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:
    /* 
     * UMANG PANCHAL
     * DAIICT
     */
     
    import java.util.*;
    import java.io.*;
    import java.math.BigInteger;
    import java.util.Comparator;
    public class Main
    {
     
    	private static final Comparator<? super Integer> Comparator = null;
    	static LinkedList<Integer> adj[];
    	static ArrayList<Integer> adj1[];
    	static int[] color,visited1;
    	static boolean b[],visited[],possible;
    	static int level[];
    	static Map<Integer,HashSet<Integer>> s;
    	static int totalnodes,colored;
    	static int count[];
    	static long sum[];
    	static int nodes;
    	static long ans=0;
    	static long[] as=new long[10001];
    	static long c1=0,c2=0;
    	static int[] a,d,k;
    	static int max=100000000;
    	static long MOD = (long) (1e9+7),sm=0,m=Long.MIN_VALUE;
    	static boolean[] prime=new boolean[1000005];
    	static int[] levl;
        static int[] eat;
        static int price[];
        static int res[],par[];
        static int result=0;
        static int[] root,size;
        static int[][] K,p;
        static boolean yes = true;
        static long P=Long.MAX_VALUE;
        static int start,end;
    	// --------------------My Code Starts Here----------------------
    	
    	public static void main(String[] args) throws IOException
    	{
    		in=new InputReader(System.in);
    		w=new PrintWriter(System.out);
   int n=ni(),m=ni();
   char[][] c=new char[n+2][m+2];
   for(int i=1;i<=n;i++)
   {
	   String s=ns();
	   for(int j=1;j<=m;j++)
	   {
		   c[i][j]=s.charAt(j-1);
	   }
   }
   boolean ans=true;
   for(int i=1;i<=n;i++)
   {
	   for(int j=1;j<=m;j++)
	   {
		   if(c[i][j]=='S')
		   {
			 
				   if(c[i+1][j]=='W' || c[i-1][j]=='W' || c[i][j+1]=='W' || c[i][j-1]=='W')
				   {
					   ans=false;
					   break;
				   }
			
		   }
	   }
   }
   if(!ans)
	   w.print("No");
   else
   {
	   w.println("Yes");
	   for(int i=1;i<=n;i++)
	   {
		   for(int j=1;j<=m;j++)
		   {
			   if(c[i][j]=='.')
				   c[i][j]='D';
			   w.print(c[i][j]);
		   }
		   w.println();
	   }
   }
   
            w.close();
        }
     
     
    	
     
     
    	// --------------------My Code Ends Here------------------------
         
    	
    	/*
    	 *  PriorityQueue<Integer> pq = new PriorityQueue<Integer>(new Comparator<Integer>()
      			{
      				public int compare(Integer o1, Integer o2)
      				{
      					return Integer.compare(o2,o1);
      				}
      			});
    	 * 
    	 * 
    	 */
     
    	 
    	 
    	 public static void buildgraph(int n)
    	 {
             adj=new LinkedList[n];
             visited=new boolean[n];
             level=new int[n];
             par=new int[n];
             for(int i=0;i<n;i++)
             	{
            	 adj[i]=new LinkedList<Integer>();
             	
             	}
          
    	 }
    	
    	/*public static long kruskal(Pair[] p)
    	{
    		long ans=0;
    		int w=0,x=0,y=0;
    		for(int i=0;i<p.length;i++)
    		{
    			w=p[i].w;
    			x=p[i].x;
    			y=p[i].y;
    			if(root(x)!=root(y))
    			{
    				ans+=w;
    				union(x,y);
    			}
    		}
    		return ans;
    	}*/
    	
    	 static class Pair implements Comparable<Pair>
    	 {
    		int[] a;
    		long ct;
    		long c;
    	
    		Pair(int[] a,long ct,long c)
    		{
    			this.a=a;
    			this.ct=ct;
    			this.c=c;
    		}
    		public int compareTo(Pair o)
    		{
    			if(this.c==o.c)
    				return Long.compare(this.ct,o.ct);
    		  return Long.compare(this.c,o.c);
    		} 
    		
    	}
    	
    	public static int root(int i)
    	{
    		while(root[i]!=i)
    		{
    			root[i]=root[root[i]];
    			i=root[i];
    		}
    		return i;
    	}
    	
    	public static void init(int n)
    	{
    		root=new int[n+1];
    		for(int i=1;i<=n;i++)
    			root[i]=i;
    	}
    	public static void union(int a,int b)
    	{
    	    int root_a=root(a);	
    	    int root_b=root(b);
    	    root[root_a]=root_b;
    	   // size[root_b]+=size[root_a];
    	}
     
