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: Accepted)

{-# LANGUAGE
  ScopedTypeVariables, BangPatterns, TupleSections, ExplicitForAll,
  LambdaCase, MultiWayIf, Unsafe, RecordWildCards, FlexibleContexts, CPP,
  NoMonomorphismRestriction, GADTs, PatternGuards,
  RankNTypes, EmptyDataDecls, EmptyCase, ViewPatterns #-}


import Data.Bits
import Data.List
import Data.Maybe
import Data.Tuple
import Data.Ord
import Data.Int
import Data.Word
import Data.Char
import Data.Function
import Data.STRef
import Data.IORef
import Data.Monoid
import Data.Functor
import System.IO
import Control.Arrow
import Control.Applicative
import Control.Monad
import Control.Monad.Primitive
import Control.Monad.State.Strict
import Control.Monad.ST
import Control.Monad.ST.Lazy (strictToLazyST, lazyToStrictST)
import qualified Control.Monad.ST.Lazy as STL
-- import Control.Monad.ST.Safe
import Control.DeepSeq
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy.Char8 as BSL
import qualified Data.ByteString.Builder as BSB
import Data.IntMap (IntMap)
import qualified Data.IntMap.Strict as IMS
import qualified Data.IntMap.Lazy as IML
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Array.IArray as A
import qualified Data.Array.MArray.Safe as A
import qualified Data.Array.MArray as A
import Data.Array (Array)
import Data.Array.Unboxed (UArray)
import Data.Array.IArray (IArray)
import Data.Array.MArray.Safe (MArray)
import Data.Array.IO.Safe (IOArray, IOUArray)
import Data.Array.ST.Safe (STArray, STUArray, runSTArray, runSTUArray)
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Primitive as VP
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import qualified Data.Attoparsec.ByteString.Char8 as Atto
import qualified Data.Primitive as Pr

main :: IO ()
main = do
  [h,w] <- map readInt . words <$> getLine
  as <- VU.map (=='#') . VU.take (h*w) . VU.filter (>='!') .
    VU.unfoldr BSL.uncons <$> BSL.getContents
  print $ query h w as

query :: Int -> Int -> VU.Vector Bool -> Int
query h w !as = runST $ do
  !queue <- initQueue (h*w)
  forM_ [0..h-1] $ \ !r ->
    forM_ [0..w-1] $ \ !c ->
      when (as VU.! (r*w+c)) $ putQueue queue (r,c,0)
  mas <- VU.unsafeThaw as
  let loop (!r,!c,!d) = do
        forM_ [rc | (b,rc) <- [(r>0,   (r-1, c)),
                               (r<h-1, (r+1, c)),
                               (c>0,   (r, c-1)),
                               (c<w-1, (r, c+1))], b]
          $ \(r1,c1) -> unlessM (VUM.read mas (r1*w+c1)) $ do
          VUM.write mas (r1*w+c1) True
          putQueue queue (r1,c1,d+1)
        maybe (return d) loop =<< takeQueue queue
  maybe (return $! -1) loop =<< takeQueue queue
  
type QueueEntry = (Int,Int,Int)

data Queue s = Queue {-# UNPACK #-} !(Pr.MutableByteArray s)
               {-# UNPACK #-} !(VUM.MVector s QueueEntry)

{-# INLINE initQueue #-}
initQueue :: Int -> ST s (Queue s)
initQueue len = do
  startEnd <- Pr.newByteArray (2 * Pr.sizeOf (0::Int))
  Pr.setByteArray startEnd 0 2 (0::Int)
  place <- VUM.new len
  return $! (Queue startEnd place)

{-# INLINE putQueue #-}
putQueue :: Queue s -> QueueEntry -> ST s ()
putQueue (Queue startEnd place) val = do 
  end <- Pr.readByteArray startEnd 1
--  unsafeIOToPrim $ putStrLn $ "putQueue " ++ show val ++ " with end:"
--                               ++ show end
  if end >= VUM.length place then error "putQueue: capacity full" else do
  Pr.writeByteArray startEnd 1 $! end+1
  VUM.unsafeWrite place end val

