Closed Rooms

AtCoder

IDagc014_c

Time2000ms

Memory256MB

Difficulty—

Takahashi is locked within a building. This building consists of $H×W$ rooms, arranged in $H$ rows and $W$ columns. We will denote the room at the $i$\-th row and $j$\-th column as $(i,j)$. The state of this room is represented by a character $A_{i,j}$. If $A_{i,j}=$ `#`, the room is locked and cannot be entered; if $A_{i,j}=$ `.`, the room is not locked and can be freely entered. Takahashi is currently at the room where $A_{i,j}=$ `S`, which can also be freely entered. Each room in the $1$\-st row, $1$\-st column, $H$\-th row or $W$\-th column, has an exit. Each of the other rooms $(i,j)$ is connected to four rooms: $(i-1,j)$, $(i+1,j)$, $(i,j-1)$ and $(i,j+1)$. Takahashi will use his magic to get out of the building. In one cast, he can do the following: * Move to an adjacent room at most $K$ times, possibly zero. Here, locked rooms cannot be entered. * Then, select and unlock at most $K$ locked rooms, possibly zero. Those rooms will remain unlocked from then on. His objective is to reach a room with an exit. Find the minimum necessary number of casts to do so. It is guaranteed that Takahashi is initially at a room without an exit. ## Constraints * $3 ≤ H ≤ 800$ * $3 ≤ W ≤ 800$ * $1 ≤ K ≤ H×W$ * Each $A_{i,j}$ is `#` , `.` or `S`. * There uniquely exists $(i,j)$ such that $A_{i,j}=$ `S`, and it satisfies $2 ≤ i ≤ H-1$ and $2 ≤ j ≤ W-1$. ## Input Input is given from Standard Input in the following format: $H$ $W$ $K$ $A_{1,1}A_{1,2}$...$A_{1,W}$ : $A_{H,1}A_{H,2}$...$A_{H,W}$ [samples]

Samples

Input #1

3 3 3
#.#
#S.
###

Output #1

1

Takahashi can move to room $(1,2)$ in one cast.

Input #2

3 3 3
###
#S#
###

Output #2

2

Takahashi cannot move in the first cast, but can unlock room $(1,2)$. Then, he can move to room $(1,2)$ in the next cast, achieving the objective in two casts.

Input #3

7 7 2
#######
#######
##...##
###S###
##.#.##
###.###
#######

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Closed Rooms",
    "description": {
      "content": "Takahashi is locked within a building. This building consists of $H×W$ rooms, arranged in $H$ rows and $W$ columns. We will denote the room at the $i$\\-th row and $j$\\-th column as $(i,j)$. The state ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc014_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is locked within a building.\nThis building consists of $H×W$ rooms, arranged in $H$ rows and $W$ columns. We will denote the room at the $i$\\-th row and $j$\\-th column as $(i,j)$. The state ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments