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 Python (3.4.3) (judge verdict: Wrong Answer)

import sys

line_size, row_size = map(int, input().split())
mapmap = []#地図初期化

for i in range(line_size):
    mapmap.append(list(input()))

#探索関数
def Dfs(px, py):
    global mapmap
    #自分のいるところを変換→globalにして更新
    mapmap[py][py] = '.'

    #自分の動けるところ定義
    move_x = [1, -1, 0, 0]
    move_y = [0, 0, 1, -1]
    for i in range(len(move_x)):#動ける範囲で探索
        nx = px + move_x[i]
        ny = py + move_y[i]
        if 0 <= nx and line_size > nx and 0 <= ny and row_size > ny:
            if mapmap[nx][ny] == '#':#もし黒塗りなら
                Dfs(nx, ny)#自分のいるところから突き進むむからfirst in last out

#開始条件探索
def Start_check(mapmap, px, py):
    start_flg = False
    move_x = [1, -1, 0, 0]
    move_y = [0, 0, 1, -1]
    for i in range(len(move_x)):#動ける範囲で探索
        nx = px + move_x[i]
        ny = py + move_y[i]
        if 0 <= nx and line_size > nx and 0 <= ny and row_size > ny:
            if mapmap[nx][ny] == '#':#もし黒塗りなら
                start_flg = True
    
    if start_flg == True:
        print('No')
        sys.exit()


#Main
count = 0#探索回数（塗り絵した回数）
for i in range(line_size):
    for j in range(row_size):
        if mapmap[i][j] == '#':
            Start_check(mapmap, i, j)
            Dfs(i, j)
            count += 1

#何もしなかった場合
if count == 0:
    print('No')
else:
    print('Yes')