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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	sg: 2014-09-23 17:01:16 nice one!!
	Kartik Khare: 2014-08-23 13:09:39 AC in first go..Used STL and graphs Last edit: 2014-08-23 13:09:51
	Ajay Prasadh: 2014-08-12 07:45:31 Excellent question :D
	|RAMSDEN|: 2014-08-02 11:07:42 Nice problem:) AC at first attempt Last edit: 2014-08-02 11:08:23
	Kennethnlogn: 2014-07-23 16:04:40 MY SOLUTION SHOWS TLE ON MY SUBMISSION HOWEVER WHEN I SUBMITTED ON UVA AND GOT AC. WHAT COULD BE THE PROBLEM HERE?
	Somesh Maurya™: 2014-07-02 08:05:54 Go for LUCKYNUM And ONEZERO after this...
	NARUTO (y): 2014-06-15 22:16:17 @Kashish Mittal for 1373 8017 ans is 7 if u consider MSD 0 also then 5 came that is wrong because in question it is written that "The first digit must be nonzero" Last edit: 2014-06-15 22:17:19
	kancha: 2014-06-10 07:37:53 ans of 2nd test case is 5 .. ? i got ac with 5 .. and bruteforce also giving same i.e 5 for 1033 8017 please check this
	(Tjandra Satria Gunawan)(曾毅昆): 2014-05-09 12:04:28 Small Graph :)
	Bharath Reddy: 2014-04-02 14:43:41 Good problem... Straight Forward