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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

let
  H, W = map(x -> parse(Int, x), split(readline()))
  grid = []
  for i=1:H
    push!(grid, split(readline(), ""))
  end
  A = [[if grid[h][w]=="#" 0 else H*W end for w=1:W] for h=1:H]

  black = []
  white = []

  for h = 1:H
    for w = 1:W
      if A[h][w] == 0
        push!(black, (h,w))
      else
        push!(white, (h,w))
      end
    end
  end

  m = 0
  for w in white
    for b in black
      dis = abs(b[1] - w[1]) + abs(b[2] - w[2])
      A[w[1]][w[2]] = min(A[w[1]][w[2]], dis)
    end
    m = max(m, A[w[1]][w[2]])
  end

  println(m)
end