Problem: You have a large rectangular board which is divided into n × m cells (the board has n rows and m columns). Each cell is either white or black.

You paint each white cell either red or blue. Obviously, the number of different ways to paint them is 2^w, where w is the number of white cells.

After painting the white cells of the board, you want to place the maximum number of dominoes on it, according to the following rules:

  * each domino covers two adjacent cells; 
  * each cell is covered by at most one domino; 
  * if a domino is placed horizontally (it covers two adjacent cells in one of the rows), it should cover only red cells; 
  * if a domino is placed vertically (it covers two adjacent cells in one of the columns), it should cover only blue cells. 



Let the value of the board be the maximum number of dominoes you can place. Calculate the sum of values of the board over all 2^w possible ways to paint it. Since it can be huge, print it modulo 998 244 353.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 3 ⋅ 10^5; nm ≤ 3 ⋅ 10^5) — the number of rows and columns, respectively.

Then n lines follow, each line contains a string of m characters. The j-th character in the i-th string is * if the j-th cell in the i-th row is black; otherwise, that character is o.

Output

Print one integer — the sum of values of the board over all 2^w possible ways to paint it, taken modulo 998 244 353.

Examples

Input


3 4
**oo
oo*o
**oo


Output


144


Input


3 4
**oo
oo**
**oo


Output


48


Input


2 2
oo
o*


Output


4


Input


1 4
oooo


Output


9

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;

/**
 *
 * @Har_Har_Mahadev
 */

public class E {

	private static long INF = 2000000000000000000L, M = 1000000007, MM = 998244353;
	private static int N = 0;

	public static void process() throws IOException {

		int n = sc.nextInt(),m = sc.nextInt();
		char[][] arr = new char[n][m];
		for(int i = 0; i<n; i++) {
			arr[i] = sc.next().toCharArray();
		}
		long a = solve(arr,n,m);
		char[][] arr2 = new char[m][n];
		for(int j = 0; j<m; j++) {
			for(int i = 0; i<n; i++) {
				arr2[j][i] = arr[i][j];
			}
		}
		long b = solve(arr2, m, n);
		println((a+b)%MM);
		

	}
	

//	a^n % mod
	private static long power(long a, long n,long mod) {
		long res = 1;
		while(n > 0) {
			if(n%2 == 0) {
				a = (a%mod * a%mod)%mod;
				n/=2;
			}
			else {
				res = (res%mod * a%mod)%mod;
				n--;
			}
		}
		return res%mod;
	}
	
	// Inverse Of a Number
	private static long ModInverse(long a, long mod) {
		
		return power(a, mod-2,mod);
	}

	private static long solve(char[][] arr, int n, int m) {
		long dp[][] = new long[n][m];
		int total = 0;
		for(int i = 0;i<n; i++) {
			for(int j = 0; j<m; j++) {
				if(arr[i][j] == 'o')total++;
			}
		}
		long mod4 = ModInverse(4, MM);
		long ans = 0;
		for(int i = 0;i<n; i++) {
			for(int j = 0; j<m-1; j++) {
				if(arr[i][j] == '*' || arr[i][j+1] == '*') {
					dp[i][j] = 0;
				}
				else {
					if(j == 0 || arr[i][j-1] == '*') {
						dp[i][j] = power(2, total-2, MM);
					}
					else if(j == 1 || arr[i][j-2] == '*') {
						dp[i][j] = power(2, total-3, MM);
					}
					else {
						long val1 = (dp[i][j-2] * mod4)%MM;
						long val2 = power(2, total-3, MM);
						dp[i][j] = (val1+val2)%MM;
					}
				}
				ans = (ans + dp[i][j])%MM;
			}
		}
		return ans;
	}

	//=============================================================================
	//--------------------------The End---------------------------------
	//=============================================================================

	static FastScanner sc;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		boolean oj = true;
		if (oj) {
			sc = new FastScanner();
			out = new PrintWriter(System.out);
		} else {
			sc = new FastScanner(100);
			out = new PrintWriter("output.txt");
		}
		int t = 1;
//		t = sc.nextInt();
		while (t-- > 0) {
			process();
		}
		out.flush();
		out.close();
	}

	static class Pair implements Comparable<Pair> {
		int x, y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			return Integer.compare(this.x, o.x);
		}

		//		 @Override
		//		    public boolean equals(Object o) {
		//		        if (this == o) return true;
		//		        if (!(o instanceof Pair)) return false;
		//		        Pair key = (Pair) o;
		//		        return x == key.x && y == key.y;
		//		    }
		//		 
		//		    @Override
		//		    public int hashCode() {
		//		        int result = x;
		//		        result = 31 * result + y;
		//		        return result;
		//		    }
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static void println(Object o) {
		out.println(o);
	}

	static void println() {
		out.println();
	}

	static void print(Object o) {
		out.print(o);
	}

	static void pflush(Object o) {
		out.println(o);
		out.flush();
	}

	static int ceil(int x, int y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static long ceil(long x, long y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static int max(int x, int y) {
		return Math.max(x, y);
	}

	static int min(int x, int y) {
		return Math.min(x, y);
	}

	static int abs(int x) {
		return Math.abs(x);
	}

	static long abs(long x) {
		return Math.abs(x);
	}

	static int log2(int N) {
		int result = (int) (Math.log(N) / Math.log(2));
		return result;
	}

	static long max(long x, long y) {
		return Math.max(x, y);
	}

	static long min(long x, long y) {
		return Math.min(x, y);
	}

	public static int gcd(int a, int b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.intValue();
	}

	public static long gcd(long a, long b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.longValue();
	}

	public static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int lcm(int a, int b) {
		return (a * b) / gcd(a, b);
	}

	public static int lower_bound(int[] arr, int x) {
		int low = 0, high = arr.length, mid = -1;

		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] >= x)
				high = mid;
			else
				low = mid + 1;
		}

		return low;
	}

	public static int upper_bound(int[] arr, int x) {
		int low = 0, high = arr.length, mid = -1;

		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] > x)
				high = mid;
			else
				low = mid + 1;
		}

		return low;
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() throws FileNotFoundException {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		FastScanner(int a) throws FileNotFoundException {
			br = new BufferedReader(new FileReader("input.txt"));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		String nextLine() throws IOException {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] readArray(int n) throws IOException {
			int[] A = new int[n];
			for (int i = 0; i != n; i++) {
				A[i] = sc.nextInt();
			}
			return A;
		}

		long[] readArrayLong(int n) throws IOException {
			long[] A = new long[n];
			for (int i = 0; i != n; i++) {
				A[i] = sc.nextLong();
			}
			return A;
		}
	}

	static void ruffleSort(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}

	static void ruffleSort(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}
}