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:
//package CodeForces;

/*In the name of Allah the Most Merciful.
 * Author
 * Md. Toufiqul Islam
 * Dept. Of CSE
 * Ahsanullah University Of Science And Technology
*/
import java.io.*;
import java.util.*;
import java.math.*;

public class R470A {

    public static void main(String[] args) {
        InputReader sc = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        int r = sc.nextInt();
        int c = sc.nextInt();
      char[][] rect = new char[r][c];

        for (int i=0;i<r;i++){
           for (int j=0;j<c;j++){
               rect[i][j] = sc.nextCharacter();
           }

        }



           List<Position> list = new ArrayList<>();
        List<Position> wPos = new ArrayList<>();

        for (int i=0;i<r;i++){


           for(int j=0;j<c;j++){
               if(rect[i][j]=='S'){
                   list.add(new Position(i,j));
               }
               if(rect[i][j]=='W'){
                   wPos.add(new Position(i,j));
               }
           }
        }

        for (int i=0;i<list.size();i++){
            Position pos = list.get(i);
            int sR  = pos.x;
            int sC = pos.y;

            for (int j = sC;j<c;j++){

                if(rect[sR][j]=='.'){
                    rect[sR][j] = 'D';
                    break;
                }
                else if(rect[sR][j]=='D'){
                  break;
                }
            }

            for (int j = sC;j>=0;j--){
                if(rect[sR][j]=='.'){
                    rect[sR][j] = 'D';
                    break;
                }
                else if(rect[sR][j]=='D'){
                    break;
                }
            }

            for (int j = sR;j<r;j++){
               if((rect[j][sC])=='.'){
                  rect[j][sC] ='D';
                  break;
               }
            }

            for (int j = sR;j>=0;j--){
                if(rect[j][sC]=='.'){
                    rect[j][sC] = 'D';
                    break;
                }

            }




        }

        boolean isPossible = true;

        for(int i=0;i<wPos.size();i++){
            Position W = wPos.get(i);
            int sR = W.x;
            int sC = W.y;

            for (int j = sC;j<c;j++){

                if(rect[sR][j]=='D'){
                    break;
                }
                else if(rect[sR][j]=='S'){
                   isPossible = false;
                    break;
                }

            }

            for (int j = sC;j>=0;j--){

                if(rect[sR][j]=='D'){
                    break;
                }
                else

                if(rect[sR][j]=='S'){
                    isPossible = false;
                    break;
                }

            }

            for (int j = sR;j<r;j++){
                if(rect[j][sC]=='D'){
                    break;
                }
                else if((rect[j][sC])=='S'){
                    isPossible = false;
                   break;
                }
            }

            for (int j = sR;j>=0;j--){
                if(rect[j][sC]=='D'){
                    break;
                }
                else
                if((rect[j][sC])=='S'){
                    isPossible = false;
                    break;
                }

            }





        }
        if(isPossible){
            out.println("Yes");

            for (int i=0;i<r;i++){
                for (int j=0;j<c;j++){
                    out.print(rect[i][j]);
                }

                out.println();
            }
        }
        else {
            out.println("No");
        }





        out.close();
    }
    static class Position{
        int x;
        int y;

        public Position(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
     public static class InputReader {
             private boolean finished = false;

             private InputStream stream;
             private byte[] buf = new byte[1024];
             private int curChar;
             private int numChars;
             private SpaceCharFilter filter;

             public InputReader(InputStream stream) {
                 this.stream = stream;
             }

             public int read() {
                 if (numChars == -1) {
                     throw new InputMismatchException();
                 }
                 if (curChar >= numChars) {
                     curChar = 0;
                     try {
                         numChars = stream.read(buf);
                     } catch (IOException e) {
                         throw new InputMismatchException();
                     }
                     if (numChars <= 0) {
                         return -1;
                     }
                 }
                 return buf[curChar++];
             }

             public int peek() {
                 if (numChars == -1) {
                     return -1;
                 }
                 if (curChar >= numChars) {
                     curChar = 0;
                     try {
                         numChars = stream.read(buf);
                     } catch (IOException e) {
                         return -1;
                     }
                     if (numChars <= 0) {
                         return -1;
                     }
                 }
                 return buf[curChar];
             }

             public int nextInt() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 int sgn = 1;
                 if (c == '-') {
                     sgn = -1;
                     c = read();
                 }
                 int res = 0;
                 do {
                     if (c < '0' || c > '9') {
                         throw new InputMismatchException();
                     }
                     res *= 10;
                     res += c - '0';
                     c = read();
                 } while (!isSpaceChar(c));
                 return res * sgn;
             }

             public long nextLong() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 int sgn = 1;
                 if (c == '-') {
                     sgn = -1;
                     c = read();
                 }
                 long res = 0;
                 do {
                     if (c < '0' || c > '9') {
                         throw new InputMismatchException();
                     }
                     res *= 10;
                     res += c - '0';
                     c = read();
                 } while (!isSpaceChar(c));
                 return res * sgn;
             }

             public String nextString() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 StringBuilder res = new StringBuilder();
                 do {
                     if (Character.isValidCodePoint(c)) {
                         res.appendCodePoint(c);
                     }
                     c = read();
                 } while (!isSpaceChar(c));
                 return res.toString();
             }

