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.*;
import java.util.*;
import java.math.BigInteger;
public class Main {
    private static StringBuilder sb = new StringBuilder();
    private static void s(String s){
        System.out.print(s);
    }
    private static void s(Double s){
        System.out.print(s);
    }
    private static void s(char s){
        System.out.print(s);
    }
    private static void sn(String s){
        System.out.println(s);
    }
    private static void sn(Boolean s){
        System.out.println(s);
    }
    private static void sn(long s){
        System.out.println(s);
    }
    private static void sn(Double s){
        System.out.println(s);
    }
    private static void sn(String s, Object o){
        sb.append(s+"\n");
    }
    private static void s(String s, Object o){
        sb.append(s);
    }
    private static void sn(long s, Object o){
        sb.append(s+"\n");
    }
    private static void sn(boolean s, Object o){
        sb.append(s+"\n");
    }
    private static void pr() throws Exception{
        BufferedWriter bw =new BufferedWriter(new OutputStreamWriter(System.out));
        bw.write(sb.toString());
        bw.flush();
    }
    static class Reader{
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[51]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
    private static boolean isPrime(Integer ii){
        return new BigInteger(ii+"").isProbablePrime(1);
    }
    private static boolean isDigit(int ii){
        return Character.isDigit((char)ii);
    }
    private static long fact(int f){
        if(f==0){
            return 1;
        }
        return (long)f * (long)fact(f-1);
    }
    private static Reader r = new Reader();
    private static int ni() throws Exception{
        return r.nextInt();
    }
    private static String ns() throws Exception{
            return r.readLine();
        }
    private static long nl() throws Exception{
        return r.nextLong();
    }
    private static int[] na(int a) throws Exception{
        int arr[] = new int[a];
        for(int i=0;i<a;i++){
            arr[i] = r.nextInt();
        }
        return arr;
    }
    private static long[] nal(int a) throws Exception{
        long arr[] = new long[a];
        for(int i=0;i<a;i++){
            arr[i] = r.nextLong();
        }
        return arr;
    }
        static void printSubsets(char set[])
    {
        int n = set.length;
 
        // Run a loop for printing all 2^n
        // subsets one by obe
        for (int i = 0; i < (1<<n); i++)
        {
            System.out.print("{ ");
 
            // Print current subset
            for (int j = 0; j < n; j++)
 
                // (1<<j) is a number with jth bit 1
                // so when we 'and' them with the
                // subset number we get which numbers
                // are present in the subset and which
                // are not
                if ((i & (1 << j)) > 0)
                    System.out.print(set[j] + " ");
 
            System.out.println("}");
        }
    }
    
    static class Query implements Comparable<Query>{
        int l,r,blk,idx;
        long an;
        Query(int l, int r, int blk, int f){
            this.l = l;
            this.r = r;
            this.blk = blk;
            idx= f;
        }
        
        public int compareTo(Query q){
            if(blk==q.blk){
                if((blk & 1) != 1){
                    return r - q.r;
                } else return q.r - r;
                
            }
            else{
                return blk-q.blk;
            }
        }
        public String toString(){
            return l+" "+r+ " "+blk+" "+idx;
        }
        
    }
    
    
    
    private static void add(int ind, int arr[]){
        ans+=(++cnt[arr[ind]]==1?1:0);
    }
    
    private static void remove(int ind, int arr[]){
        ans-=(cnt[arr[ind]]--==1?1:0);
    }
    
    
    static int ans =0;
    static int curl = 0;
   static int curr = 0;
   static int cnt[] = new int[1000006];
   class Sol{
       int idx,cnt;
       char rr;
   }
    private static void solve() throws Exception{

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String s = br.readLine();
        int n = Integer.valueOf(s.split(" ")[0]);
        int c = Integer.valueOf(s.split(" ")[1]);
        char arr[][]  = new char[n+2][c+2];
        for(int i=1;i<=n;i++){
            String str = br.readLine();
            for(int ii=1;ii<=c;ii++){
                arr[i][ii] = str.charAt(ii-1);
            }
        }
        for(int i=1;i<=n;i++){
            for(int ii=1;ii<=c;ii++){
                if(arr[i][ii] == 'S' && (arr[i][ii-1] == 'W' || arr[i][ii+1] == 'W' || arr[i+1][ii] == 'W' || arr[i-1][ii] == 'W')){
                    sn("No");
                    return;
                } else if(arr[i][ii] == 'S') {
                    if(arr[i][ii-1]!='S')
                    arr[i][ii-1] = 'D'; 
                    if(arr[i][ii+1]!='S')
                    arr[i][ii+1] = 'D';
                    if(arr[i+1][ii]!='S')
                    arr[i+1][ii] = 'D' ;
                    if(arr[i-1][ii] != 'S')
                    arr[i-1][ii] = 'D';
                }
            }
        }
        sn("Yes");
        for(int i=1;i<=n;i++){
            for(int ii=1;ii<=c;ii++){
                s(arr[i][ii]+"");
            }
            sn("");
        }
    }
    
	public static void main (String[] args) throws Exception{
	    int tc =1;
	    while(tc-->0){
	        solve();
	    }
	}
}