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 = {}
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_used = {}
while true do
    local all_black = true
    local blacks = {}
    for i=1, H do
        for j=1, W do
            local c = grid[i][j]
            if c == '.' then
                all_black = false
            end
            if c == '#' then
                if not blacks_used[i*1000+j] then
                    table.insert(blacks, {i, j})
                    blacks_used[i*1000+j] = true
                end
            end
        end
    end
    if all_black then
        print(count)
        return
    end
    for _, t in ipairs(blacks) do
        local i, j = t[1], t[2]
        if i >= 2 then
            grid[i-1][j] = '#'
        end
        if i <= H - 1 then
            grid[i+1][j] = '#'
        end
        if j >= 2 then
            grid[i][j-1] = '#'
        end
        if j <= W - 1 then
            grid[i][j+1] = '#'
        end
    end
    --[[
    print(count, #blacks)
    for i=1, H do
        print(table.concat(grid[i], ''))
    end
    ]]
    count = count + 1
end