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: Accepted)

const H,W=map(x->parse(Int,x),split(readline()))
const S=readlines()
const P=Pair{Int,Int}[]
const D=-ones(Int,H,W)
function init()
	for i=1:H,j=1:W
		if S[i][j]=='#'
			push!(P,i=>j)
			D[i,j]=0
		end
	end
end
function ev(x,y)
	for (dx,dy)=[0=>1,0=>-1,1=>0,-1=>0]
		tx=x+dx
		ty=y+dy
		if 1<=tx<=H&&1<=ty<=W&&D[tx,ty]==-1
			D[tx,ty]=D[x,y]+1
			push!(P,tx=>ty)
		end
	end
end
function main()
	init()
	while !isempty(P)
		(x,y)=shift!(P)
		ev(x,y)
	end
	println(maximum(D))
end
main()