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 (5.3.2) (judge verdict: Time Limit Exceeded)

local function str2tbl(s)
    local t = {string.byte(s, 1, #s)}
    for i=1, #t do
        t[i] = string.char(t[i])
    end
    return t
end

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

function List:pushleft(value)
  local first = self.first - 1
  self.first = first
  self[first] = value
end

function List:pushright(value)
  local last = self.last + 1
  self.last = last
  self[last] = value
end

function List:popleft()
  local first = self.first
  if first > self.last then error("list is empty") end
  local value = self[first]
  self[first] = nil        -- to allow garbage collection
  self.first = first + 1
  return value
end

function List:popright()
  local last = self.last
  if self.first > last then error("list is empty") end
  local value = self[last]
  self[last] = nil         -- to allow garbage collection
  self.last = last - 1
  return value
end

function List:count()
    return self.last - self.first + 1
end

------
local H, W = io.read("*n", "*n", "*l")
local grid = {}
for i=1, H do
    grid[i] = str2tbl(io.read("*l"))
end
--[[
for i=1, H do
    for j=1, W do
        print(i,j, grid[i][j])
    end
end
]]
local count = 0
local blacks = List.new()
local blacks_used = {}
local function not_blacks_used(i, j)
    if not blacks_used[i*1000+j] then
        blacks_used[i*1000+j] = true
        return true
    end
    return false
end
for i=1, H do
    for j=1, W do
        local c = grid[i][j]
        if c == '#' then
            if not_blacks_used(i, j) then
                blacks:pushright({i, j})
            end
        end
    end
end
local tuples = {{-1,0},{1,0},{0,-1},{0,1}}
local next = List.new()
while blacks:count() > 0 do
    while blacks:count() > 0 do
        local t = blacks:popleft()
        local i, j = t[1], t[2]
        for _, tuple in ipairs(tuples) do
            local x,y = i + tuple[1], j + tuple[2]
            if x >= 1 and x <= H and y >= 1 and y <= W then
                if not_blacks_used(x, y) then
                    next:pushright({x, y})
                end
            end
        end
    end
    count = count + 1
    blacks, next = next, blacks
end
print(count-1)