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: Accepted)

(* O(h w) *)
let h, w = Scanf.scanf " %d %d" @@ fun a b -> a, b
let q = Queue.create ()
let ds = Array.make_matrix h w @@ -1
let a_ss = Array.init h @@ fun i -> Array.init w @@ fun j -> Scanf.scanf " %c" @@ fun a ->
  if a = '#' then (ds.(i).(j) <- 0; Queue.push (i, j) q); a
let ans = ref 0
let _ =
  while not @@ Queue.is_empty q do
    let y0, x0 = Queue.pop q in
    let f (dy, dx) =
      let y, x = y0 + dy, x0 + dx in
      if 0 <= y && y < h && 0 <= x && x < w && ds.(y).(x) = -1 then
        (ans := ds.(y0).(x0) + 1; ds.(y).(x) <- !ans; Queue.push (y, x) q) in
    List.iter f [-1, 0; 0, -1; 1, 0; 0, 1]
  done;
  Printf.printf "%d\n" !ans