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)

function main()
  h, w = map(n -> parse(Int,n), split(readline()))
  grid = fill(1000000000, (w,h))

  for y in 1:h
    s = readline()
    for x in 1:w
      if s[x] == '#'
        grid[x,y] = 0
      end
    end
  end

  for y in 1:h
    for x in 2:w
      if grid[x,y] > grid[x-1,y]+1
        grid[x,y] = grid[x-1,y]+1
      end
      if grid[w-x+1,y] > grid[w-x+2,y]+1
        grid[w-x+1,y] = grid[w-x+2,y]+1
      end
    end
  end

  for x in 1:w
    for y in 2:h
      if grid[x,y] > grid[x,y-1]+1
        grid[x,y] = grid[x,y-1]+1
      end
      if grid[x,h-y+1] > grid[x,h-y+2]+1
        grid[x,h-y+1] = grid[x,h-y+2]+1
      end
    end
  end

  println(maximum(grid))
end

main()