Alternating Path

AtCoder

IDaising2019_c

Time2000ms

Memory256MB

Difficulty—

There is a grid with $H$ rows and $W$ columns, where each square is painted black or white. You are given $H$ strings $S_1, S_2, ..., S_H$, each of length $W$. If the square at the $i$\-th row from the top and the $j$\-th column from the left is painted black, the $j$\-th character in the string $S_i$ is `#`; if that square is painted white, the $j$\-th character in the string $S_i$ is `.`. Find the number of pairs of a black square $c_1$ and a white square $c_2$ that satisfy the following condition: * There is a path from the square $c_1$ to the square $c_2$ where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white... ## Constraints * $1 \leq H, W \leq 400$ * $|S_i| = W$ ($1 \leq i \leq H$) * For each $i$ ($1 \leq i \leq H$), the string $S_i$ consists of characters `#` 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

10

Some of the pairs satisfying the condition are $((1, 2), (3, 3))$ and $((3, 1), (3, 2))$, where $(i, j)$ denotes the square at the $i$\-th row from the top and the $j$\-th column from the left.

Input #2

2 4
....
....

Output #2

Input #3

4 3
###
###
...
###

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Alternating Path",
    "description": {
      "content": "There is a grid with $H$ rows and $W$ columns, where each square is painted black or white. You are given $H$ strings $S_1, S_2, ..., S_H$, each of length $W$. If the square at the $i$\\-th row from th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "aising2019_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $H$ rows and $W$ columns, where each square is painted black or white.\nYou are given $H$ strings $S_1, S_2, ..., S_H$, each of length $W$. If the square at the $i$\\-th row from th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments