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: Time Limit Exceeded)

--https://www.lua.org/pil/11.4.html
local List = {}
function List.new ()
  return {first = 0, last = -1}
end

function List.pushleft (list, value)
  local first = list.first - 1
  list.first = first
  list[first] = value
end

function List.pushright (list, value)
  local last = list.last + 1
  list.last = last
  list[last] = value
end

function List.popleft (list)
  local first = list.first
  if first > list.last then return false end
  local value = list[first]
  list[first] = nil
  list.first = first + 1
  return value
end

function List.popright (list)
  local last = list.last
  if list.first > last then return false end
  local value = list[last]
  list[last] = nil
  list.last = last - 1
  return value
end

----------

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

local dist={}
local iue=List.new()
local jue=List.new()
for i=1,h do
    dist[i]={}
    for j=1,w do
        if a[i][j]==35 then
            dist[i][j]=0
            List.pushright(iue,i)
            List.pushright(jue,j)
        else
            dist[i][j]=-1
        end
    end
end

local di={1,0,-1,0}
local dj={0,1,0,-1}
while true do
    local i=List.popleft(iue)
    if not i then
        break
    end
    local j=List.popleft(jue)
    for k=1,4 do
        local ni=i+di[k]
        local nj=j+dj[k]
        if ni<1 or ni>h or nj<1 or nj>w then
            goto continue
        end
        if dist[ni][nj]==-1 then
            dist[ni][nj]=dist[i][j]+1
            List.pushright(iue,ni)
            List.pushright(jue,nj)
        end
        ::continue::
    end
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)