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H - Advance or Eat

Score : $600$ points

Problem Statement

There is a grid with $N$ rows and $N$ columns, where each square has one white piece, one black piece, or nothing on it.
The square at the $i$-th row from the top and $j$-th column from the left is described by $S_{i,j}$. If $S_{i,j}$ is W, the square has a white piece; if $S_{i,j}$ is B, it has a black piece; if $S_{i,j}$ is ., it is empty.

Takahashi and Snuke will play a game, where the players take alternate turns, with Takahashi going first.

In Takahashi's turn, he does one of the following operations.

• Choose a white piece that can move one square up to an empty square, and move it one square up (see below).
• Eat a black piece of his choice.

In Snuke's turn, he does one of the following operations.

• Choose a black piece that can move one square up to an empty square, and move it one square up.
• Eat a white piece of his choice.

The player who becomes unable to do the operation loses the game. Which player will win when both players play optimally?

Here, moving a piece one square up means moving a piece at the $i$-th row and $j$-th column to the $(i-1)$-th row and $j$-th column.
Note that this is the same for both players; they see the board from the same direction.

Constraints

• $1 \leq N \leq 8$
• $N$ is an integer.
• $S_{i,j}$ is W, B, or ..

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Input

Input is given from Standard Input in the following format:

$N$

$S_{1,1}S_{1,2}\ldots S_{1,N}$

$S_{2,1}S_{2,2}\ldots S_{2,N}$

$\vdots$

$S_{N,1}S_{N,2}\ldots S_{N,N}$

Output

If Takahashi will win, print Takahashi; if Snuke will win, print Snuke.

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3
BB.
.B.
...

Takahashi

If Takahashi eats the black piece at the $1$-st row and $1$-st columns, the board will become:

``` .B. .B. ... ```

Then, Snuke cannot do an operation, making Takahashi win.
Note that it is forbidden to move a piece out of the board or to a square occupied by another piece.

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2
..
WW

Snuke

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4
WWBW
WWWW
BWB.
BBBB

Snuke