Score : $600$ points

问题陈述

有一个 $N$ 行和 $N$ 列的网格，其中每个格子上有一个白色棋子、一个黑色棋子或什么都没有。

从顶部数第 $i$ 行、从左边数第 $j$ 列的格子由 $S_{i,j}$ 描述。如果 $S_{i,j}$ 是 W，则该格子上有白色棋子；如果 $S_{i,j}$ 是 B，则有黑色棋子；如果 $S_{i,j}$ 是 ., 则为空。

Takahashi 和 Snuke 将进行一场游戏，两位玩家轮流行动，Takahashi 先手。

在 Takahashi 的回合，他执行以下操作之一：

• 选择一个可以向上移动一格到空格的 白色 棋子，并将其向上移动一格（见下文）。
• 吃掉他选择的一个 黑色 棋子。

在 Snuke 的回合，他执行以下操作之一：

• 选择一个可以向上移动一格到空格的 黑色 棋子，并将其向上移动一格。
• 吃掉他选择的一个 白色 棋子。

当玩家无法执行操作时，该玩家输掉游戏。当双方都采取最优策略时，哪位玩家会获胜？

这里，将棋子向上移动一格意味着将位于第 $i$ 行第 $j$ 列的棋子移动到第 $(i-1)$ 行第 $j$ 列。
请注意，这对两名玩家来说是相同的；他们从相同的方向看棋盘。

以上为通义千问 qwen-max 翻译，仅供参考。

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 ..

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.

Sample Input 1

3
BB.
.B.
...

Sample Output 1

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.

Sample Input 2

2
..
WW

Sample Output 2

Snuke

Sample Input 3

4
WWBW
WWWW
BWB.
BBBB

Sample Output 3

Snuke

update @ 2024/3/10 10:02:23