There are nine clocks on a $3 \times 3$ array labeled **A** to **I**.The goal is to return all the dials to **12 o'clock** with as few moves as possible.

There are nine different allowed ways to turn the dials on the clocks. Each such way is called a move. Select for each move a number 1 to 9. That number will turn the dials 90' (degrees) clockwise on those clocks which are affected according to the table below.

Move | Affected clocks |

1 | ABDE |

2 | ABC |

3 | BCEF |

4 | ADG |

5 | BDEFH |

6 | CFI |

7 | DEGH |

8 | GHI |

9 | EFHI |

For the configuration in the picture above, let $L$ be the shortest possible sequence of moves that will lead to all the clocks being $12$ o'clock. Off all possible values of $L$,what is the smallest **prime** value of $L$?

**Explanatory examples**

We do not care about the clocks minute hand in this problem. A clock at

**6**after one move(rotated clock wise) becomes**9**and a clock at**12**after one move becomes**3**and so on.If the sequence of moves had been $L=$ $1$ and $3$, the answer would have been $13$ instead of $31$ because it is the smallest prime value of $L$.

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