Zebraness

AtCoder

IDabc193_f

Time2000ms

Memory256MB

Difficulty—

We have a grid with $N$ horizontal rows and $N$ vertical columns. Let $(i, j)$ denote the square at the $i$\-th row from the top and $j$\-th column from the left. A character $c_{i,j}$ describes the color of $(i, j)$. `B` means the square is painted black; `W` means the square is painted white; `?` means the square is not yet painted. Takahashi will complete the black-and-white grid by painting each unpainted square black or white. Let the **zebraness** of the grid be the number of pairs of a black square and a white square sharing a side. Find the maximum possible zebraness of the grid that Takahashi can achieve. ## Constraints * $1 ≤ N ≤ 100$ * $c_{i, j}$ is `B`, `W`, or `?`. ## Input Input is given from Standard Input in the following format: $N$ $c_{1,1} \dots c_{1,N}$ $\hspace{20pt}\vdots$ $c_{N,1} \dots c_{N,N}$ [samples]

Samples

Input #1

2
BB
BW

Output #1

2

We have two pairs of a black square and a white square sharing a side: $(1, 2), (2, 2)$ and $(2, 1), (2, 2)$, so the zebraness of this grid is $2$.

Input #2

3
BBB
BBB
W?W

Output #2

4

Painting $(3, 2)$ white makes the zebraness $3$, and painting it black makes the zebraness $4$.

Input #3

5
?????
?????
?????
?????
?????

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Zebraness",
    "description": {
      "content": "We have a grid with $N$ horizontal rows and $N$ vertical columns.   Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. A character $c_{i,j}$ describes the",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc193_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $N$ horizontal rows and $N$ vertical columns.  \nLet $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. A character $c_{i,j}$ describes the...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments