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 LuaJIT (2.0.4) (judge verdict: Runtime Error)

local ior = io.input()
local h, w = ior:read("*n", "*n", "*l")
local map = {}
for i = 1, h * w do map[i] = 0 end
local str = ""

local function getidx(wid, hgt)
  return (hgt - 1) * w + wid
end

local tasks = {}
local tasknum = 0
local done = 0

for i = 1, h do
  str = ior:read()
  for j = 1, w do
    local idx = getidx(i, j)
    if(str:sub(j, j) == ".") then
      map[idx] = 3000
    else
      table.insert(tasks, idx)
      tasknum = tasknum + 1
    end
  end
end

local function walk(src, dst)
  if(map[src] + 1 < map[dst]) then
    map[dst] = map[src] + 1
    table.insert(tasks, dst)
    tasknum = tasknum + 1
  end
end

while(done < tasknum) do
  done = done + 1
  local curidx = tasks[done]
  if(w < curidx) then walk(curidx, curidx - w) end
  if(curidx <= w * (h - 1)) then walk(curidx, curidx + w) end
  if(curidx % w ~= 0) then walk(curidx, curidx + 1) end
  if(curidx % w ~= 1) then walk(curidx, curidx - 1) end
end
local max = 0
local mma = math.max
for i = 1, h * w do
  max = mma(max, map[i])
end
print(max)