Prime Path

Description

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
8179

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

3

1033 8179

1373 8017

1033 1033

Sample Output

6

7

0