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: Runtime Error)

let
  H, W = map(x -> parse(Int, x), split(readline()))
  
  A = []
  for i=1:H
    push!(A, readline())
  end
  
  black = []
  initBCount = 0
  white = zeros(H*W)
  wcount = 0

  h = 0
  for ah in A
    w = 0
    for aw in ah
      if aw === '#'
        push!(black, W * h + w + 1)
        white[W * h + w + 1] = 0
        initBCount += 1
      else
        white[W * h + w + 1] = 1
        wcount += 1
      end
      w += 1
    end
    h += 1
  end
  retCount = 0
  nextBCount = 0

  while true
    
    b = pop!(black)
    initBCount -= 1
    addNum = []
    if b > W
      push!(addNum, b - W)
    end
    if b <= W * (H - 1)
      push!(addNum, b + W)
    end
    if b % W != 0
      push!(addNum, b + 1)
    end
    if b % W != 1
      push!(addNum, b - 1)
    end
    for num in addNum
      if white[num] == 1
        white[num] = 0
        black = append!([num], black)
        nextBCount += 1
        wcount -= 1
      end
    end
    if initBCount == 0
      retCount += 1
      if wcount == 0
        break
      end

      initBCount = nextBCount
      nextBCount = 0
    end 
  end 
  print(retCount)


end