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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	garry_555: 2019-08-13 22:26:29 nyc qs on BFS! use sieve for prime :D !! must do
	cenation007: 2019-06-03 06:47:13 good question just sieve and bfs AC in one go :) Last edit: 2019-06-03 06:48:21
	shan61916: 2019-05-23 23:35:11 "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." can be ignored.
	jha_shashank: 2019-05-10 15:19:56 Nice problem:) AC in one go! Wondering if there were any impossible cases.
	Jumpy: 2019-03-31 09:28:26 Nice question. 1) First get the list of primes. 2) Create a graph and 3) Do the dfs/bfs to find the answer.
	sourav01: 2019-03-10 14:40:01 awesome problem_/\_
	kuchnahiaata: 2019-03-02 09:25:40 the real stuff lies in the construction of graph rest is just bfs!! but awesome problem _/\_
	vickyand_27: 2019-01-30 18:45:36 In bfs who have to maintain a distnce array :)) MY 12
	xtmosphere: 2019-01-15 19:55:45 Im(Its)-Possible :D Nice problem ..
	sonuexpc: 2018-12-28 20:19:12 good problem for beginners...my first bfs accepted in 1 go :)