Problem:
Score: 300 points

Problem Statement

We have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).

Initially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= #, and to make Square (i, j) white when s_{i, j}= ..

However, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.

Determine if square1001 can achieve his objective.

Constraints

H is an integer between 1 and 50 (inclusive).

W is an integer between 1 and 50 (inclusive).

For every (i, j) (1 \leq i \leq H, 1 \leq j \leq W), s_{i, j} is # or ..

Input

Input is given from Standard Input in the following format:

H W
s_{1, 1} s_{1, 2} s_{1, 3} ... s_{1, W}
s_{2, 1} s_{2, 2} s_{2, 3} ... s_{2, W}
: :
s_{H, 1} s_{H, 2} s_{H, 3} ... s_{H, W}

Output

If square1001 can achieve his objective, print Yes; if he cannot, print No.

Sample Input 1

3 3
.#.
###
.#.

Sample Output 1

Yes

One possible way to achieve the objective is shown in the figure below. Here, the squares being painted are marked by stars.

Sample Input 2

5 5
#.#.#
.#.#.
#.#.#
.#.#.
#.#.#

Sample Output 2

No

square1001 cannot achieve his objective here.

Sample Input 3

11 11
...#####...
.##.....##.
#..##.##..#
#..##.##..#
#.........#
#...###...#
.#########.
.#.#.#.#.#.
##.#.#.#.##
..##.#.##..
.##..#..##.

Sample Output 3

Yes

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import Control.Applicative
import qualified Data.Map as Map

main = do
    [h,w] <- map read . words <$> getLine :: IO [Int]
    d <- forM [1..h] $ \raw -> do
       line <- map f <$> getLine 
       return (g raw line)
    putStrLn $ solve (Map.fromList (concat d)) h w

solve :: Arr -> Int -> Int -> String
solve dict h w = if solvable dict h w
                    then "Yes"
                    else "No"

solvable :: Arr -> Int -> Int -> Bool
solvable dict h w = and $ map (okay dict h w) keys
    where keys = Map.keys dict 


type Arr = Map.Map (Int,Int) Bool

adj :: Int -> Int -> (Int,Int) -> [(Int,Int)]
adj h w (i,j) = filter fil [(i-1,j),(i+1,j),(i,j-1),(i,j+1)]
    where fil (x,y) = and [1<=x,x<=h,1<=y,y<=w]

okay :: Arr -> Int -> Int -> (Int,Int) -> Bool
okay dict h w (i,j) = if ok dict (i,j)
                         then or (map (ok dict) (adj h w (i,j)))
                         else True

ok dict (i,j) = dict Map.! (i,j)

dic :: Int -> Int -> Map.Map (Int,Int) Bool
dic h w= Map.fromList (zip keys falses)
    where falses = repeat False
          keys = [(i,j)| i <- [1..h], j <- [1..w]]

f :: Char -> Bool
f '#' = True
f '.' = False

g :: Int -> [Bool] -> [((Int,Int),Bool)]
g raw line = map h line'
    where h = \(col,b) -> ((raw,col),b)
          line' = zip [1..] line