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## PPATH - Prime Path |

The ministers of the cabinet were quite upset by the
message from the Chief of Security stating that they
would all have to change the four-digit room numbers
on their offices.

— It is a matter of security to change such things
every now and then, to keep the enemy in the dark.

— But look, I have chosen my number 1033 for good
reasons. I am the Prime minister, you know!

— I know, so therefore your new number 8179 is also
a prime. You will just have to paste four new
digits over the four old ones on your office door.

— No, it's not that simple. Suppose that I change the
first digit to an 8, then the number will read 8033
which is not a prime!

— I see, being the prime minister you cannot stand
having a non-prime number on your door even for a
few seconds.

— Correct! So I must invent a scheme for going from
1033 to 8179 by a path of prime numbers where
only one digit is changed from one prime to the
next prime.

Now, the minister of finance, who had been eavesdropping,
intervened.

— No unnecessary expenditure, please! I happen to
know that the price of a digit is one pound.

— Hmm, in that case I need a computer program to
minimize the cost. You don't know some very cheap
software gurus, do you?

— In fact, I do. You see, there is this programming
contest going on...

Help the prime minister to find the cheapest prime path between any two given four-digit primes! The first digit must be nonzero, of course. Here is a solution in the case above.

1033 1733 3733 3739 3779 8779 8179The cost of this solution is 6 pounds. Note that the digit 1 which got pasted over in step 2 can not be reused in the last step – a new 1 must be purchased.

### Input

One line with a positive number: the number of test cases (at most 100). Then for each test case, one line with two numbers separated by a blank. Both numbers are four-digit primes (without leading zeros).

### Output

One line for each case, either with a number stating the minimal cost
or containing the word `Impossible`.

### Example

Input:3 1033 8179 1373 8017 1033 1033Output:6 7 0

Added by: | overwise |

Date: | 2007-10-02 |

Time limit: | 2s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |

Resource: | ACM ICPC NWERC 2006 |