Now, the minister of finance, who had been eavesdropping,
— 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$\ldots $
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.
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).
One line for each case, either with a number stating the minimal cost or containing the word “Impossible”.
|Sample Input 1||Sample Output 1|
3 1033 8179 1373 8017 1033 1033
6 7 0