| You are designing a new encryption system that works in the following way: | |
| For server-client communication you need a key **k**, composed of **m** | |
| sections, each of length **l**, and the key consists only of lowercase | |
| characters in the set {a, b, c, d, e, f}. The server has a key **k1** and the | |
| client has a key **k2** where: | |
| * k1 = f(k). **f** is a function that receives a key and replace some random letters by ? indicating that those characters can be any lowercase letter of the set described before. | |
| * k2 = f(g(k)). **g** is a function that takes a key and produces a random permutation of its m sections. And **f** is the function defined above. | |
| For example: let m = 3, l = 2 | |
| * f('abacbc') = '?ba??c' | |
| * g('abacbc') = 'acbcab' (each section was moved one place to the left). | |
| Your task is given **k1** and **k2**, find key **k**. If there are several | |
| solutions, print the lexicographically smallest key. And if there is no | |
| solution at all, print "IMPOSSIBLE" (without the quotes). | |
| ## Input description: | |
| The first line has a single integer **T**, which corresponds to the number of | |
| test cases. **T** test cases follows: the first line of the test case | |
| corresponds to the integer **m**, the second line contains the string **k1** | |
| and the third line contains the string **k2**. | |
| ## Constraints: | |
| * T ≤ 20 | |
| * 0 < |k1| ≤ 100 | |
| * 0 < m ≤ 50 | |
| * |k2| = |k1| | |
| * It is guaranteed that m is always a divisor of |k1| | |
| * k1 and k2 consist of {a, b, c, d, e, f, ?} | |
| ## Output description: | |
| For test case **i**, numbered from **1** to **T**, output "Case #i: ", | |
| followed by the lexicographically smallest key or "IMPOSSIBLE". | |