#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef string str;

#define pb push_back
#define ppp pop_back
#define pii pair<int,int>
#define fi first
#define se second
#define stie std::tie
#define vec vector
#define	forn(i, l, r) for (int i=l; i<=r; i++)
#define forb(i, r, l) for (int i=r; i>=l; i--)
#define emp empty
#define beg begin
#define ins insert
#define cle clear
#define era erase
#define que queue
#define pque priority_queue
#define mset multiset
#define deq deque
#define sta stack
#define con const
#define rsz resize
#define ass assign
#define lowb lower_bound
#define uppb upper_bound

template<class T> void mini(T& a, T b) { a = min(a, b); }
template<class T> void maxi(T& a, T b) { a = max(a, b); }
template<class T1, class T2> ostream& operator<<(ostream &out, pair<T1, T2> a) { return out << a.first << " " << a.second; }
template<class T> ostream& operator<<(ostream& out, vector<T> a) { for (auto& i : a) out << i << " "; return out; }
template<class T> ostream& operator<<(ostream& out, set<T> a) { for (auto& i : a) out << i << " "; return out; }
template<class T> ostream& operator<<(ostream& out, multiset<T> a) { for (auto& i : a) out << i << " "; return out; }
template<class T1, class T2> ostream& operator<<(ostream& out, map<T1, T2> a) { for (auto& i : a) out << i << "\n"; return out; }
template<class T1, class T2> ostream& operator<<(ostream& out, unordered_map<T1, T2> a) { for (auto& i : a) out << i << "\n"; return out; }
template<class T> ostream& operator<<(ostream& out, queue<T> a) { while (!a.empty()) { out << a.front() << " "; a.pop(); } return out; }
template<class T> ostream& operator<<(ostream& out, deque<T> a) { while (!a.empty()) { out << a.front() << " "; a.pop_front(); } return out; }
template<class T> ostream& operator<<(ostream& out, priority_queue<T> a) { while (!a.empty()) { out << a.top() << "\n"; a.pop(); } return out; }
template<class T> void out(T a) { cout << a << endl; }
template<class T1, class T2> void out(T1 a, T2 b) { cout << a << " " << b << endl; }
template<class T1, class T2, class T3> void out(T1 a, T2 b, T3 c) { cout << a << " " << b << " " << c << endl; }
template<class T1, class T2, class T3, class T4> void out(T1 a, T2 b, T3 c, T4 d) { cout << a << " " << b << " " << c << " " << d << endl; }
template<class T> void out(vector<vector<T>> a) { for (vector<T> i : a) out(i); }
template<class T> void out_(T a[], int l, int r) { for (int i = l; i <= r; i++) cout << a[i] << " "; cout << endl; }
void out() { cout << "OK" << endl; }
template<class T> void sort(vector<T>& a) { sort(a.begin(), a.end()); }
template<class T> void uniq(vector<T>& a) { sort(a); a.erase(unique(a.begin(), a.end()), a.end()); }
template<class T> vector<T> set_int(vector<T> a, vector<T> b) { sort(a); sort(b); vector<T> res; set_intersection(a.begin(), a.end(), b.begin(), b.end(), back_inserter(res)); return res; }
clock_t start_time; void start_timer() { start_time = clock(); }
double get_time() { return (double)(clock() - start_time) / CLOCKS_PER_SEC; }
#if __SIZEOF_INT128__ >= 16
typedef __int128 LL;
istream& operator>>(istream& in, __int128& a) { int64_t b; cin >> b; a = b; return in; }
ostream& operator<<(ostream& out, const __int128 a) {
	unsigned __int128 b = a < 0 ? -a : a; char buf[128]; char* c = end(buf); do { --c; *c = "0123456789"[b % 10]; b /= 10; } while (b);
	if (a < 0) { --c; *c = '-'; } int len = end(buf) - c; out.rdbuf()->sputn(c, len); return out;
}
#endif