     
    	
    	public static boolean isPrime(int n)
    	{
    	    // Corner cases
    	    if (n <= 1)  return false;
    	    if (n <= 3)  return true;
    	 
    	    // This is checked so that we can skip 
    	    // middle five numbers in below loop
    	    if (n%2 == 0 || n%3 == 0)
    	    	return false;
    	 
    	    for (int i=5; i*i<=n; i=i+6)
    	        if (n%i == 0 || n%(i+2) == 0)
    	           return false;
    	 
    	    return true;
    	}
    	
     
    	
    	public static String ns()
    	{
    		return in.nextLine();
    	}
    	public static int ni()
    	{
    		return in.nextInt();
    	}
    	public static long nl()
    	{
    		return in.nextLong();
    	}
    	public static int[] na(int n)
    	{
    		a=new int[n];
    		for(int i=0;i<n;i++)
    		a[i]=ni();
    		return a;
    	}
    	public static void sieve()
    	    {
    	       int n=prime.length;
    	        for(int i=0;i<n;i++)
    	            prime[i] = true;
    	         
    	        for(int p = 2; p*p <=n; p++)
    	        {
    	            if(prime[p] == true)
    	            {
    	                for(int i = p*2; i <n; i += p)
    	                    prime[i] = false;
    	            }
    	        }
    	    }
     
      public static String rev(String s)
    	{
    		StringBuilder sb=new StringBuilder(s);
    		sb.reverse();
    		return sb.toString();
    	}
    	static long lcm(long a, long b)
    	{
    	    return a * (b / gcd(a, b));
    	}
    	static long gcd(long a, long b)
    	{
    	    while (b > 0)
    	    {
    	        long temp = b;
    	        b = a % b; // % is remainder
    	        a = temp;
    	    }
    	    return a;
    	}
    	static InputReader in;
    	static PrintWriter w;
    static class InputReader 
    {
     
    private final InputStream stream;
    private final byte[] buf = new byte[8192];
    private int curChar, snumChars;
    private SpaceCharFilter filter;
     
    public InputReader(InputStream stream)
    {
      this.stream = stream;
    }
     
    public int snext()
    {
      if (snumChars == -1)
        throw new InputMismatchException();
      if (curChar >= snumChars)
      {
        curChar = 0;
        try 
        {
          snumChars = stream.read(buf);
        }
        catch (IOException e)
        {
          throw new InputMismatchException();
        }
        if (snumChars <= 0)
          return -1;
      }
      return buf[curChar++];
    }
     
    public int nextInt() 
    {
      int c = snext();
      while (isSpaceChar(c)) 
      {
        c = snext();
      }
      int sgn = 1;
      if (c == '-')
      {
        sgn = -1;
        c = snext();
      }
      int res = 0;
      do
      {
        if (c < '0' || c > '9')
          throw new InputMismatchException();
        res *= 10;
        res += c - '0';
        c = snext();
      }
      while (!isSpaceChar(c));
      return res * sgn;
    }
     
    public long nextLong() 
    {
      int c = snext();
      while (isSpaceChar(c)) 
      {
        c = snext();
      }
      int sgn = 1;
      if (c == '-')
      {
        sgn = -1;
        c = snext();
      }
      long res = 0;
      do
      {
        if (c < '0' || c > '9')
          throw new InputMismatchException();
        res *= 10;
        res += c - '0';
        c = snext();
      }
      while (!isSpaceChar(c));
      return res * sgn;
    }	    
    public String readString() 
    {
      int c = snext();
      while (isSpaceChar(c)) 
      {
        c = snext();
      }
      StringBuilder res = new StringBuilder();
      do
      {
        res.appendCodePoint(c);
        c = snext();
      }
      while (!isSpaceChar(c));
      return res.toString();
    }
     
    public String nextLine() 
    {
      int c = snext();
      while (isSpaceChar(c))
        c = snext();
      StringBuilder res = new StringBuilder();
      do
      {
        res.appendCodePoint(c);
        c = snext();
      }
      while (!isEndOfLine(c));
      return res.toString();
    }
     
    public boolean isSpaceChar(int c)
    {
      if (filter != null)
        return filter.isSpaceChar(c);
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
     
    private boolean isEndOfLine(int c) 
    {
      return c == '\n' || c == '\r' || c == -1;
    }
     
    public interface SpaceCharFilter
    {
      public boolean isSpaceChar(int ch);
    }
    }
    	
    }