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)

let () = Scanf.scanf "%d %d\n" @@ fun h w ->
  let ass = Array.init h @@ fun _ -> Scanf.scanf "%s\n" @@ fun s -> s in
  let rec bfs n ijs =
    match
      List.fold_left (fun (b, ijs) (i, j) ->
        if
          i < 0 || h <= i ||
          j < 0 || w <= j ||
          ass.(i).[j] = '#'
        then (b, ijs)
        else begin
          ass.(i).[j] <- '#';
          (false, (i - 1, j) :: (i + 1, j) :: (i, j - 1) :: (i, j + 1) :: ijs)
        end) (true, []) ijs
    with
    | (true, _) -> n
    | (false, ijs) -> bfs (n + 1) ijs in
  Printf.printf "%d\n" @@ bfs 0 @@
  List.concat @@ Array.to_list @@ Array.init h @@ fun i ->
    List.concat @@ Array.to_list @@ Array.init w @@ fun j ->
      if ass.(i).[j] = '.'
      then []
      else [(i - 1, j); (i + 1, j); (i, j - 1); (i, j + 1)]