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)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	h,w = readline() |> split |> parseMap
	a = ["" for i in 1:h]
	chk = -ones(Int,h,w)
	k = 0
	b = Tuple[]
	for i in 1:h
		a[i] = readline() |> chomp
		for j in 1:w
			if a[i][j] == '#'
				chk[i,j] = 0
				k += 1
				push!(b,(i,j))
			end
		end
	end
	while k < h*w
		x,y = shift!(b)
		if x>1
			if chk[x-1,y] < 0
				push!(b,(x-1,y))
				chk[x-1,y] = chk[x,y]+1
				k += 1
			end
		end
		if x<h
			if chk[x+1,y] < 0
				push!(b,(x+1,y))
				chk[x+1,y] = chk[x,y]+1
				k += 1
			end
		end
		if y>1
			if chk[x,y-1] < 0
				push!(b,(x,y-1))
				chk[x,y-1] = chk[x,y]+1
				k += 1
			end
		end
		if y<w
			if chk[x,y+1] < 0
				push!(b,(x,y+1))
				chk[x,y+1] = chk[x,y]+1
				k += 1
			end
		end
	end
	println(maximum(chk))
end

main()