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.util.concurrent.ArrayBlockingQueue;
import java.lang.*;
import java.math.*;
import java.text.DecimalFormat;
import java.lang.reflect.Array;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigDecimal;
public class B{
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	static long MOD = (long)(1e9+7);
	//static int MOD = 998244353;
	static long MOD2 = MOD*MOD;
	static FastReader sc = new FastReader();
	static int pInf = Integer.MAX_VALUE;
	static int nInf = Integer.MIN_VALUE;
	//static ArrayList<Long> A;
	public static void main(String[] args){
		int test = 1;
		//test = sc.nextInt();
		while(test-->0)solve();
		out.flush();
		out.close();
	}
	static int n,m,di[]= new int[] {1,0,-1,0},dj[]= new int[] {0,1,0,-1};;
	static char[][] c;
	static boolean e(int i, int j) {
		return i>=0&&i<n&&j>=0&&j<m;
	}
	public static void solve() {
		n = sc.nextInt();
		m = sc.nextInt();
		c = new char[n][m];
		for(int i = 0;i <n; i++) {
			c[i] = sc.next().toCharArray();
		}
		for(int i = 0; i < n; i++) {
			for(int j = 0; j < m; j++) {
				if(c[i][j] == 'W') {
					for(int k = 0; k < 4; k++) {
						int ni = i+di[k];
						int nj = j+dj[k];
						if(e(ni,nj)) {
							if(c[ni][nj]=='.') {
								c[ni][nj] = 'D';
							}
							if(c[ni][nj]=='S') {
								out.print("No");
								return;
							}
						}
					}
				}
			}
		}
		out.println("Yes");
		for(int i = 0; i < n; i++) {
			out.println(new String(c[i]));
		}
	}
	static long nC2(long n) {
		return add((n*(n+1))/2, 0);
	}
	public static int maxRight(int x,int[] a) {
		int l = -1;      //a[l]<=x
		int r = a.length;//a[r]>x
		while(r-l>1) {
			int m = l+(r-l)/2;
			if(a[m]<=x) {
				l = m;
			}
			else {
				r = m;
			}
		}
		return l+1;
	}
	public static int minLeft(int x,int[] a) {
		int l = -1;      //a[l]<x
		int r = a.length;//a[r]>=x
		while(r-l>1) {
			int m = l+(r-l)/2;
			if(a[m]<x) {
				l = m;
			}
			else {
				r = m;
			}
		}
		return r+1;
	}
	public static int lowerBound(int key, int[] a) {
		int s = 0;
		int e = a.length-1;
		if(e==-1) {
			return 0;
		}
		int ans = -1;
		while(s<=e) {
			int m = s+(e-s)/2;
			if(a[m]>=key) {
				ans = m;
				e = m-1;
			}
			else {
				s = m+1;
			}
		}
		return ans==-1?s:ans;
	}
	public static int upperBound(int key, int[] a) {
		int s = 0;
		int e = a.length-1;
		if(e==-1) {
			return 0;
		}
		int ans = -1;
		while(s<=e) {
			int m = s+(e-s)/2;
			if(a[m]>key) {
				ans = m;
				e = m-1;
			}
			else {
				s = m+1;
			}
		}
		return ans==-1?s:ans;
	}
	public static long c2(long n) {
		if((n&1)==0) {
			return mul(n/2, n-1);
		}
		else {
			return mul(n, (n-1)/2);
		}
	}
	public static long mul(long a, long b){
	    return ((a%MOD)*(b%MOD))%MOD;
	}
	public static long add(long a, long b){
	    return ((a%MOD)+(b%MOD))%MOD;
	}
	public static long sub(long a, long b){
	    return ((a%MOD)-(b%MOD))%MOD;
	}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//Integer.lowestOneBit(i)   Equals k where k is the position of the first one in the binary
//Integer.highestOneBit(i)  Equals k where k is the position of the last one in the binary
//Integer.bitCount(i)       returns the number of one-bits
//Collections.sort(A,(p1,p2)->(int)(p2.x-p1.x)) To sort ArrayList in descending order wrt values of x.
//            Arrays.parallelSort(a,new Comparator<TPair>() {
//      		public int compare(TPair a,TPair b) {
//        			if(a.y==b.y) return a.x-b.x;
//        			return b.y-a.y;
//        		}
//        	});
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//PrimeFactors    
    public static ArrayList<Long> primeFactors(long n) {
        ArrayList<Long> arr = new ArrayList<>();
        if (n % 2 == 0)
            arr.add((long) 2);
        while (n % 2 == 0)
            n /= 2;
        for (long i = 3; i <= Math.sqrt(n); i += 2) {
            int flag = 0;
            while (n % i == 0) {
                n /= i;
                flag = 1;
            }
            if (flag == 1)
                arr.add(i);
        }
        if (n > 2)
            arr.add(n);
        return arr;
    }
//Pair Class
	static class Pair implements Comparable<Pair>{
		int x;
		int y;
		int len;
		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
			this.len = y-x-1;
		}
		@Override
		public int compareTo(Pair o) {
			if(this.len==o.len){
			    return (this.x-o.x);
			}
			return (this.len-o.len);
		}
	}
	static class TPair implements Comparable<TPair>{
		int l;
		int r;
		int index;
		public TPair(int l, int r, int index) {
			this.l = l;
			this.r = r;
			this.index = index;
		}
		@Override
		public int compareTo(TPair o) {
			if(this.l==o.l){
			    return -1*(this.r-o.r);
			}
			return -1*(this.l-o.l);
		}
	}
//nCr
	static long[] facts, factInvs;
	static long exp(long base, long e) {
		if (e==0) return 1;
		long half=exp(base, e/2);
		if (e%2==0) return mul(half, half);
		return mul(half, mul(half, base));
	}
	
