Problem:
Score : 200 points

Problem Statement

You are given an H × W grid.

The squares in the grid are described by H strings, S_1,...,S_H.

The j-th character in the string S_i corresponds to the square at the i-th row from the top and j-th column from the left (1 \leq i \leq H,1 \leq j \leq W).

. stands for an empty square, and # stands for a square containing a bomb.

Dolphin is interested in how many bomb squares are horizontally, vertically or diagonally adjacent to each empty square.

(Below, we will simply say "adjacent" for this meaning. For each square, there are at most eight adjacent squares.)

He decides to replace each . in our H strings with a digit that represents the number of bomb squares adjacent to the corresponding empty square.

Print the strings after the process.

Constraints

1 \leq H,W \leq 50

S_i is a string of length W consisting of # and ..

Input

Input is given from Standard Input in the following format:

H W
S_1
:
S_H

Output

Print the H strings after the process.

The i-th line should contain a string T_i of length W, where the j-th character in T_i corresponds to the square at the i-th row from the top and j-th row from the left in the grid (1 \leq i \leq H, 1 \leq j \leq W).

Sample Input 1

3 5
.....
.#.#.
.....

Sample Output 1

11211
1#2#1
11211

For example, let us observe the empty square at the first row from the top and first column from the left.

There is one bomb square adjacent to this empty square: the square at the second row and second column.

Thus, the . corresponding to this empty square is replaced with 1.

Sample Input 2

3 5
#####
#####
#####

Sample Output 2

#####
#####
#####

It is possible that there is no empty square.

Sample Input 3

6 6
#####.
#.#.##
####.#
.#..#.
#.##..
#.#...

Sample Output 3

#####3
#8#7##
####5#
4#65#2
#5##21
#4#310

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies  #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances       #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf           #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables       #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications    #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns  #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.Reader
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bifunctor
import           Data.Bool
import qualified Data.ByteString                   as B
import qualified Data.ByteString.Builder           as B
import qualified Data.ByteString.Char8             as C
import qualified Data.ByteString.Internal          as B
import qualified Data.ByteString.Unsafe            as B
import           Data.Char
import qualified Data.Foldable                     as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict                as IM
import qualified Data.IntSet                       as IS
import qualified Data.List                         as L
import qualified Data.Map.Strict                   as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Proxy
import           Data.Ratio
import           Data.Semigroup
import qualified Data.Set                          as S
import           Data.Tuple
import qualified Data.Vector                       as V
import qualified Data.Vector.Algorithms.Intro      as Intro
import qualified Data.Vector.Fusion.Stream.Monadic as MS
import qualified Data.Vector.Fusion.Bundle.Monadic as MB
import           Data.Vector.Fusion.Util
import qualified Data.Vector.Generic               as G
import qualified Data.Vector.Generic.Mutable       as GM
import qualified Data.Vector.Mutable               as VM
import qualified Data.Vector.Primitive             as P
import qualified Data.Vector.Primitive.Mutable     as PM
import qualified Data.Vector.Unboxed               as U
import qualified Data.Vector.Unboxed.Mutable       as UM
import           Debug.Trace
import           Foreign                           hiding (void)
import           GHC.Exts
import           GHC.TypeLits
import           System.IO
import           Unsafe.Coerce

#define MOD 1000000007

main :: IO ()
main = do
    [h, w] <- map read.words <$> getLine
    cs <- U.unfoldrN (h*w) (runParser char) . C.filter (not.isSpace)
        <$> C.getContents
    let res = solve h w cs
    putStr$unlines[U.toList $ U.slice (i * w) w res|i<-[0..h-1]]

conv '.' = '0'
conv c = c

solve :: Int -> Int -> U.Vector Char -> U.Vector Char
solve h w (U.map conv -> mat0) = U.create $ do
    mat <- U.thaw mat0
    rep h $ \i -> do
        rep w $ \j -> do
            mij <- UM.unsafeRead mat (ix i j)
            when (mij == '#') $ do
                neighbor8 i j $ \i' j' -> when (inGrid h w i' j' ) $ do
                    mij' <- UM.unsafeRead mat (ix i' j')
                    when (mij' /= '#') $ do
                        UM.unsafeModify mat succ (ix i' j')
    return mat
  where
    ix x y = x * w + y
    {-# INLINE ix #-}

inGrid :: Int -> Int -> Int -> Int -> Bool
inGrid h w x y = 0 <= x && x < h && 0 <= y && y < w
{-# INLINE inGrid #-}

neighbor4 :: (Applicative f) => Int -> Int -> (Int -> Int -> f ()) -> f ()
neighbor4 x y f = f (x - 1) y *> f x (y - 1) *> f x (y + 1) *> f (x + 1) y
{-# INLINE neighbor4 #-}

neighbor8 :: (Applicative f) => Int -> Int -> (Int -> Int -> f ()) -> f ()
neighbor8 x y f
    =  f (x - 1) (y - 1) *> f (x - 1) y *> f (x - 1) (y + 1)
    *> f (x    ) (y - 1)                *> f (x    ) (y + 1)
    *> f (x + 1) (y - 1) *> f (x + 1) y *> f (x + 1) (y + 1)
{-# INLINE neighbor8 #-}

-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: (Monad m) => Int -> (Int -> m ()) -> m ()
rep n = flip MS.mapM_ (stream 0 n)
{-# INLINE rep #-}
rev :: (Monad m) => Int -> (Int -> m ()) -> m ()
rev !n = flip MS.mapM_ (streamR 0 n)
{-# INLINE rev #-}
stream :: (Monad m) => Int -> Int -> MS.Stream m Int
stream !l !r = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream #-}
streamR :: (Monad m) => Int -> Int -> MS.Stream m Int
streamR !l !r = MS.Stream step (r - 1) where { step x | x >= l = return $ MS.Yield x (x - 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] streamR #-}
stream' :: (Monad m) => Int -> Int -> Int -> MS.Stream m Int
stream' !l !r !d = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + d) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream' #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL :: Int -> Int -> Int
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL :: Int -> Int -> Int
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}
skipSpaces :: Parser ()
skipSpaces = modify' (C.dropWhile isSpace)
{-# INLINE skipSpaces #-}
lowerBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
lowerBoundM low high p = go low high where { go !low !high | high <= low = return high | otherwise = p mid >>= bool (go (mid + 1) high) (go low mid) where { mid = low + unsafeShiftRL (high - low) 1}}
{-# INLINE lowerBoundM #-}
upperBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
upperBoundM low high p = do { flg <- p high; if flg then return high else subtract 1 <$!> lowerBoundM low high (fmap not . p)}
{-# INLINE upperBoundM #-}
lowerBound :: Int -> Int -> (Int -> Bool) -> Int
lowerBound low high p = runIdentity (lowerBoundM low high (return . p))
{-# INLINE lowerBound #-}
upperBound :: Int -> Int -> (Int -> Bool) -> Int
upperBound low high p = runIdentity (upperBoundM low high (return . p))
{-# INLINE upperBound #-}