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 8.8.3) (judge verdict: Wrong Answer)

import Data.List

main = do
  getLine
  co <- getContents
  let css = lines co
  let ans = compute css
  putStrLn $ if ans then "Yes" else "No"

-- 全ての'#'について、上下左右のいずれかに'#'があればよい。
-- 端については '.' にして失敗させる

compute :: [String] -> Bool
compute css = and $ map and chkSs
  where
    chk '.' _   = True
    chk '#' '#' = True
    chk _   _   = False
    cssN = repeat '.' : css -- 上
    cssS = tail css ++ [repeat '.'] -- 下
    cssE = map (tail.(++ ".")) css -- 右
    cssW = map ('.' :) css -- 左
    chkNs = zipWith (zipWith chk) css cssN
    chkSs = zipWith (zipWith chk) css cssS
    chkEs = zipWith (zipWith chk) css cssE
    chkWs = zipWith (zipWith chk) css cssW
    chkNSs = zipWith (zipWith (||)) chkNs chkSs
    chkEWs = zipWith (zipWith (||)) chkEs chkWs
    chk4s = zipWith (zipWith (||)) chkNSs chkEWs