Problem: Bob is a farmer. He has a large pasture with many sheep. Recently, he has lost some of them due to wolf attacks. He thus decided to place some shepherd dogs in such a way that all his sheep are protected.

The pasture is a rectangle consisting of R × C cells. Each cell is either empty, contains a sheep, a wolf or a dog. Sheep and dogs always stay in place, but wolves can roam freely around the pasture, by repeatedly moving to the left, right, up or down to a neighboring cell. When a wolf enters a cell with a sheep, it consumes it. However, no wolf can enter a cell with a dog.

Initially there are no dogs. Place dogs onto the pasture in such a way that no wolf can reach any sheep, or determine that it is impossible. Note that since you have many dogs, you do not need to minimize their number. 

Input

First line contains two integers R (1 ≤ R ≤ 500) and C (1 ≤ C ≤ 500), denoting the number of rows and the numbers of columns respectively.

Each of the following R lines is a string consisting of exactly C characters, representing one row of the pasture. Here, 'S' means a sheep, 'W' a wolf and '.' an empty cell.

Output

If it is impossible to protect all sheep, output a single line with the word "No".

Otherwise, output a line with the word "Yes". Then print R lines, representing the pasture after placing dogs. Again, 'S' means a sheep, 'W' a wolf, 'D' is a dog and '.' an empty space. You are not allowed to move, remove or add a sheep or a wolf.

If there are multiple solutions, you may print any of them. You don't have to minimize the number of dogs.

Examples

Input

6 6
..S...
..S.W.
.S....
..W...
...W..
......


Output

Yes
..SD..
..SDW.
.SD...
.DW...
DD.W..
......


Input

1 2
SW


Output

No


Input

5 5
.S...
...S.
S....
...S.
.S...


Output

Yes
.S...
...S.
S.D..
...S.
.S...

Note

In the first example, we can split the pasture into two halves, one containing wolves and one containing sheep. Note that the sheep at (2,1) is safe, as wolves cannot move diagonally.

In the second example, there are no empty spots to put dogs that would guard the lone sheep.

In the third example, there are no wolves, so the task is very easy. We put a dog in the center to observe the peacefulness of the meadow, but the solution would be correct even without him.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class Main {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskC {
		static boolean visited[]  ;
		static boolean found = false; 
		static int steps = 0 ;
		static int n ; 
		static int[][] memo ;
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int r = in.nextInt() ; 
			int c = in.nextInt() ; 

			char [][] matrix = new char[r][c] ; 
			for (int i = 0; i < r; i++)
			{
				String x = in.next() ; 
				for (int j = 0; j < c; j++)
				{
					matrix[i][j] = x.charAt(j) ;
				}
			}

			for (int i = 0; i < r; i++)
			{
				for (int j = 0; j < c; j++)
				{
					if(matrix[i][j] == '.')
						matrix[i][j] = 'D' ;
				}
			}
			boolean res =  true ; 
			for (int i = 0; i <r; i++)
			{
				for (int j = 0; j <c; j++)
				{
					if(matrix[i][j]=='S' && i>0 && matrix[i-1][j]=='W')
					{
						res= false ; 
						System.out.println("NO");
						return ;
					}
					if(matrix[i][j]=='S' && j>0 && matrix[i][j-1]=='W')
					{
						res= false ; 
						System.out.println("NO");
						return ;
					}
					if(matrix[i][j]=='S' && i<r-1 && matrix[i+1][j]=='W')
					{
						res= false ; 
						System.out.println("NO");
						return ;
					}
					if(matrix[i][j]=='S' && j<c-1 && matrix[i][j+1]=='W')
					{
						res= false ; 
						System.out.println("NO");
						return ;
					}
				}
			}
			System.out.println("YES");
			for (int i = 0; i < r; i++)
			{
				for (int j = 0; j < c; j++)
				{
					System.out.print(matrix[i][j]+"");
				}
				System.out.println("");
			}


		}

		public static String solve(String x){

			int n = x.length() ; 
			String y = "" ;
			for (int i = 0; i < n-2; i+=2)
			{
				if(ifPalindrome(x.substring(i, i+2)))
					y+= x.substring(i, i+2) ;
				else 
					break ;
			}
			return y+ solve1(x.substring(y.length(),x.length())) ;

		}
		public static String solve1(String x){
			String y = x.substring(0 , x.length()/2) ; 
			return "" ;

