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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	manohar_4139: 2016-06-07 16:59:01 AC in one go..) nice problem
	ajay_5097: 2016-05-26 16:11:07 My first on BFS !! Nice one :) Last edit: 2016-05-26 16:11:36
	hulk_baba: 2016-05-25 00:00:02 It's not necessary that the transitioning prime number lies between the 2 numbers, it may be greater. so be careful while bfs;
	vijay kumar paliwal: 2016-05-23 13:32:11 M Lovin' It!
	Sơn Tùng M-TP: 2016-05-15 22:28:59 Easy problem! :) BFS
	rraj001: 2016-05-15 12:21:45 nice problem,AC in one go!!!
	dwij28: 2016-04-11 08:26:36 Bfs and Sieve of Eratosthenes.. :) Time limit and test cases are very lenient so it passes even if algorithm for checking single digit difference takes 0(n^2), where n is the no. of 4 digit primes..
	karthik1997: 2016-03-23 14:33:41 Simple Sieve and a BFS . Ac in one go . Learnt the importance of implementation rather than the algo :P
	hardik agrawal: 2016-02-27 13:36:20 nice problem :D
	dhumketu: 2016-01-27 15:51:46 Literally Nothing is IMPOSSIBLE!! :D Didn't even consider a possibility of impossible.