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
local function List_new()
    local tbl = {}
    local first = 1
    local last = 0
    local function count()
        return last - first + 1
    end
    local function pushright(value)
        local new_last = last + 1
        last = new_last
        tbl[last] = value
    end
    local function popleft(value)
        --if first > last then error("list is empty") end
        local value = tbl[first]
        tbl[first] = nil
        first = first + 1
        return value
    end
    return {pushright, popleft, count}
end
local pushright, popleft, count = 1, 2, 3

------
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 ans = 0
local blacks = List_new()
local blacks_used = {}
for i=1, 1000*1000+1000 do
    blacks_used[i] = false
end
local function not_blacks_used(i, j)
    local k = i*1000+j
    local used = blacks_used[k]
    blacks_used[k] = true
    return not used
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)
                blacks[pushright](j)
            end
        end
    end
end
local dx = {-1, 1, 0, 0}
local dy = {0, 0, -1, 1}

local next = List_new()
while blacks[count]() > 0 do
    while blacks[count]() > 0 do
        local i = blacks[popleft]()
        local j = blacks[popleft]()
        for k=1, 4 do
            local x, y = i + dx[k], j + dy[k]
            if x >= 1 and x <= H and y >= 1 and y <= W then
                if not_blacks_used(x, y) then
                    next[pushright](x)
                    next[pushright](y)
                end
            end
        end
    end
    ans = ans + 1
    blacks, next = next, blacks
end
print(ans-1)