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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< Previous 4 5 6 7 8 9 10 11 12 13 14 Next >
	rohit1507: 2017-07-24 10:26:28 Easy. Think Simple. Nice!!
	nikhil2504: 2017-07-10 17:48:59 AC 0.0 <3
	leafbebop: 2017-06-02 14:27:04 Note: No leading Zero allowed. I do not understand why...
	akashmandal21: 2017-05-24 20:34:16 Took a long time but AC in a single shot :) Though implementation is not that easy!!! Last edit: 2017-05-24 20:36:30
	akash619j: 2017-05-02 14:21:37 Got AC in first go! Was fearing a TLE :p
	holmesherlock: 2017-03-28 15:34:10 good question ,,beginners must give it a try
	sultania23: 2017-03-27 15:09:14 nice problem ....test cases are weak...
	ashu121: 2017-03-24 13:26:29 very good application of BFS :)
	sucide: 2017-03-23 07:50:21 Ac in one go! Think as graph connect primes.
	lord_poseidon: 2017-03-18 15:49:33 Accepted in one go, use bfs and sieve :-)