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: Wrong Answer)

let () =
  let (h, w) = Scanf.scanf "%d %d" (fun a b -> (a, b)) in
  let queue = Queue.create () in
  let dp = Array.make_matrix h w 0 in
  let field = Array.init h @@ fun i -> Array.init w @@
    fun j -> Scanf.scanf "%c"
      (fun c -> if c == '#' then Queue.push (i,j) queue; c)
  in
  let count = ref 0 in
  while not @@ Queue.is_empty queue do
    let (i,j) = Queue.pop queue in
    List.iter (fun (y, x) ->
        count := dp.(i).(j);
        dp.(y).(x) <- !count + 1;
        Queue.push (y,x) queue;
        field.(y).(x) <- '#'
      ) @@
    List.filter (fun (y, x) -> y >= 0 && y < h && x >= 0 && x < w && field.(y).(x) == '.') [(i+1,j);(i-1,j);(i,j+1);(i,j-1)];
  done;
  Printf.printf "%d\n" !count