Cross

AtCoder

IDabc300_c

Time2000ms

Memory256MB

Difficulty—

We have a grid with $H$ horizontal rows and $W$ vertical columns. We denote by $(i, j)$ the cell at the $i$\-th row from the top and $j$\-th column from the left of the grid. Each cell in the grid has a symbol `#` or `.` written on it. Let $C[i][j]$ be the character written on $(i, j)$. For integers $i$ and $j$ such that at least one of $1 \leq i \leq H$ and $1 \leq j \leq W$ is violated, we define $C[i][j]$ to be `.`. $(4n+1)$ squares, consisting of $(a, b)$ and $(a+d,b+d),(a+d,b-d),(a-d,b+d),(a-d,b-d)$ $(1 \leq d \leq n, 1 \leq n)$, are said to be a **cross of size $n$ centered at $(a,b)$** if and only if all of the following conditions are satisfied: * $C[a][b]$ is `#`. * $C[a+d][b+d],C[a+d][b-d],C[a-d][b+d]$, and $C[a-d][b-d]$ are all `#`, for all integers $d$ such that $1 \leq d \leq n$, * At least one of $C[a+n+1][b+n+1],C[a+n+1][b-n-1],C[a-n-1][b+n+1]$, and $C[a-n-1][b-n-1]$ is `.`. For example, the grid in the following figure has a cross of size $1$ centered at $(2, 2)$ and another of size $2$ centered at $(3, 7)$. ![image](https://img.atcoder.jp/ghi/abc300c_aa5161e20f55652dc61ad221348765bb002e4eed378c352bc0e44c7555148ebc.jpg) The grid has some crosses. No `#` is written on the cells except for those comprising a cross. Additionally, no two squares that comprise two different crosses share a corner. The two grids in the following figure are the examples of grids where two squares that comprise different crosses share a corner; **such grids are not given as an input**. For example, the left grid is invalid because $(3, 3)$ and $(4, 4)$ share a corner. ![image](https://img.atcoder.jp/ghi/abc300c2_796c45899f018c995738383146a76562824a9f6b7a3d931621da691d49d6f3cc.jpg) Let $N = \min(H, W)$, and $S_n$ be the number of crosses of size $n$. Find $S_1, S_2, \dots, S_N$. ## Constraints * $3 \leq H, W \leq 100$ * $C[i][j]$ is `#` or `.`. * No two different squares that comprise two different crosses share a corner. * $H$ and $W$ are integers. ## Input The input is given from Standard Input in the following format: $H$ $W$ $C[1][1]C[1][2]\dots C[1][W]$ $C[2][1]C[2][2]\dots C[2][W]$ $\vdots$ $C[H][1]C[H][2]\dots C[H][W]$ [samples]

Samples

Input #1

5 9
#.#.#...#
.#...#.#.
#.#...#..
.....#.#.
....#...#

Output #1

1 1 0 0 0

As described in the Problem Statement, there are a cross of size $1$ centered at $(2, 2)$ and another of size $2$ centered at $(3, 7)$.

Input #2

3 3
...
...
...

Output #2

0 0 0

There may be no cross.

Input #3

3 16
#.#.....#.#..#.#
.#.......#....#.
#.#.....#.#..#.#

Output #3

3 0 0

Input #4

15 20
#.#..#.............#
.#....#....#.#....#.
#.#....#....#....#..
........#..#.#..#...
#.....#..#.....#....
.#...#....#...#..#.#
..#.#......#.#....#.
...#........#....#.#
..#.#......#.#......
.#...#....#...#.....
#.....#..#.....#....
........#.......#...
#.#....#....#.#..#..
.#....#......#....#.
#.#..#......#.#....#

Output #4

5 0 1 0 0 0 1 0 0 0 0 0 0 0 0

API Response (JSON)

{
  "problem": {
    "name": "Cross",
    "description": {
      "content": "We have a grid with $H$ horizontal rows and $W$ vertical columns. We denote by $(i, j)$ the cell at the $i$\\-th row from the top and $j$\\-th column from the left of the grid.   Each cell in the grid h",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc300_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ horizontal rows and $W$ vertical columns. We denote by $(i, j)$ the cell at the $i$\\-th row from the top and $j$\\-th column from the left of the grid.  \nEach cell in the grid h...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments