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 id x = x
let split_string ?(pattern="") = Str.split @@ Str.regexp pattern

let (h, w) = Scanf.scanf "%d %d\n" @@ fun h w -> (h, w)
let a = Array.init h (fun _ -> Array.of_list (split_string (Scanf.scanf "%s\n" id)))

let da = Array.init h @@ fun x -> Array.init w @@ fun y -> if a.(x).(y) = "#" then 0 else max_int

let rec f arr x y d = 
  if 0 <= x && x < h && 0 <= y && y < w then
    if arr.(x).(y) >= d then begin
      arr.(x).(y) <- d;
      f arr (x + 1) y (d + 1);
      f arr (x - 1) y (d + 1);
      f arr x (y + 1) (d + 1);
      f arr x (y - 1) (d + 1);
    end

let () =
  for x = 0 to (h - 1) do
    for y = 0 to (w - 1) do
      if da.(x).(y) = 0 then f da x y 0
    done
  done;
  print_int @@ Array.fold_left max 0 @@ Array.map (Array.fold_left max 0) da