template<int m>
struct mint {
    int x = 0;
    mint(int64_t a = 0) { if (a < 0) a = a % m + m; if (a >= m) a %= m; x = a; }
    friend istream& operator>>(istream& in, mint& a) { int64_t y; in >> y; a = y; return in; }
    friend ostream& operator<<(ostream& out, mint a) { return out << a.x; }
    explicit operator int() const { return x; }
    static int mod_inv(int a, int mod = m) {
        // https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Example
        int g = mod, r = a, z = 0, y = 1;
        while (r != 0) { int q = g / r; g %= r; swap(g, r); z -= q * y; swap(z, y); }
        return z < 0 ? z + mod : z;
    }
    mint inv() const { return mod_inv(x, m); }
    friend mint binpow(mint a, int64_t b) { mint res = 1; while (b) { if (b & 1) res *= a; b >>= 1; a *= a; } return res; }
    mint pow(int64_t b) const { return binpow(*this, b); }
    mint operator-() const { return x ? m - x : 0; }
    mint& operator+=(const mint& a) { x += a.x; if (x >= m) x -= m; return *this; }
    mint& operator-=(const mint& a) { x -= a.x; if (x < 0) x += m; return *this; }
    static unsigned fast_mod(uint64_t x, unsigned mod = m) {
#if !defined(_WIN32) || defined(_WIN64)
        return x % mod;
#endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * mod for this to work, so that x / mod fits in a 32-bit integer.
        unsigned x_high = x >> 32, x_low = (unsigned) x; unsigned quot, rem;
        asm("divl %4\n" : "=a" (quot), "=d" (rem) : "d" (x_high), "a" (x_low), "r" (mod));
        return rem;
    }
    mint& operator*=(const mint& a) { x = fast_mod((uint64_t) x * a.x); return *this; }
    mint& operator/=(const mint& a) { return *this *= a.inv(); }
    friend mint operator+(mint a, const mint& b) { return a += b; }
    friend mint operator-(mint a, const mint& b) { return a -= b; }
    friend mint operator*(mint a, const mint& b) { return a *= b; }
    friend mint operator/(mint a, const mint& b) { return a /= b; }
    mint& operator++() { x = x == m - 1 ? 0 : x + 1; return *this; }
    mint& operator--() { x = x == 0 ? m - 1 : x - 1; return *this; }
    mint operator++(int) { mint a = *this; ++*this; return a; }
    mint operator--(int) { mint a = *this; --*this; return a; }
    bool operator==(const mint& a) const { return x == a.x; }
    bool operator!=(const mint& a) const { return x != a.x; }
};

con int mod = 998244353;

#define mi mint<mod>

con int N = 3e5 + 5;

mi cnt[N][3];
mi sum[N][3];
mi dp[N];
int w = 0;

mi sol(vec<vec<int>>& a) {
	mi res = 0;
	for (auto& r : a) {
		int n = r.size();
		int cur = 0;
		forn(i, 0, n-1) {
			if (r[i]) {
				cur++;
			}
			else if (cur) {
				res += dp[cur] * mi(2).pow(w - cur);
				cur = 0;
			}
		}
		if (cur) {
			res += dp[cur] * mi(2).pow(w - cur);
		}
	}
	return res;
}

vec<vec<int>> a;
vec<vec<int>> b;

void Solve() {
	cnt[1][0] = 1;
	cnt[1][1] = 1;
	forn(i, 2, N-1) {
		cnt[i][0] += cnt[i-1][0];
		sum[i][0] += sum[i-1][0];
		cnt[i][1] += cnt[i-1][0];
		sum[i][1] += sum[i-1][0];

		cnt[i][0] += cnt[i-1][1];
		sum[i][0] += sum[i-1][1];
		cnt[i][2] += cnt[i-1][1];
		sum[i][2] += sum[i-1][1] + cnt[i-1][1];

		cnt[i][0] += cnt[i-1][2];
		sum[i][0] += sum[i-1][2];
		cnt[i][1] += cnt[i-1][2];
		sum[i][1] += sum[i-1][2];
	}
	forn(i, 1, N-1) {
		forn(j, 0, 2) {
			dp[i] += sum[i][j];
		}
	}
    int n, m;
	cin >> n >> m;
	a.rsz(n, vec<int>(m, 0));
	b.rsz(m, vec<int>(n, 0));
	forn(i, 0, n-1) {
		forn(j, 0, m-1) {
			char c;
			cin >> c;
			if (c == 'o') {
				a[i][j] = b[j][i] = 1;
				w++;
			}
		}
	}
	mi ans = sol(a) + sol(b);
	out(ans);
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
#endif
	start_timer();
	Solve();
	return 0;
}

### Prompt

Please formulate a cpp solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef string str;

#define pb push_back
#define ppp pop_back
#define pii pair<int,int>
#define fi first
#define se second
#define stie std::tie
#define vec vector
#define	forn(i, l, r) for (int i=l; i<=r; i++)
#define forb(i, r, l) for (int i=r; i>=l; i--)
#define emp empty
#define beg begin
#define ins insert
#define cle clear
#define era erase
#define que queue
#define pque priority_queue
#define mset multiset
#define deq deque
#define sta stack
#define con const
#define rsz resize
#define ass assign
#define lowb lower_bound
#define uppb upper_bound

template<class T> void mini(T& a, T b) { a = min(a, b); }
template<class T> void maxi(T& a, T b) { a = max(a, b); }
template<class T1, class T2> ostream& operator<<(ostream &out, pair<T1, T2> a) { return out << a.first << " " << a.second; }
template<class T> ostream& operator<<(ostream& out, vector<T> a) { for (auto& i : a) out << i << " "; return out; }
template<class T> ostream& operator<<(ostream& out, set<T> a) { for (auto& i : a) out << i << " "; return out; }
template<class T> ostream& operator<<(ostream& out, multiset<T> a) { for (auto& i : a) out << i << " "; return out; }
template<class T1, class T2> ostream& operator<<(ostream& out, map<T1, T2> a) { for (auto& i : a) out << i << "\n"; return out; }
template<class T1, class T2> ostream& operator<<(ostream& out, unordered_map<T1, T2> a) { for (auto& i : a) out << i << "\n"; return out; }
template<class T> ostream& operator<<(ostream& out, queue<T> a) { while (!a.empty()) { out << a.front() << " "; a.pop(); } return out; }
template<class T> ostream& operator<<(ostream& out, deque<T> a) { while (!a.empty()) { out << a.front() << " "; a.pop_front(); } return out; }
template<class T> ostream& operator<<(ostream& out, priority_queue<T> a) { while (!a.empty()) { out << a.top() << "\n"; a.pop(); } return out; }
template<class T> void out(T a) { cout << a << endl; }
template<class T1, class T2> void out(T1 a, T2 b) { cout << a << " " << b << endl; }
template<class T1, class T2, class T3> void out(T1 a, T2 b, T3 c) { cout << a << " " << b << " " << c << endl; }
template<class T1, class T2, class T3, class T4> void out(T1 a, T2 b, T3 c, T4 d) { cout << a << " " << b << " " << c << " " << d << endl; }
template<class T> void out(vector<vector<T>> a) { for (vector<T> i : a) out(i); }
template<class T> void out_(T a[], int l, int r) { for (int i = l; i <= r; i++) cout << a[i] << " "; cout << endl; }
void out() { cout << "OK" << endl; }
template<class T> void sort(vector<T>& a) { sort(a.begin(), a.end()); }
template<class T> void uniq(vector<T>& a) { sort(a); a.erase(unique(a.begin(), a.end()), a.end()); }
template<class T> vector<T> set_int(vector<T> a, vector<T> b) { sort(a); sort(b); vector<T> res; set_intersection(a.begin(), a.end(), b.begin(), b.end(), back_inserter(res)); return res; }
clock_t start_time; void start_timer() { start_time = clock(); }
double get_time() { return (double)(clock() - start_time) / CLOCKS_PER_SEC; }
#if __SIZEOF_INT128__ >= 16
typedef __int128 LL;
istream& operator>>(istream& in, __int128& a) { int64_t b; cin >> b; a = b; return in; }
ostream& operator<<(ostream& out, const __int128 a) {
	unsigned __int128 b = a < 0 ? -a : a; char buf[128]; char* c = end(buf); do { --c; *c = "0123456789"[b % 10]; b /= 10; } while (b);
	if (a < 0) { --c; *c = '-'; } int len = end(buf) - c; out.rdbuf()->sputn(c, len); return out;
}
#endif

