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     

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.

Example

Input:
3
1033 8179
1373 8017
1033 1033

Output:
6
7
0

---

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	noobiesag_0206: 2020-07-18 20:48:27 Beautiful problem :)
	kumar_anubhav: 2020-07-03 14:10:00 Good Problem !! SSSD variant on src to dest with constraint that only one digit will change :)
	adikrmishra_1: 2020-06-24 05:25:39 for solution go to this link *** Edit : no spoil allowed *** Last edit: 2020-06-24 09:11:11
	mercuto: 2020-06-12 12:01:45 Tourist power activated AC in one Go!!!!
	nandadeep_2001: 2020-06-11 18:24:36 a gentle reminder to all pls stop posting comments like "AC in one go!!" ... etc this session is for doubt clarification not for expressing your personal feelings Last edit: 2020-06-11 18:28:17
	kgargdunregret: 2020-06-04 21:03:14 one of the best questions ever
	chaudhary_19: 2020-04-22 19:45:38 There is no impossible case
	upen3103: 2020-04-21 07:38:57 AC in one go!!!
	aman5898: 2020-04-08 18:03:01 Ac: In one go
	ysk99: 2020-04-02 07:55:11 after many attempts solution got accepted . I don't know why they rejected directed graph after many combinations and tried undirected graph got accepted .. anyway enjoyed solving.... (: