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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.
