# Prime Path

# Prime Path

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**.

2 1033 8179 1373 8017

6 7