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.awt.List;
			    		import java.io.*;
			import java.math.BigInteger;
			import java.util.*;

			    		
			    		
			    		/*
			    		 * 
			    		 * daiict
			    		 *
			    		 * 
			    		 * 
			    		 */
			    		
			    		
			    		public class pprac {
			    			 FastScanner in;
			    			 PrintWriter out;
			    		
			    			static ArrayList[] adj;
			    			static ArrayList[] aadj;
			    		    static int last;
			    			static int n;
			    			static int m;
			    			
			    			static int[] dp1;
			    			static int[] dp2;
			    			static int color[];
			    			static int visited[];
			    			static long[] arr;
			    			static long[] brr;
			    			static double ans;
			    			static int array[];
			    			static int start[];
			    			static int finish[];
			    			static int pref[];
			    			static int tree[];
			    			static int maxval = 32;
			    		
			    			static int ttt[];
			    			static int sum = 0;
			    			static String s;
			    		
			    			static int cc = 0;
			    			static long min = Long.MAX_VALUE;
			    			
			    			static ArrayList<Integer> segt[];
			    			
			    		//for dfs do not delete
			    			static int dir[][] ={{1,0},{0,1},{0,-1},{-1,0}};
			    			
			    		
			    			static int[] seg;
			    			static long count = 1;
			    			static long mod = (long)1e9 + 7;
			    	
			    			static int parent[];
			    			static int size[];
			    			
			    		    static int[] l;
			    		    static int[] r;
			    		    static int[] next;
			    		    static int[] cnt;
			    		    static int[] block;
			    		    
			    		    static int bblock = 1001;
			    		    
			    			static HashSet<String> set;
			    			static HashSet<String> set2;
			    			
			    			static int low[];
			    			static int disc[];
			    			static int time;
			    			static int acn[];
			    			
			    			static HashMap<Long,Integer> map;
			    			
			    			static class Pair implements Comparable<Pair>
			    		    {
			    				int x;int y;int i;
			    				
			    		        Pair(int l, int m,int i) {
			    		          
			    		        	this.x = l;
			    		            this.y = m;
			    		            this.i = i;
			    		          
			    		        }
			    		        
			    		        public int compareTo(Pair p) {
			    		      
			    		        	
			    		            if (this.x/bblock == p.x/bblock) {
			    		                return (int)(this.y-p.y);
			    		            }
			    		            return (int)(this.x/bblock - p.x/bblock);
			    		        }
			    		        
			    		        public String toString(){
			    		        	return x + " " + y;
			    		        }
			    		        
			    		        public boolean equals(Object o){
			    		        	if(o instanceof Pair){
			    		        		Pair a = (Pair)o;
			    		        		
			    		        		return this.x == a.x;
			    		        	}
			    		        	
			    		        	return false;
			    		        }
			    		        
			    		        public int hashCode(){
			    		        	return new Long(x).hashCode()*31 + new Long(y).hashCode();
			    		        }
			    		    
			    		    }
			    		    
			    			
			    			public static int gcd(int a, int b) {
			    				if (b == 0) return a;
			    				return gcd(b, a%b);
			    			}
			    	
			    			void build(int n) {  // build the tree
			  				  for (int i = n - 1; i > 0; --i) seg[i] = Math.min(seg[i<<1],seg[i<<1|1]);
			  				}
		
			  			public static void modify(int p, int val,int n) {  // set value at position p
			  				  for (seg[p += n] = val; p > 1; p >>= 1) seg[p>>1] = Math.min(seg[p],seg[p^1]);
			  				}
		
			  				int query(int l, int r,int n) {  // sum on interval [l, r)
			  				  int res = Integer.MAX_VALUE;
			  				  
			  				  if(l>r){
			  					  return res;
			  				  }
			  				  
			  				  for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
			  				    if ((l&1) == 1) res = Math.min(res, seg[l++]);
			  				    if ((r&1) == 1) res = Math.min(res, seg[--r]);
			  				  }
			  				  return res;
			  				}
			    				
