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)

{-# LANGUAGE ScopedTypeVariables #-}

import Data.Array.IO
import Data.Array
import Data.IORef
import Control.Monad
import Control.Applicative

paint :: IOUArray (Int, Int) Char -> [(Int,Int)] -> [(Int,Int)] -> IO [(Int,Int)]
paint grid [] newq = return newq
paint grid (p@(y,x):queue) newq = do
  ((miny,minx),(maxy,maxx)) <- getBounds grid
  rd <- readArray grid p
  writeArray grid p '#'
  next <- filterM (\(ny,nx) ->
            if (ny < miny || nx < minx || ny > maxy || nx > maxx) then
              return False
            else do
              ng <- readArray grid (ny,nx)
              return (ng /= '#' && (ny,nx) `notElem` newq)
            ) [(y-1,x),(y+1,x),(y,x-1),(y,x+1)]
  paint grid queue (newq ++ next)

solve :: IOUArray (Int, Int) Char -> [(Int,Int)] -> Int -> IO Int
solve _ [] cnt = return cnt
solve grid black cnt = do
  black' <- paint grid black []
  solve grid black' (cnt+1)

main = do
  [h,w] <- map read . words <$> getLine :: IO [Int]
  strs <- replicateM h getLine :: IO [String]
  (grid :: IOUArray (Int, Int) Char) <- thaw $ listArray ((1,1),(h,w)) $ concat strs
  grid' <- freeze grid
  let black = [i | (i,e) <- assocs grid', e == '#']
  res <- solve grid black (-1) 
  print res