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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	thirupathireddy: 2015-09-17 07:39:01 nice one on bfs.............
	ALi Ibrahim: 2015-08-01 22:22:17 Nice problem, first Accepted :)
	sHaShAnK sHeKhAr: 2015-05-21 11:21:23 Nice question, can be solved from both Dijkstra and simple BFS :) since cost of each edge is 1($).
	i_am_looser: 2015-05-08 06:55:03 Literally very nice problem : ) Hint - Dijkstra + Implementation.
	Shubham Bansal: 2015-03-29 14:20:18 a very nice problem...
	pandu ranga rao: 2015-03-06 21:36:40 Nice QN..!
	Anubhav Gupta: 2015-02-11 21:46:28 Awesome question!!
	epsilon: 2015-01-24 12:01:02 my 50th on spoj...........till now it's best question i had ever sloved!!!!!!!!!
	fanatique: 2015-01-08 14:42:37 good one... :)
	Mitch Schwartz: 2015-01-02 08:55:39 "Piece of Cake!! Simple [hint] it is!!! Skilled implementation is the key though :P" Here we see clearly one of the main reasons people keep leaving spoilers in comments: to brag. Another reason could be that they dislike thinking so much that they consider it a kindness to save other people from the hassle. Last edit: 2015-01-02 11:33:33