Prime Path

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 16272		Accepted: 9195

 

Description

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

 

单向BFS水题，但是双向让我调试了很久，因为写单向的时候是分4种情况，然后想着双向用for来放在一个循环里好了，结果样例输出答案完全不对，只有答案为1或2的时候可能会对，不解一个早上= =刚才想着算了把for去掉写麻烦点，结果又因为忘记删掉调试输出的语句，WA几发。现在还是不知道为什么原来的for是错的。双向BFS给我一个感觉：代码真长（虽然大部分是重复的）嗯这题写完之后上学期遗留的题除了一道题意本身不清楚+大部分AC代码本身也有明显错误的那道题之外全部A掉了。看看专题训练status里我刷了好几页的历史。真是个悲伤的故事……双向的时候要按层搜索

代码：

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