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 Lua (LuaJIT 2.1.0) (judge verdict: Accepted)

local h,w=io.read("n","n","l")
local a={}
local dist={}
for i=1,h do
    local input=io.read()
    a[i]={}
    dist[i]={}
    for j=1,w do
        a[i][j]=input:byte(j)
        dist[i][j]=-1
    end
end

local que={}
for i=1,h do
    for j=1,w do
        if a[i][j]==35 then
            dist[i][j]=0
            table.insert(que,{i,j})
        end
    end
end

local di={1,0,-1,0}
local dj={0,1,0,-1}
local l=1
while que[l] do
    local i=que[l][1]
    local j=que[l][2]
    for k=1,4 do
        local ni=i+di[k]
        local nj=j+dj[k]
        if dist[ni] and dist[ni][nj] and dist[ni][nj]==-1 then
            dist[ni][nj]=dist[i][j]+1
            table.insert(que,{ni,nj})
        end 
    end
    l=l+1
end

local max=0
for i=1,h do
    for j=1,w do
        max=math.max(max,dist[i][j])
    end
end
print(max)