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.

 

Sample Input

31033 81791373 80171033 1033 Sample Output

670 题意：给你四位数字a,b;每一不只能改变一位数字，且新的数字只能是素数， 要你输出最小步数 题解：bfs，每次向下遍历40个方向 代码：

#include
      
       #include
       
        #include
        
         using namespace std;typedef long long ll;typedef unsigned long long ull;#define mod 1000000007#define INF 0x3f3f3f3fstruct niu{    int prime,step;    niu(){}    niu(int pr,int st)    {        prime=pr,step=st;    }};int a,b;int ans=INF;bool check(int a){    for(int i=2;i*i<=a;i++)        if(a%i==0)return false;    return a!=1;}queue
         
          q;bool vis[10005];int bfs(){    memset(vis,false,sizeof(vis));    while(q.size())q.pop();    q.push(niu(a,0));    vis[a]=true;    while(q.size())    {        niu tmp=q.front();q.pop();//cout<
          
           <
           
            <
            
             >T; while(T--) { ans=INF;//注意这里的ans要初始化 cin>>a>>b; if(bfs()==-1) cout<<"Impossible"<