Flip and Rectangles

AtCoder

IDarc081_d

Time2000ms

Memory256MB

Difficulty—

We have a board with an $H \times W$ grid. Each square in the grid is painted in black or white. The square at the $i$\-th row from the top and $j$\-th column from the left is black if the $j$\-th character in $S_i$ is `#`, and white if that character is `.`. Snuke can perform the following operation on the grid any number of times: * Select a row or column in the grid, and invert the color of all the squares in that row or column (that is, black squares become white and vice versa). Then, Snuke draws a rectangle along grid lines. Here, all the squares contained in the rectangle must be painted in black. Find the maximum possible area of Snuke's rectangle when the operation is performed optimally. ## Constraints * $2 \leq H \leq 2000$ * $2 \leq W \leq 2000$ * $|S_i| = W$ * $S_i$ consists of `#` and `.`. ## Input Input is given from Standard Input in the following format: $H$ $W$ $S_1$ $S_2$ $:$ $S_H$ [samples]

Samples

Input #1

3 3
..#
##.
.#.

Output #1

6

If the first row from the top and the third column from the left are inverted, a $2 \times 3$ rectangle can be drawn, as shown below:
![image](https://atcoder.jp/img/arc081/2995c3921ed4dffc8ee528b63b9c6118.png)

Input #2

4 4
....
....
....
....

Output #2

Input #3

10 8
##...#.#
##...#.#
..###.#.
#.##.#.#
.#..#.#.
..##.#.#
##.#.#..
...#.#..
###.#.##
###..###

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Flip and Rectangles",
    "description": {
      "content": "We have a board with an $H \\times W$ grid. Each square in the grid is painted in black or white. The square at the $i$\\-th row from the top and $j$\\-th column from the left is black if the $j$\\-th cha",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc081_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a board with an $H \\times W$ grid. Each square in the grid is painted in black or white. The square at the $i$\\-th row from the top and $j$\\-th column from the left is black if the $j$\\-th cha...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments