Stronger Takahashi

AtCoder

IDabc213_e

Time2000ms

Memory256MB

Difficulty—

There is a town divided into a grid of cells with $H$ rows and $W$ columns. The cell at the $i$\-th row from the top and $j$\-th column from the left is a passable space if $S_{i,j}$ is `.` and a block if $S_{i,j}$ is `#`. Takahashi will go from his house to a fish market. His house is in the cell at the top-left corner, and the fish market is in the cell at the bottom-right corner. Takahashi can move one cell up, down, left, or right to a passable cell. He cannot leave the town. He cannot enter a block, either. However, his physical strength allows him to destroy all blocks in a square region with $2\times 2$ cells of his choice with one punch, making these cells passable. Find the minimum number of punches needed for Takahashi to reach the fish market. ## Constraints * $2 \leq H,W \leq 500$ * $H$ and $W$ are integers. * $S_{i,j}$ is `.` or `#`. * $S_{1,1}$ and $S_{H,W}$ are `.`. ## Input Input is given from Standard Input in the following format: $H$ $W$ $S_{1,1} \ldots S_{1,W}$ $\vdots$ $S_{H,1} \ldots S_{H,W}$ [samples]

Samples

Input #1

5 5
..#..
#.#.#
##.##
#.#.#
..#..

Output #1

1

He can reach the fish market by, for example, destroying the blocks in the square region with $2\times 2$ cells marked `*` below.

..#..
#.**#
##**#
#.#.#
..#..

It is not required that all of the $2\times 2$ cells in the region to punch are blocks.

Input #2

5 7
.......
######.
.......
.######
.......

Output #2

0

He can reach the fish market without destroying blocks, though he has to go a long way around.

Input #3

8 8
.#######
########
########
########
########
########
########
#######.

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Stronger Takahashi",
    "description": {
      "content": "There is a town divided into a grid of cells with $H$ rows and $W$ columns. The cell at the $i$\\-th row from the top and $j$\\-th column from the left is a passable space if $S_{i,j}$ is `.` and a bloc",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc213_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a town divided into a grid of cells with $H$ rows and $W$ columns. The cell at the $i$\\-th row from the top and $j$\\-th column from the left is a passable space if $S_{i,j}$ is `.` and a bloc...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments