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: 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

------
local H, W = io.read("*n", "*n", "*l")
local grid = {}
local distance = {}
for i=1, H do
    grid[i] = str2tbl(io.read("*l"))
    distance[i] = {}
    for j=1, W do
        distance[i][j] = 2001
    end
end
--[[
for i=1, H do
    for j=1, W do
        print(i,j, grid[i][j])
    end
end
]]
local blacks = {}
for i=1, H do
    for j=1, W do
        local c = grid[i][j]
        if c == '#' then
            table.insert(blacks, {i, j})
        end
    end
end
for _, t in ipairs(blacks) do
    local i, j = t[1], t[2]
    distance[i][j] = 0
end
local function dfs(d, i, j)
    d = d + 1
    local x, y
    x, y = i-1, j
    if x >= 1 and distance[x][y] > d then
        distance[x][y] = d
        dfs(d, x, y)
    end
    x, y = i+1, j
    if x <= H and distance[x][y] > d then
        distance[x][y] = d
        dfs(d, x, y)
    end
    x, y = i, j-1
    if y >= 1 and distance[x][y] > d then
        distance[x][y] = d
        dfs(d, x, y)
    end
    x, y = i, j+1
    if y <= W and distance[x][y] > d then
        distance[x][y] = d
        dfs(d, x, y)
    end
end
for _, t in ipairs(blacks) do
    local i, j = t[1], t[2]
    dfs(0, i, j)
end
local dmax = 0
for i=1, H do
    for j=1, W do
        dmax = math.max(distance[i][j], dmax)
    end
end
print(dmax)