| Many people are avid fans of the daily crossword in the paper, but not you. I | |
| mean, the format is pretty terrible, right? You only get to use English words, | |
| and any hack can look those up in a dictionary. Also, it takes forever to make | |
| just one puzzle. What a waste of time. | |
| You've written a letter to the editor describing a new word game. It's really | |
| easy to make new puzzles because the only thing you give the solver is a | |
| permutation **P1..N** of the first **N** positive integers. It's then up to | |
| the solver to find any string that's _salient_ for the given permutation. | |
| A string is _salient_ for the permutation **P1..N** if it consists of **N** | |
| uppercase letters ("A"..."Z"), such that when its **N** non-empty suffixes are | |
| sorted in lexicographical order, the suffix starting at the _i_th character is | |
| the **Pi**th suffix in the sorted list. It's possible that a given permutation | |
| has no salient strings. | |
| You need some example puzzles to include in your letter. You already have some | |
| permutations generated, so all you need is to supply an answer for each | |
| permutation (if possible). | |
| ### Input | |
| Input begins with an integer **T**, the number of different permutations | |
| you've generated. For each permutation, there is first a line containing the | |
| integer **N**. Then **N** lines follow, the _i_th of which contains the | |
| integer **Pi**. It is guaranteed that each integer from 1 to **N** shows up | |
| exactly once in **P**. | |
| ### Output | |
| For the _i_th permutation, print a line containing "Case #**i**: " followed by | |
| any salient string for that permutation (note that any valid string consisting | |
| of **N** uppercase letters will be accepted), or "-1" if there are no such | |
| strings. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 2,000 | |
| 1 ≤ **N** ≤ 1,000 | |
| 1 ≤ **Pi** ≤ **N** | |
| ### Explanation of Sample | |
| In the first case, if we sort the suffixes of FACEBOOK we get: | |
| 1. ACEBOOK | |
| 2. BOOK | |
| 3. CEBOOK | |
| 4. EBOOK | |
| 5. FACEBOOK | |
| 6. K | |
| 7. OK | |
| 8. OOK | |
| If we read the indices of the suffixes back in order of decreasing length, we | |
| get 5 1 3 4 2 8 7 6, which is the given permutation. Therefore "FACEBOOK" is | |
| salient for this permutation, and is one possible accepted answer. | |