B'Oh, no! The coronavirus has caught you, and now you 're sitting in a dark cellar, with tied legs (but not hands). You have a delicious cookie, a laptop in front of you, and your ideal development environment is open. The coronavirus convinces you to solve the following problem. You are given two arrays A and B of size n . You can do operations of two types with array A : You need to understand if you can get an array B from the array A . If it is possible, you will have to restore the order of these operations by minimizing the number of operations of the second type. Fortunately, the coronavirus is good today, so he has allowed you not to restore actions if the minimum number of second type operations is more than 2 cdot 10^5 . But coronavirus resents you, so if you restore the answer, the total number of operations should not exceed 5 cdot 10^5 . Solve this problem and get the cookie, or the coronavirus will extend the quarantine for five years and make the whole economy collapse! The first line contains a single integer n ( 1 <= n <= 2 cdot 10^5 ). The second line contains n integers A_1, A_2, ldots, A_n ( 1 <= A_i <= 10 ^ {12} ). The third line contains n integers B_1, B_2, ldots, B_n ( 1 <= B_i <= 10 ^ {12} ). If you cannot get B from the A array, print "IMPOSSIBLE" (without quotes) on a single line. If the minimum number of operations of the second type exceeds 2 cdot 10^5 , print "BIG" (without quotes). In the second line print the number of operations of the second type, that needs to be applied to get array B from A . Otherwise, in the first line print "SMALL" (without quotes). In the second line print the total number of operations of the first and second types m <= 5 cdot 10^5 (it is guaranteed that in this case there is such a sequence of actions). In the third line print a line of length m , consisting of charact'...