobo back to its standard arrangement.
Input
Your program will be tested on one or more test cases. Each test case is specified on a line by itself. Each line is made of 10 decimal digits. Let's call the first digit Y . The remaining 9 digits are nonzeros and describe the current arrangement of the Tobo in a rowmajor topdown, lefttoright ordering. The first sample case corresponds to figure (c).
The last line of the input file is a sequence of 10 zeros.
Output
For each test case, print the result using the following format:
k. R
where k is the test case number (starting at 1,) is a single space, and R is the minimum number of rotations needed to bring the Tobo back to its standard arrangement. If this can't be done in Y dials or less, then R = 1.
Example
Input:
3413569728
1165432789
0000000000
Output:
1. 2
2. 1
hide comments
masterassassin:
20190612 14:27:05
meet in the middle...try to reach to "123456789" from the start in half of y


ahm_55:
20181018 21:51:51
pre processing


Archit Jain:
20140722 19:59:07
enjoyed solving it


majid:
20090708 17:23:46
Time limit is very very very strict :( . We can't solve it with java. Plz increase time limit ... 

Seckin Can Sahin:
20090704 21:27:51
The problem description is wrong and misleading.


Eigenray:
20090703 04:25:26
Apparently we don't care about the orientations of the numbers even though the diagram makes a point of showing them. That was a bit confusing.

Added by:  Ahmed Aly 
Date:  20090702 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ANARC 2008 