Problem:
Score : 300 points

Problem Statement

You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

We will repeatedly perform the following operation until all the squares are black:

Every white square that shares a side with a black square, becomes black.

Find the number of operations that will be performed.
The initial grid has at least one black square.

Constraints

1 \leq H,W \leq 1000

A_{ij} is # or ..

The given grid has at least one black square.

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the number of operations that will be performed.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......
#..#..
......
.#....
....#.

Sample Output 2

3

Solution in OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

module S = Set.Make (struct type t = int * int let compare = compare end) ;;

Scanf.sscanf (read_line ()) "%d %d" (fun h w ->
    let a = Array.init h (fun _ -> Bytes.of_string @@ read_line ()) in
    let rec loop_y y acc =
        let rec loop_x x acc =
            if x < 0 then acc else loop_x (x - 1) (if Bytes.get a.(y) x = '#' then (x, y) :: acc else acc)
        in
        if y < 0 then acc else loop_y (y - 1) (loop_x (w - 1) acc)
    in

    let rec bfs step next = function
        | [] -> if S.is_empty next then step - 1 else bfs (step + 1) S.empty (S.elements next)
        | (x, y) :: tl ->
                let next = if x > 0     && Bytes.get a.(y) (x - 1) = '.' then (Bytes.set a.(y) (x - 1) '#'; S.add (x - 1, y) next) else next in
                let next = if y > 0     && Bytes.get a.(y - 1) (x) = '.' then (Bytes.set a.(y - 1) (x) '#'; S.add (x, y - 1) next) else next in
                let next = if x < w - 1 && Bytes.get a.(y) (x + 1) = '.' then (Bytes.set a.(y) (x + 1) '#'; S.add (x + 1, y) next) else next in
                let next = if y < h - 1 && Bytes.get a.(y + 1) (x) = '.' then (Bytes.set a.(y + 1) (x) '#'; S.add (x, y + 1) next) else next in
                bfs step next tl
    in
    bfs 1 S.empty (loop_y (h - 1) []) |> Printf.printf "%d\n"
)