| The 2019 Hacker Cup Finals have just concluded! There were **N** participants |
| (numbered 1 to **N**), including yourself (competing as participant 1), and |
| **M** problems (numbered 1 to **M**). |
|
|
| Participant _i_ solved problem _j_ if **Si,j** = "Y", and otherwise they |
| didn't solve it (if **Si,j** = "N"). Problem _i_'s point value is 2i, and each |
| participant's score is the sum of the point values of the problems that they |
| solved. No two participants solved exactly the same set of problems, which |
| also means that all participants have distinct scores. |
|
|
| Before the final results get announced, you have an opportunity to rearrange |
| the **M** columns of the scoreboard **S** into any permutation of problems 1 |
| to **M**. For example, if you swap columns 1 and 2, then everybody who had |
| originally solved problem 1 will now be considered to have solved problem 2 |
| (thus earning 4 points for it rather than 2), and vice versa. |
|
|
| Of course, you'd like to use this opportunity to your benefit — it would be |
| irresponsible to just let it pass by! However, it would be too suspicious if |
| you simply made yourself win the whole competition. As such, you'd like to |
| cause yourself to end up in 2nd place, such that you (participant 1) have |
| exactly the second-highest score out of all **N** participants. Now you just |
| need to determine whether or not this is achievable... |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of scoreboards. |
| For each scoreboard, there is first a line containing the space-separated |
| integers **N** and **M**. |
| Then, **N** lines follow, the _i_th of which contains a length-**M** string, |
| the characters **Si,1** through **Si,M**. |
|
|
| ### Output |
|
|
| For the _i_th scoreboard, print a line containing "Case #_i_: " followed by |
| one character, either "Y" if you can end up in 2nd place, or "N" otherwise. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 200 |
| 2 ≤ **N** ≤ 400 |
| 1 ≤ **M** ≤ 400 |
|
|
| The sum of **N** * **M** across all **T** test cases is no greater than |
| 1,000,000. |
|
|
| ### Explanation of Sample |
|
|
| In the first case, there's only one possible permutation of problems: [1]. |
| This results in you having a score of 2 and participant 2 having a score of 0, |
| which puts you in 1st place rather than 2nd. |
|
|
| In the second case, if you preserve the original permutation of problems, [1, |
| 2], you'll have a score of 2 while participant 2 has a score of 4, putting you |
| in 2nd place, as required. The permutation [2, 1] would have put you in 1st |
| place instead. |
|
|
| In the third case, if you choose the problem permutation [2, 1], the 4 |
| participants' scores will be 4, 0, 6, and 2, respectively. This puts you in |
| 2nd place, as required. The problem permutation [1, 2] would have put you in |
| 3rd place instead. |
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|
