hackercupai/hackercup huggingface dataset:
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.