# Problem F

Prime Path

— 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$\ldots $

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 8179

The 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`”.

Sample Input 1 | Sample Output 1 |
---|---|

3 1033 8179 1373 8017 1033 1033 |
6 7 0 |