	static long modInv(long x) {
		return exp(x, MOD-2);
	}
	
	static void precomp() {
		facts=new long[1_000_000];
		factInvs=new long[1_000_000];
		factInvs[0]=facts[0]=1;
		for (int i=1; i<facts.length; i++)
			facts[i]=mul(facts[i-1], i);
		factInvs[facts.length-1]=modInv(facts[facts.length-1]);
		for (int i=facts.length-2; i>=0; i--)
			factInvs[i]=mul(factInvs[i+1], i+1);
	}
	
	static long nCk(int n, int k) {
		return mul(facts[n], mul(factInvs[k], factInvs[n-k]));
	}
//Kadane's Algorithm    
    static long maxSubArraySum(ArrayList<Long> a) { 
    	if(a.size()==0) {
    		return 0;
    	}
    	long max_so_far = a.get(0); 
    	long curr_max = a.get(0); 
    	for (int i = 1; i < a.size(); i++) { 
           curr_max = Math.max(a.get(i), curr_max+a.get(i)); 
           max_so_far = Math.max(max_so_far, curr_max); 
    	} 
    	return max_so_far; 
    } 
//Shuffle Sort
    static final Random random=new Random();
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
//Merge Sort
	static void merge(long arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;
 
        /* Create temp arrays */
        long L[] = new long [n1];
        long R[] = new long [n2];
 
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];
 
 
        /* Merge the temp arrays */
 
        // Initial indexes of first and second subarrays
        int i = 0, j = 0;
 
        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
 
        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
 
        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
 
    // Main function that sorts arr[l..r] using
    // merge()
    static void sort(long arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;
 
            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);
 
