A puzzle game

Problem code: H1

All submissions for this problem are available.

Johnny has some difficulty memorizing the small prime numbers. So, his computer science teacher has asked him to play with the following puzzle game frequently.

The puzzle is a 3x3 board consisting of numbers from 1 to 9. The objective of the puzzle is to swap the tiles until the following final state is reached:

1 2 3
4 5 6
7 8 9

At each step, Johnny may swap two adjacent tiles if their sum is a prime number. Two tiles are considered adjacent if they have a common edge.

Help Johnny to find the shortest number of steps needed to reach the goal state.

Input

The first line contains t, the number of test cases (about 50). Then t test cases follow. Each test case consists of a 3x3 table describing a puzzle which Johnny would like to solve.

The input data for successive test cases is separated by a blank line.

Output

For each test case print a single line containing the shortest number of steps needed to solve the corresponding puzzle. If there is no way to reach the final state, print the number -1.

Example

Input:
2

7 3 2 
4 1 5 
6 8 9 

9 8 5 
2 4 1 
3 7 6  

Output:
6
-1

Output details

The possible 6 steps in the first test case are described in the following figure:

Date: 2009-09-15
Time limit: 2

s
Source limit: 50000
Languages: C C99 strict C++ PAS gpc PAS fpc JAVA NICE JAR C# C#2 NEM ST ASM D FORT ADA BASH PERL PYTH RUBY LUA ICON PIKE PHP SCM guile SCM qobi LISP sbcl LISP clisp SCALA HASK CAML CLPS PRLG WSPC BF ICK TEXT


Comments

I have my code thats

ankur2136 @ 16 Oct 2009 10:15 PM

I have my code thats perfectly all right running on my laptop.

I dont know whats the problem with ur compiler....

please have a look...

Have you read the FAQ?

triplem @ 17 Oct 2009 02:41 AM

Have you read the FAQ?

I know its not the place to

tarun_kumar @ 13 Dec 2010 09:44 AM

I know its not the place to ask this question: sorry for that.

Can anyone please tell me where can i get explanations to the problems i dont understand??

Like for every contest there is an explanation page, similarly is there any explanation page for the practice problems?

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