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 fourdigit 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
nonprime 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 fourdigit 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 fourdigit
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
