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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;

namespace ABC
{
    class ABC096C
    {
        public static int H = 0;
        public static int W = 0;
        public static char[,] Masu = null;

        static int[] dx = new int[4] { 1, -1, 0, 0 };
        static int[] dy = new int[4] { 0, 0, 1, -1 };

        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');
            H = int.Parse(str[0]);//高さ
            W = int.Parse(str[1]);//幅

            Masu = new char[H, W];
            for (int h = 0; h < H; ++h)
            {
                int w = 0;
                var line = Console.ReadLine();
                foreach (char s in line)
                {
                    Masu[h, w] = s;
                    ++w;
                }
            }

            bool ans = Judge();
            Console.WriteLine("{0}", ans ? "Yes" : "No");
        }
        //# : 塗りたい
        //. : 塗れない
        //@ : 塗った

        static bool Judge()
        {
            //与えられた図形に対して、#を点としてグラフを構築
            //グラフ上の点がすべて連結(== 縦か横に別の点がある)であればtrue,孤立点があればfalse
            var graph = new int[H, W];
            for (int h = 0; h < H; ++h)
            {
                for (int w = 0; w < W; ++w)
                {
                    graph[h, w] = 0;
                }
            }
            for (int h = 0; h < H; ++h)
            {
                for (int w = 0; w < W; ++w)
                {
                    //#マスを見つけたら
                    if (Masu[h, w] == '#')
                    {
                        //隣接マスを黒くぬれるか調べる
                        int dir = -1;
                        bool canPaint = isConnect(h, w, out dir);
                        if (canPaint == true)
                        {
                            //塗ったマスは@とする
                            Masu[h, w] = '@';
                            Masu[h + dy[dir], w + dx[dir]] = '@';
                        }
                    }
                }
            }

            for (int h = 0; h < H; ++h)
            {
                for (int w = 0; w < W; ++w)
                {
                    //塗りたいのに塗れないマスがあったら失敗
                    if (Masu[h, w] == '#') return false;
                }
            }

            return true;
        }

        static bool isConnect(int h, int w, out int dir)
        {
            for (int i = 0; i < 4; ++i)
            {
                int targetH = h + dy[i];
                int targetW = w + dx[i];
                //キャンバス外なら飛ばす
                if(targetH < 0 || H <= targetH) { continue; }
                if(targetW < 0 || W <= targetW) { continue; }

                if (Masu[targetH, targetW] == '#' || Masu[targetH, targetW] == '@')
                {
                    dir = i;
                    return true;
                }
            }
            dir = -1;
            return false;
        }
    }
}