| The 2018 Hacker Cup finals are underway! The contest is being held in a room |
| with 2 rows of **N** desks each, with finalists sitting at some of them. |
|
|
| One of the finalists, Alex, is sitting at the leftmost desk in the front row. |
| Another finalist, Borys, is sitting at the rightmost desk in the front row. |
| Unfortunately, both of them find themselves distracted by the contest room's |
| environment — Alex is a bit too hot on his side of the room, while Borys is a |
| bit too cold. If only they could switch places! Unfortunately, this would be |
| against the rules, but if they work together with some other contestants, |
| perhaps they can manage it without the contest organizers noticing... |
|
|
| The initial state of each row of desks can be represented by a string of **N** |
| characters, with the _i_th character corresponding to the _i_th desk from the |
| left in that row. Each character is one of the following: |
|
|
| * `A` \- Alex's desk (guaranteed to appear exactly once, as the leftmost desk in the front row) |
| * `B` \- Borys's desk (guaranteed to appear exactly once, as the rightmost desk in the front row) |
| * `*` \- A cooperative finalist's desk |
| * `#` \- An uncooperative finalist's desk |
| * `.` \- An unoccupied desk |
|
|
| At any point, a single finalist may move from their current desk to an |
| adjacent, currently-unoccupied desk. Two desks are considered adjacent if |
| either they're in the same column, or they're directly side-by-side in the |
| same row. However, the finalists won't be foolish enough to move sideways |
| between two desks in the front row, as that would surely attract the contest |
| organizers' attention. |
|
|
| Alex, Borys, and any cooperative finalists may all move between desks in this |
| fashion. On the other hand, uncooperative finalists are too busy actually |
| competing, and will never move from their original desks. |
|
|
| Assuming that Alex, Borys, and the cooperative finalists all work together, is |
| it possible for Alex and Borys to switch seats (in other words, for Alex to |
| occupy the front row's rightmost desk while Borys simultaneously occupies its |
| leftmost desk) without the contest organizers noticing? |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of parallel universes in which |
| the 2018 Hacker Cup is occurring. For each universe, there are two lines of |
| **N** characters each, as described above. The first line is the front row of |
| desks, and the second line is the back row of desks. |
|
|
| ### Output |
|
|
| For the _i_th universe, output a line containing "Case #_i_: " followed by the |
| string "Possible" if Alex and Borys can successfully switch seats, or |
| "Impossible" otherwise. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 200 |
| 2 ≤ **N** ≤ 2,000 |
|
|
| ### Explanation of Sample |
|
|
| In the first case, the contest room looks as follows (with grey lines |
| indicating adjacent desks which finalists may potentially move between). The |
| blue circle denotes a cooperative finalist, and the gray square denotes an |
| uncooperative finalist. A and B denote Alex and Borys respectively. |
|
|
| One possible sequence of moves resulting in Alex and Borys switching places is |
| as follows (with some moves omitted): |
|
|
| In the second case, Alex and Borys are unable to get past one another and |
| switch seats. |
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|
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|
