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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import Data.List

main = do
  [h,w] <- map read . words <$> getLine
  as <- zip [1..] <$> replicateM h (fmap (zip [1..]) getLine)
  print $ paints (getPos as) (h,w) 0

getPos :: [(Int,[(Int,Char)])] -> [(Int,Int)]
getPos [] = []
getPos ((_,[]):zs) = getPos zs
getPos ((x,(y,'#'):ys):zs) = (x,y) : getPos ((x,ys):zs)
getPos ((x,_:ys):zs) = getPos ((x,ys):zs)
getPos (_:zs)              = getPos zs

paint (x,y) = [(x,y),(x+1,y),(x-1,y),(x,y+1),(x,y-1)]

paints as (h,w) acc = if length as == h*w then acc else paints as' (h,w) (acc+1)
  where 
    as' = nub . filter p . concat $ map paint as
    p (x,y) = 1 <= x && x <= h && 1 <= y && y <= w