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 \textbf{1033} for good reasons. I am the Prime minister, you know! --- I know, so therefore your new number \textbf{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 \textbf{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 \textbf{1033} to \textbf{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. \textbf{1033} \textbf{1733} \textbf{3733} \textbf{3739} \textbf{3779} \textbf{8779} \textbf{8179} The cost of this solution is 6 pounds. Note that the digit \textbf{1} which got pasted over in step \textbf{2} can not be reused in the last step -- a new \textbf{1} must be purchased. \InputFile One line with a positive number: the number of test cases (at most \textbf{100}). Then for each test case, one line with two numbers separated by a blank. Both numbers are four-digit primes (without leading zeros). \OutputFile One line for each case, either with a number stating the minimal cost or containing the word \textbf{Impossible}.