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: Wrong Answer)

{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}

import Control.Monad
import Data.Maybe (mapMaybe, isNothing)
import Data.List (foldl', partition)
import Data.Array.Unboxed ((!), UArray)
import qualified Data.Array.Unboxed as U

main = do
    [h, w] <- map (read :: String -> Int) . words <$> getLine
    -- a <- concat . words <$> getContents
    a <- concat <$> replicateM h getLine
    let ls = U.listArray ((1, 1), (w, h)) a :: UArray (Int, Int) Char
    let (black, white) = partition (\(i, e) -> e == '#') $ U.assocs ls
    let (!blacks, !whites) = (map fst black, map fst white)
    let answer = foldl' (hoge h w blacks) 0 whites
    print answer
    where getRange (ex, ey) (x, y) = abs (ex - x) + abs (ey - y)
          minRange h w blacks !ec = foldl' (hoho ec) (h + w) blacks 
          hoge h w blacks a b = max a (minRange h w blacks b)
          hoho ec a b = min a (getRange ec b)