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 (Lua 5.3.5) (judge verdict: Accepted)

local h, w = io.read("*n", "*n", "*l")
local tasks = {}
local len = {}
for i = 1, h do
  s = io.read()
  for j = 1, w do
    local idx = (i - 1) * w + j
    if s:sub(j, j) == "#" then
      len[idx] = 0
      table.insert(tasks, idx)
    else
      len[idx] = 1000000007
    end
  end
end
local done = 0

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

while done < #tasks do
  done = done + 1
  local idx = tasks[done]
  if w < idx then walk(idx, idx - w) end
  if idx <= (h - 1) * w then walk(idx, idx + w) end
  if 1 < w then
    if idx % w ~= 0 then walk(idx, idx + 1) end
    if idx % w ~= 1 then walk(idx, idx - 1) end
  end
end
local ans = len[1]
for i = 2, h * w do
  ans = math.max(ans, len[i])
end
print(ans)