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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.
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.
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.
7 3 2
4 1 5
6 8 9
9 8 5
2 4 1
3 7 6