{-# INLINE takeQueue #-}
takeQueue :: Queue s -> ST s (Maybe QueueEntry)
takeQueue (Queue startEnd place) = do
  start <- Pr.readByteArray startEnd 0
  end <- Pr.readByteArray startEnd 1
--  unsafeIOToPrim $ putStrLn $ "takeQueue start:" ++ show start ++ " end:"
--    ++ show end
  if start >= end then return Nothing else do
  Pr.writeByteArray startEnd 0 $! start+1
  Just <$> VUM.unsafeRead place start
  

#define IL(f) {-# INLINE f #-}; f

rInt :: StateT BSL.ByteString Maybe Int
IL(rInt) = StateT $ BSL.readInt . BSL.dropWhile (<'!')
rIntS :: StateT BS.ByteString Maybe Int
IL(rIntS) = StateT $ BS.readInt . BS.dropWhile (<'!')

-- unlessM, whenM :: (Monad m) => m Bool -> m () -> m ()
IL(whenM) = (. flip when) . (>>=)
IL(unlessM) = (. flip unless) . (>>=)

IL(wrA) = A.writeArray
IL(rdA) = A.readArray
IL(mdA) = \arr f !i -> do
  ai <- rdA arr i
  let fai = f ai 
  wrA arr i fai
  return (ai,fai)
{-# INLINE mdA' #-}
mdA' = \arr f !i -> do
  !ai <- rdA arr i
  let !fai = f ai
  wrA arr i fai
  return (ai,fai)
IL(swapA) = \arr !i !j -> do
  ai <- rdA arr i
  wrA arr i =<< rdA arr j
  wrA arr j ai

#define D(f,r,d)\
  IL(f) :: Integral a=>a->d; f=fromIntegral;\
  IL(r) :: String->d; r=read
#define C(f,r,g,h,d) D(f,r,d);\
  g,h :: RealFrac a=>a->d; IL(g)=floor; IL(h)=ceiling
C(_toInteger_,readInteger,floorInteger,ceilInteger,Integer)
C(toInt,readInt,floorInt,ceilInt,Int)
C(toI8,readI8,floorI8,ceilI8,Int8)
C(toI16,readI16,floorI16,ceilI16,Int16)
C(toI32,readI32,floorI32,ceilI32,Int32)
C(toI64,readI64,floorI64,ceilI64,Int64)
C(toWord,readWord,floorWord,ceilWord,Word)
C(toW8,readW8,floorW8,ceilW8,Word8)
C(toW16,readW16,floorW16,ceilW16,Word16)
C(toW32,readW32,floorW32,ceilW32,Word32)
C(toW64,readW64,floorW64,ceilW64,Word64)
D(toDouble,readDouble,Double)
D(toFloat,readFloat,Float)
#undef D
#undef C

#define N(f,g,h,a,m)\
  IL(f) :: forall e i s. (C(a,m)A.Ix i) => (i,i) -> e -> m (a i e);\
  f=A.newArray;\
  IL(g) :: forall e i s. (C(a,m)A.Ix i) => (i,i) -> m (a i e);\
  g=A.newArray_;\
  IL(h) :: forall e i s. (C(a,m)A.Ix i) => (i,i) -> [e] -> m (a i e);\
  h=A.newListArray
#define C(a,m)
N(newIOA,newIOA_,newIOAL,IOArray,IO)
N(newSTA,newSTA_,newSTAL,STArray s,ST s)
#undef C
#define C(a,m) MArray (a) e (m), 
N(newIOUA,newIOUA_,newIOUAL,IOUArray,IO)
N(newSTUA,newSTUA_,newSTUAL,STUArray s,ST s)
#undef C
#undef N

#undef IL