Advance or Eat

AtCoder

IDabc229_h

Time2000ms

Memory256MB

Difficulty—

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: $N$ $S_{1,1}S_{1,2}\ldots S_{1,N}$ $S_{2,1}S_{2,2}\ldots S_{2,N}$ $\vdots$ $S_{N,1}S_{N,2}\ldots S_{N,N}$ [samples]

Samples

Input #1

3
BB.
.B.
...

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.

Input #2

2
..
WW

Output #2

Snuke

Input #3

4
WWBW
WWWW
BWB.
BBBB

Output #3

Snuke

API Response (JSON)

{
  "problem": {
    "name": "Advance or Eat",
    "description": {
      "content": "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 i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc229_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $N$ rows and $N$ columns, where each square has one white piece, one black piece, or nothing on it.  \nThe square at the $i$\\-th row from the top and $j$\\-th column from the left i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments