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: Accepted)

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] = {}
    local grid_i, distance_i = grid[i], distance[i]
    for j=1, W do
        distance_i[j] = grid_i[j] == '#' and 0 or 2001
    end
end
local math_min = math.min
for i=1, H do
    local distance_i = distance[i]
    for j=2, W do
        distance_i[j] = math_min(distance_i[j], distance_i[j-1] + 1)
    end
end
for i=1, H do
    local distance_i = distance[i]
    for j=W-1, 1, -1 do
        distance_i[j] = math_min(distance_i[j], distance_i[j+1] + 1)
    end
end
for i=2, H do
    local distance_i = distance[i]
    local distance_im1 = distance[i-1]
    for j=1, W do
        distance_i[j] = math_min(distance_i[j], distance_im1[j] + 1)
    end
end
for i=H-1, 1, -1 do
    local distance_i = distance[i]
    local distance_ip1 = distance[i+1]
    for j=1, W do
        distance_i[j] = math_min(distance_i[j], distance_ip1[j] + 1)
    end
end
local ans = 0
local math_max = math.max
for i=1, H do
    local distance_i = distance[i]
    for j=1, W do
        ans = math_max(ans, distance_i[j])
    end
end
print(ans)