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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

1033

for good reasons. I am the Prime minister, you know!— I know, so therefore your new number

$$

8179

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

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

1033

to

$$

8179

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

6

pounds. Note that the digit

$$

1

1

which got pasted over in step

$$

2

2

can not be reused in the last step – a new

$$

1

1

must be purchased.

Input

One line with a positive number: the number of test cases (at most

$$

100

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

n,m

，要求

$$

n

n

每次只能变换一位，并且变换后的数字依旧是素数。求

$$

n

n

经过多少步变换能够变成

$$

m

m

；如果

$$

n

n

无法变成

$$

m

m

，输出Impossible

思路

将

$$

n

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

m

相等，或队列为空

AC代码

#include 
   
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     #include 
     
      #include 
      
       #include 
       
        #include 
        
         #include 
         
        
       
      
     
    
   

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