	//		    			public static void update(int x,int val){
	//		    				while(x<=maxval){
	//		    					tree[x] += val;
	//		    					x = (x&-x);
	//		    				}
	//		    			}
			    			
			    			public static int read(int idx){
			    				int sum = 0;
			    				
			    				while(idx>= 0){
			    					sum += tree[idx];
			    					idx -= (idx&(-idx));
			    				}
			    				
			    				return sum;
			    			}
			    			
			    			public static int find(int i){
			    				if(parent[i] != i){
			    					return find(parent[i]);
			    				}
			    				
			    				return i;
			    			}
			    			
			    			public static void union(int a,int b){
			    				int x = find(a);
			    				int y = find(b);
			    				
			    				if(x!=y){
			    					if(size[x] > size[y]){
			    						size[x] += size[y];
			    						parent[y] = x;
			    					}else{
			    						size[y] += size[x];
			    						parent[x] = y;
			    				}
			    				}
			    			}
			    			
			    			
			    			
			    			
			    			
			    		    /*static */ void solve() throws NumberFormatException,InputMismatchException, IOException {
			    		    
			    		    	//Scanner in = new Scanner(System.in);
			    		    	
			    		    	int n = in.nextInt();
			    		    	int m = in.nextInt();
			    		    	
			    		    	char arr[][] = new char[n][m];
			    		    	
			    		    	for(int i = 0;i<n;i++){
			    		    		String s = in.next();
			    		    		for(int j = 0;j<m;j++){
			    		    			arr[i][j] = s.charAt(j);
			    		    		}
			    		    	}
			    		    	
			    		    	int g = 0;
			    		    	
			    		    	for(int i = 0;i<n;i++){
			    		    		int h = 0;
			    		    		for(int j = 0;j<m;j++){
			    		    			if(arr[i][j] == 'S'){
			    		    				int f = 0;
			    		    				for(int p = 0;p<4;p++){
			    		    					int x = dir[p][0] + i;
			    		    					int y = dir[p][1] + j;
			    		    					
			    		    					if(x >= n || y >=m || x < 0 || y < 0){
			    		    						
			    		    					}else{
			    		    						if(arr[x][y] == 'W'){
			    		    							f = 1;
			    		    							break;
			    		    						}else{
			    		    							if(arr[x][y] != 'S')
			    		    							arr[x][y] = 'D';
			    		    						}
			    		    					}
			    		    				}
			    		    				
			    		    				if(f == 1){
			    		    					h = 1;
			    		    					break;
			    		    				}
			    		    				
			    		    			}
			    		    			
			    		    			
			    		    		}
			    		    		
			    		    		if(h == 1){
			    		    			g = 1;
			    		    			break;
			    		    		}
			    		    		
			    		    	}
			    		    	
			    		    	
			    		    	if(g == 1){
			    		    		out.println("No");
			    		    	}else{
			    		    		out.println("Yes");
			    		    		
			    		    		for(int i = 0;i<n;i++){
			    		    			for(int j = 0;j<m;j++){
			    		    				out.print(arr[i][j]);
			    		    			}
			    		    			out.println();
			    		    		}
			    		    	}
			    		    		
			    		    	
			    		    	
			    	    	}
			    			
			    	    	public static void add(int i){
			    	    		low[disc[i]]++;
			    	    		disc[i]++;
			    	    	}
			    		    
			    		    
			    		    public static void uu(int arr[],int i,int f){
			    		    	if(i == 1){
			    		    		return;
			    		    	}
			    		    	int next = i/2;
			    		    	int x = 0;
			    		    	if(i%2 == 0){
			    		    		x = i+1;
			    		    	}else{
			    		    		x = i-1;
			    		    	}
			    		    	
			    		    	if(f == 1){
			    		    		arr[next] = arr[i] ^ arr[x];
			    		    	}else{
			    		    		arr[next] = arr[i]|arr[x];
			    		    	}
			    		    	
			    		    	uu(arr,next,1-f);
			    		    }
			    		    
			    		   
				    
			    		   
			    		  
			    		
			    		    public static String reverse(String s){
			    		    	
			    		    	String ans = "";
			    		    	
			    		    	for(int i = s.length()-1;i>=0;i--){
			    		    		ans += s.charAt(i);
			    		    	}
			    		    	
			    		    	return ans;
			    		    	
			    		    }
			    			
			    			
			    		    