		}
		public static String reverse(String x){
			String y ="" ;
			for (int i = 0; i < x.length(); i++)
			{
				y  = x.charAt(i) + y ;
			}
			return y ;
		}

		public static boolean ifPalindrome(String x){
			int numbers[] = new int[10] ; 
			for (int i = 0; i < x.length(); i++)
			{
				int z = Integer.parseInt(x.charAt(i)+"") ; 
				numbers[z] ++ ;
			}
			for (int i = 0; i < numbers.length; i++)
			{
				if(numbers[i]%2!=0)
					return false; 
			}
			return true ;	
		}

		public static int get(int n){
			return n*(n+1)/2 ; 
		}
		public static long getSmallestDivisor( long y){
			if(isPrime(y))
				return -1;

			for (long i = 2; i*i <= y; i++)
			{
				if(y%i ==0)
				{
					return i;
				}
			}
			return -1;
		}
		//		public static void lis(pair []a , int n){
		//			int lis[] = new int[n] ; 
		//			Arrays.fill(lis,1) ; 
		//
		//			for(int i=1;i<n;i++)
		//				for(int j=0 ; j<i; j++)
		//					if (a[i].y>a[j].y &&  lis[i] < lis[j]+1)   
		//						lis[i] = lis[j] + 1;           
		//
		//			int max = lis[0];
		//
		//			for(int i=1; i<n ; i++)
		//				if (max < lis[i])
		//					max = lis[i] ;
		//			System.out.println(max);
		//
		//			ArrayList<Integer> s = new ArrayList<Integer>() ;
		//			for (int i = n-1; i >=0; i--)
		//			{
		//				if(lis[i]==max)
		//				{
		//					s.add(a[i].z);
		//					max --; 
		//				}
		//			}
		//
		//			for (int i = s.size()-1 ; i>=0 ;  i--)
		//			{
		//				System.out.print(s.get(i)+" ");
		//			}
		//
		//			return  ; 
		//		}
		public static int calcDepth(Vertix node){
			if(node.depth>0) return node.depth; 
			// meaning it has been updated before;
			if(node.parent != null)
				return 1+ calcDepth(node.parent);
			else
				return -1;
		}
		public static int helper(int a[] , int i , int j , int d ,  int n){
			if(j==i || i==n-1 || j==0)
				return 0; 
			if(a[j] - a[i] <= d)
				return 0; 
			if(memo[i][j]!= -1)
				return memo[i][j] ; 

			if( a[j-1]-a[i]< a[j]-a[i+1])
				return memo[i][j]=1 + helper(a, i, j-1, d , n) ; 
			if( a[j-1]-a[i]> a[j]-a[i+1])
				return memo[i][j]=1+ helper(a , i+1 , j , d ,n ) ;
			return memo[i][j]=1+ Math.min(helper(a, i, j-1, d , n) , helper(a , i+1 , j , d ,n )) ;

		}
		public static boolean isPrime (long num){
			if (num < 2) return false;
			if (num == 2) return true;
			if (num % 2 == 0) return false;
			for (int i = 3; i * i <= num; i += 2)
				if (num % i == 0) return false;
			return true;
		}

		public static boolean dfs(Vertix v , int target){
			try{
				visited[v.i]= true ;
			} catch (NullPointerException e)
			{
				System.out.println(v.i);
			}
			if(v.i == target)

				return true ;
			for (int i =0 ; i< v.neighbours.size() ; i++)
			{ 

				Vertix child = v.neighbours.get(i) ;
				if(child.i == target){
					found = true  ; 
				}
				if(visited[child.i]==false){
					found |= dfs(child, target) ;
				}
			}
			return found; 
		}






	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}
	public static class Vertix{
		int i ; 
		int depth ;
		ArrayList<Vertix> neighbours ; 
		Vertix parent ; 

		public Vertix(int i){
			this.i = i ;
			this.neighbours = new ArrayList<Vertix> () ;
			this.parent = null ;
			depth =-1;
		}
	}

	public static class pair implements Comparable<pair>{
		int x ;  // neededLessonsToSkip //k
		int y ;  // value


		public pair(int x, int y){
			this.x=x ; 
			this.y=y ;

		}

		@Override
		public int compareTo(pair p) {
			if(this.x > p.x)
				return 1 ; 
			else if(this.x== p.x)
			{
				if(this.y >= p.y)
					return 1 ;
				else 
					return -1 ;
			}
			else return -1 ;


		}


	}


}