            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }
//Brian Kernighans Algorithm
    static long countSetBits(long n){
        if(n==0) return 0;
        return 1+countSetBits(n&(n-1));
    }
//Factorial
    static long factorial(long n){
        if(n==1) return 1;
        if(n==2) return 2;
        if(n==3) return 6;
        return n*factorial(n-1);
    }
//Euclidean Algorithm
    static long gcd(long A,long B){
        if(B==0) return A;
        return gcd(B,A%B);
    }
//Modular Exponentiation
    static long fastExpo(long x,long n){
        if(n==0) return 1;
        if((n&1)==0) return fastExpo((x*x)%MOD,n/2)%MOD;
        return ((x%MOD)*fastExpo((x*x)%MOD,(n-1)/2))%MOD;
    }
//AKS Algorithm
    static boolean isPrime(long n){
        if(n<=1) return false;
        if(n<=3) return true;
        if(n%2==0 || n%3==0) return false;
        for(int i=5;i<=Math.sqrt(n);i+=6)
            if(n%i==0 || n%(i+2)==0) return false;
        return true;
    }
//Reverse an array
    static <T> void reverse(T arr[],int l,int r){
    	Collections.reverse(Arrays.asList(arr).subList(l, r));
    }
  //Print array
    static void print1d(long arr[]) {
    	out.println(Arrays.toString(arr));
    }
    static void print2d(int arr[][]) {
    	for(int a[]: arr) out.println(Arrays.toString(a));
    }
//Sieve of eratosthenes
    static int[] findPrimes(int n){
        boolean isPrime[]=new boolean[n+1];
        ArrayList<Integer> a=new ArrayList<>();
        int result[];
        Arrays.fill(isPrime,true);
        isPrime[0]=false;
        isPrime[1]=false;
        for(int i=2;i*i<=n;++i){
            if(isPrime[i]==true){
                for(int j=i*i;j<=n;j+=i) isPrime[j]=false;
            }
        }
        for(int i=0;i<=n;i++) if(isPrime[i]==true) a.add(i);
        result=new int[a.size()];
        for(int i=0;i<a.size();i++) result[i]=a.get(i);
        return result;
        
    }
//Indivisual factors of all nos till n
    static ArrayList<Integer>[] indiFactors(int n){
    	ArrayList<Integer>[] A = new ArrayList[n+1];
    	for(int i = 0; i <= n; i++) {
    		A[i] = new ArrayList<>();
    	}
    	int[] sieve = new int[n+1];
    	for(int i=2;i<=n;i++) {
       		if(sieve[i]==0) {
       			for(int j=i;j<=n;j+=i) if(sieve[j]==0) {
       				//sieve[j]=i;
       				A[j].add(i);
       			}
       		}
       	}
    	return A;
    }
//Segmented Sieve
    static boolean[] segmentedSieve(long l, long r){
    	boolean[] segSieve = new boolean[(int)(r-l+1)];
    	Arrays.fill(segSieve, true);
    	int[] prePrimes = findPrimes((int)Math.sqrt(r));
    	for(int p:prePrimes) {
    		long low = (l/p)*p;
    		if(low < l) {
    			low += p;
    		}
    		if(low == p) {
    			low += p;
    		}
    		for(long j = low; j<= r; j += p) {
    			segSieve[(int) (j-l)] = false;
    		}
    	}
    	if(l==1) {
    		segSieve[0] = false;
    	}
    	return segSieve;
    }
//Euler Totent function
    static long countCoprimes(long n){
        ArrayList<Long> prime_factors=new ArrayList<>();
        long x=n,flag=0;
        while(x%2==0){
            if(flag==0) prime_factors.add(2L);
            flag=1;
            x/=2;
        }
        for(long i=3;i*i<=x;i+=2){
            flag=0;
            while(x%i==0){
                if(flag==0) prime_factors.add(i);
                flag=1;
                x/=i;
            }
        }
        if(x>2) prime_factors.add(x);
        double ans=(double)n;
        for(Long p:prime_factors){
            ans*=(1.0-(Double)1.0/p);
        }
        return (long)ans;
    }
	static long modulo = (long)1e9+7;
	public static long modinv(long x){
	    return modpow(x, modulo-2);
	}
	public static long modpow(long a, long b){
	    if(b==0){
	        return 1;
	    }
	    long x = modpow(a, b/2);
	    x = (x*x)%modulo;
	    if(b%2==1){
	        return (x*a)%modulo;
	    }
	    return x;
	}
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
}