Grid Repainting 3

AtCoder

IDarc119_d

Time2000ms

Memory256MB

Difficulty—

We have a canvas represented as a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\-th row from the top $(1 \leq i \leq H)$ and $j$\-th column from the left $(1 \leq j \leq W)$. Initially, $(i, j)$ is painted red if $s_{i, j}=$ `R` and blue if $s_{i, j}=$ `B`. For any number of times, you can choose one of the two operations below and do it. > **Operation X:** Choose a square painted red, and repaint all squares in the row containing that square (including itself) white. > **Operation Y:** Choose a square painted red, and repaint all squares in the column containing that square (including itself) white. Show one way that maximizes the number of squares painted white in the end. ## Constraints * $1 \leq H \leq 2500$ * $1 \leq W \leq 2500$ * $s_{i, j}$ is `R` or `B`. $(1 \leq i \leq H, 1 \leq j \leq W)$ * $H$ and $W$ are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $s_{1, 1}$$s_{1, 2}$$s_{1, 3}$$\cdots$$s_{1, W}$ $s_{2, 1}$$s_{2, 2}$$s_{2, 3}$$\cdots$$s_{2, W}$ $s_{3, 1}$$s_{3, 2}$$s_{3, 3}$$\cdots$$s_{3, W}$ $\vdots$ $s_{H, 1}$$s_{H, 2}$$s_{H, 3}$$\cdots$$s_{H, W}$ [samples]

Samples

Input #1

4 4
RBBB
BBBB
BBBB
RBRB

Output #1

3
X 1 1
Y 4 3
X 4 1

Here is one sequence of operations that makes $10$ squares white:

*   First, do **Operation X** choosing $(1, 1)$.
*   Then, do **Operation Y** choosing $(4, 3)$.
*   Then, do **Operation X** choosing $(4, 1)$.

There is no way to make $11$ or more squares white.
![image](https://img.atcoder.jp/arc119/b0fde87f879b9dc90ca8788945f21bf2.png)

Input #2

1 119
BBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBB

Output #2

4
Y 1 60
Y 1 109
Y 1 46
X 1 11

We can repaint all squares white.

Input #3

10 10
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB

Output #3

0

Since there is no red square, we cannot do the operations at all.

API Response (JSON)

{
  "problem": {
    "name": "Grid Repainting 3",
    "description": {
      "content": "We have a canvas represented as a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top $(1 \\leq i \\leq H)$ and $j$\\-th column from the left $(1 \\leq j \\le",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc119_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a canvas represented as a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top $(1 \\leq i \\leq H)$ and $j$\\-th column from the left $(1 \\leq j \\le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments