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.

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

Sample Output

題意

給你n,m分別是素?cái)?shù)，求由n到m變化的步驟數(shù)，規(guī)定每一步只能改變個十百千一位的數(shù)（千位不能為零），且變化得到的每一個數(shù)也為素?cái)?shù)。

思路

首先進(jìn)行素?cái)?shù)打表，打出10000以內(nèi)的所有素?cái)?shù)（或者1000-10000），然后bfs。

對n變化個十百千的每一位，變化后檢測是否為素?cái)?shù)，若是，加入隊(duì)列，同時標(biāo)記已訪問，然后對隊(duì)列中的數(shù)進(jìn)行同樣的操作，直到某一次變化產(chǎn)生m，輸出最少的變換次數(shù)。

若不可能達(dá)到m，則會在遍歷完[1000-9999]之間所有素?cái)?shù)后退出。

AC 代碼