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.

Examples

Input

31033 81791373 80171033 1033

Output

670

题意

给出两个四位的素数$n,m$，要求$n$每次只能变换一位，并且变换后的数字依旧是素数。

求$n$经过多少步变换能够变成$m$；如果$n$无法变成$m$，输出Impossible

思路

将$n$的四位数字拆分了，每次变换一位，来判断是否符合条件，如果符合条件，将新数字加入队列，至到数字和$m$相等，或队列为空

AC代码

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