			    		 
			    		    public static long sum(long x){
			    		    	return x<10?x:x%10 + sum(x/10);
			    		    }
			    			
			    			public static long gcd(long x, long y) {
			    				if (x == 0)
			    					return y;
			    				else
			    					return gcd( y % x,x);
			    			}
			    			static long inv(long x , long mod)
			    			{
			    				long r,y;
			    				for(r=1,y=mod-2;y!=0;x=x*x%mod,y>>=1)
			    				{
			    					if((y&1)==1)
			    						r=r*x%mod;
			    				
			    				}
			    				return r;
			    			}
			    			
			    			public static long pow(long x,long y,long n){
			    				if(y==0)
			    					return 1%n;
			    				if(y%2==0){
			    					long z=pow(x,y/2,n);
			    					return (z*z)%n;
			    				}
			    				return ((x%n)*pow(x,y-1,n))%n;
			    			}
			    			
			    			
			    			
			    			
			    			public static boolean isPrime(long a) {
			    				// Corner cases
			    				if (a <= 1)
			    					return false;
			    				if (a <= 3)
			    					return true;
			    		 
			    				// This is checked so that we can skip 
			    				// middle five numbers in below loop
			    				if (a % 2 == 0 || a % 3 == 0)
			    					return false;
			    		 
			    				for (long i = 5; i * i <= a; i = i + 6)
			    					if (a % i == 0 || a % (i + 2) == 0)
			    						return false;
			    		 
			    				return true;
			    			}
			    			
			    		
			    			void run() throws NumberFormatException, InputMismatchException,IOException {
			    				in = new FastScanner();
			    				out = new PrintWriter(System.out);
			    		
			    				solve();
			    		
			    				out.close();
			    			}
			    		
			    			class FastScanner {
			    				BufferedReader br;
			    				StringTokenizer st;
			    		
			    				public FastScanner() {
			    					br = new BufferedReader(new InputStreamReader(System.in));
			    				}
			    		
			    				String next() {
			    					while (st == null || !st.hasMoreTokens()) {
			    						try {
			    							st = new StringTokenizer(in.br.readLine());
			    						} catch (IOException e) {
			    							// TODO Auto-generated catch block
			    							e.printStackTrace();
			    						}
			    					}
			    					return st.nextToken();
			    				}
			    		
			    				int nextInt() {
			    					return Integer.parseInt(next());
			    				}
			    		
			    				long nextLong() {
			    					return Long.parseLong(next());
			    				}
			    		
			    				double nextDouble() {
			    					return Double.parseDouble(next());
			    				}
			    			}
			    			
			    			
			    			
			    			
			    		 
			    		
			    			public static void main(String[] args) throws NumberFormatException,InputMismatchException, IOException {
	//		    				 new Thread(null ,new Runnable(){
	//		    				       public void run(){
	//		    				           try{
	//		    				        		
	//		    				               test();
	//
	//		    				           } catch(Exception e){
	//		    				               e.printStackTrace();
	//		    				           }
	//		    				       }
	//		    				   },"1",1<<26).start();
	//		    				   	   }
	//		    				    static StringBuilder sb;
	//		    				    public static void test() throws IOException{
	//		    				    	 sb=new StringBuilder();
	//		    				    	int t=1;
	//		    				    	while(t-->0){
	//		    				    		
	//		    				    		solve();
	//		    				    		
	//		    				    	}
	//		    				    	
	
		    				    new pprac().run();
			    			}
			    				    
			    			
			    		}
			    		class Node{
			    			int a;
			    			int b;
			    			public Node(int i, int j) {
								this.a = i;
								this.b = j;
								
							}
						
			    			
			    		}
			    		
			    		class MyComp implements Comparator<String>{
			    		    
			    			int c = 0;
			    			
			    			MyComp(int d){
			    				c = d;
			    			}
			    			
			    			@Override
			    			public int compare(String a,String b) {
			    				
			    				// < == -1
			    				
			    				String arr[] = a.split(" ");
			    				String brr[] = b.split(" ");
			    				
			    				return arr[c].compareTo(brr[c]);
			    				
			    				
			    			}
			
			    			
			    		}
			    		
			    		class MyComp2 implements Comparator<Node>{
			    		    
			    		
			    			
			    			@Override
			    			public int compare(Node a,Node b) {
			    				
			    				// < == -1
			
			    				
			    				if(a.b > b.b){
			    					return -1;
			    				}else{
			    					return 1;
			    				}
			    				
			    				
			    			}
			
			    			
			    		}