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;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static System.Console;
using static System.Math;

namespace Atcoder
{
    class Program
    {
        static StreamWriter sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
        static void Main(string[] args)
        {
            try
            {
                SetOut(sw);
                Solve.Answer();
                Out.Flush();
            }
            catch (Exception ex)
            {
                WriteLine(ex.ToString());
            }
        }
    }

    public class Solve
    {
        public static void Answer()
        {
            var hw = IO.RSInt;
            string[] map = new string[hw[0]];
            for (int i = 0; i < hw[0]; i++)
            {
                map[i] = ReadLine();
            }
            // 上下左右の差分ベクトル
            int[] dx = new int[] { -1, 0, 1, 0 };
            int[] dy = new int[] { 0, -1, 0, 1 };
            for (int i = 0; i < hw[0]; i++)
            {
                for (int j = 0; j < hw[1]; j++)
                {
                    bool ok = false;
                    for (int k = 0; k < 4; k++)
                    {
                        if (map[i][j] == '#')
                        {
                            //移動できるマスに"#"があればOK！
                            if (0 <= i + dy[k] && i + dy[k] < hw[0] && 0 <= j + dx[k] && j + dx[k] < hw[1] && map[i + dy[k]][j + dx[k]] == '#')
                            {
                                ok = true;
                            }
                        }
                        else
                        {
                            ok = true;
                        }
                    }
                    if (!ok)
                    {
                        WriteLine("No");
                        return;
                    }
                }
            }
            WriteLine("Yes");
        }
    }

    public class IO
    {
        #region Input
        public static int RInt => int.Parse(ReadLine());
        public static long RLong => long.Parse(ReadLine());
        public static double RDouble => double.Parse(ReadLine());

        public static string[] RSString => ReadLine().Split();
        public static int[] RSInt => ReadLine().Split().Select(s => int.Parse(s)).ToArray();
        public static long[] RSLong => ReadLine().Split().Select(s => long.Parse(s)).ToArray();
        public static double[] RSDouble => ReadLine().Split().Select(s => double.Parse(s)).ToArray();
        #endregion

        #region Output
        public static void OutJoinSpace<T>(IEnumerable<T> list) => WriteLine(string.Join(" ", list));
        public static void WriteLineYes_or_No(bool flag) => WriteLine(flag ? "Yes" : "No");
        public static void WriteLineYES_or_NO(bool flag) => WriteLine(flag ? "YES" : "NO");
        #endregion
    }

    public class Mod
    {
        #region
        private readonly static long M = 1000000007;

        public static long Add(long a, long b) => (a * b) % M;
        public static long Sub(long a, long b) => (a - b) % M >= 0 ? (a - b) % M : (a - b) % M + M;
        public static long Multi(long a, long b) => (a * b) % M;
        #endregion
    }
}