             public boolean isSpaceChar(int c) {
                 if (filter != null) {
                     return filter.isSpaceChar(c);
                 }
                 return isWhitespace(c);
             }

             public static boolean isWhitespace(int c) {
                 return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
             }

             private String readLine0() {
                 StringBuilder buf = new StringBuilder();
                 int c = read();
                 while (c != '\n' && c != -1) {
                     if (c != '\r') {
                         buf.appendCodePoint(c);
                     }
                     c = read();
                 }
                 return buf.toString();
             }

             public String readLine() {
                 String s = readLine0();
                 while (s.trim().length() == 0) {
                     s = readLine0();
                 }
                 return s;
             }

             public String readLine(boolean ignoreEmptyLines) {
                 if (ignoreEmptyLines) {
                     return readLine();
                 } else {
                     return readLine0();
                 }
             }

             public BigInteger readBigInteger() {
                 try {
                     return new BigInteger(nextString());
                 } catch (NumberFormatException e) {
                     throw new InputMismatchException();
                 }
             }

             public char nextCharacter() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 return (char) c;
             }

             public double nextDouble() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 int sgn = 1;
                 if (c == '-') {
                     sgn = -1;
                     c = read();
                 }
                 double res = 0;
                 while (!isSpaceChar(c) && c != '.') {
                     if (c == 'e' || c == 'E') {
                         return res * Math.pow(10, nextInt());
                     }
                     if (c < '0' || c > '9') {
                         throw new InputMismatchException();
                     }
                     res *= 10;
                     res += c - '0';
                     c = read();
                 }
                 if (c == '.') {
                     c = read();
                     double m = 1;
                     while (!isSpaceChar(c)) {
                         if (c == 'e' || c == 'E') {
                             return res * Math.pow(10, nextInt());
                         }
                         if (c < '0' || c > '9') {
                             throw new InputMismatchException();
                         }
                         m /= 10;
                         res += (c - '0') * m;
                         c = read();
                     }
                 }
                 return res * sgn;
             }

             public boolean isExhausted() {
                 int value;
                 while (isSpaceChar(value = peek()) && value != -1) {
                     read();
                 }
                 return value == -1;
             }

             public String next() {
                 return nextString();
             }

             public SpaceCharFilter getFilter() {
                 return filter;
             }

             public void setFilter(SpaceCharFilter filter) {
                 this.filter = filter;
             }

             public interface SpaceCharFilter {
                 public boolean isSpaceChar(int ch);
             }
             public int[] nextIntArray(int n){
                 int[] array=new int[n];
                 for(int i=0;i<n;++i)array[i]=nextInt();
                 return array;
             }
             public int[] nextSortedIntArray(int n){
                 int array[]=nextIntArray(n);
                 Arrays.sort(array);
                 return array;
             }
             public int[] nextSumIntArray(int n){
                 int[] array=new int[n];
                 array[0]=nextInt();
                 for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
                 return array;
             }
             public long[] nextLongArray(int n){
                 long[] array=new long[n];
                 for(int i=0;i<n;++i)array[i]=nextLong();
                 return array;
             }
             public long[] nextSumLongArray(int n){
                 long[] array=new long[n];
                 array[0]=nextInt();
                 for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
                 return array;
             }
             public long[] nextSortedLongArray(int n){
                 long array[]=nextLongArray(n);
                 Arrays.sort(array);
                 return array;
             }
         }
      public static class OutputWriter {
              private final PrintWriter writer;

              public OutputWriter(OutputStream outputStream) {
                  writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
              }

              public OutputWriter(Writer writer) {
                  this.writer = new PrintWriter(writer);
              }

              public void print(char[] array) {
                  writer.print(array);
              }

              public void print(Object... objects) {
                  for (int i = 0; i < objects.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(objects[i]);
                  }
              }

              public void print(int[] array) {
                  for (int i = 0; i < array.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(array[i]);
                  }
              }

              public void print(double[] array) {
                  for (int i = 0; i < array.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(array[i]);
                  }
              }

              public void print(long[] array) {
                  for (int i = 0; i < array.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(array[i]);
                  }
              }

              public void println(int[] array) {
                  print(array);
                  writer.println();
              }

              public void println(double[] array) {
                  print(array);
                  writer.println();
              }

              public void println(long[] array) {
                  print(array);
                  writer.println();
              }

              public void println() {
                  writer.println();
              }

              public void println(Object... objects) {
                  print(objects);
                  writer.println();
              }

              public void print(char i) {
                  writer.print(i);
              }

              public void println(char i) {
                  writer.println(i);
              }

              public void println(char[] array) {
                  writer.println(array);
              }

              public void printf(String format, Object... objects) {
                  writer.printf(format, objects);
              }

              public void close() {
                  writer.close();
              }

              public void flush() {
                  writer.flush();
              }

              public void print(long i) {
                  writer.print(i);
              }

              public void println(long i) {
                  writer.println(i);
              }

              public void print(int i) {
                  writer.print(i);
              }

              public void println(int i) {
                  writer.println(i);
              }

              public void separateLines(int[] array) {
                  for (int i : array) {
                      println(i);
                  }
              }
          }

}