template<int m>
struct mint {
    int x = 0;
    mint(int64_t a = 0) { if (a < 0) a = a % m + m; if (a >= m) a %= m; x = a; }
    friend istream& operator>>(istream& in, mint& a) { int64_t y; in >> y; a = y; return in; }
    friend ostream& operator<<(ostream& out, mint a) { return out << a.x; }
    explicit operator int() const { return x; }
    static int mod_inv(int a, int mod = m) {
        // https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Example
        int g = mod, r = a, z = 0, y = 1;
        while (r != 0) { int q = g / r; g %= r; swap(g, r); z -= q * y; swap(z, y); }
        return z < 0 ? z + mod : z;
    }
    mint inv() const { return mod_inv(x, m); }
    friend mint binpow(mint a, int64_t b) { mint res = 1; while (b) { if (b & 1) res *= a; b >>= 1; a *= a; } return res; }
    mint pow(int64_t b) const { return binpow(*this, b); }
    mint operator-() const { return x ? m - x : 0; }
    mint& operator+=(const mint& a) { x += a.x; if (x >= m) x -= m; return *this; }
    mint& operator-=(const mint& a) { x -= a.x; if (x < 0) x += m; return *this; }
    static unsigned fast_mod(uint64_t x, unsigned mod = m) {
#if !defined(_WIN32) || defined(_WIN64)
        return x % mod;
#endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * mod for this to work, so that x / mod fits in a 32-bit integer.
        unsigned x_high = x >> 32, x_low = (unsigned) x; unsigned quot, rem;
        asm("divl %4\n" : "=a" (quot), "=d" (rem) : "d" (x_high), "a" (x_low), "r" (mod));
        return rem;
    }
    mint& operator*=(const mint& a) { x = fast_mod((uint64_t) x * a.x); return *this; }
    mint& operator/=(const mint& a) { return *this *= a.inv(); }
    friend mint operator+(mint a, const mint& b) { return a += b; }
    friend mint operator-(mint a, const mint& b) { return a -= b; }
    friend mint operator*(mint a, const mint& b) { return a *= b; }
    friend mint operator/(mint a, const mint& b) { return a /= b; }
    mint& operator++() { x = x == m - 1 ? 0 : x + 1; return *this; }
    mint& operator--() { x = x == 0 ? m - 1 : x - 1; return *this; }
    mint operator++(int) { mint a = *this; ++*this; return a; }
    mint operator--(int) { mint a = *this; --*this; return a; }
    bool operator==(const mint& a) const { return x == a.x; }
    bool operator!=(const mint& a) const { return x != a.x; }
};

con int mod = 998244353;

#define mi mint<mod>

con int N = 3e5 + 5;

mi cnt[N][3];
mi sum[N][3];
mi dp[N];
int w = 0;

mi sol(vec<vec<int>>& a) {
	mi res = 0;
	for (auto& r : a) {
		int n = r.size();
		int cur = 0;
		forn(i, 0, n-1) {
			if (r[i]) {
				cur++;
			}
			else if (cur) {
				res += dp[cur] * mi(2).pow(w - cur);
				cur = 0;
			}
		}
		if (cur) {
			res += dp[cur] * mi(2).pow(w - cur);
		}
	}
	return res;
}

vec<vec<int>> a;
vec<vec<int>> b;

void Solve() {
	cnt[1][0] = 1;
	cnt[1][1] = 1;
	forn(i, 2, N-1) {
		cnt[i][0] += cnt[i-1][0];
		sum[i][0] += sum[i-1][0];
		cnt[i][1] += cnt[i-1][0];
		sum[i][1] += sum[i-1][0];

		cnt[i][0] += cnt[i-1][1];
		sum[i][0] += sum[i-1][1];
		cnt[i][2] += cnt[i-1][1];
		sum[i][2] += sum[i-1][1] + cnt[i-1][1];

		cnt[i][0] += cnt[i-1][2];
		sum[i][0] += sum[i-1][2];
		cnt[i][1] += cnt[i-1][2];
		sum[i][1] += sum[i-1][2];
	}
	forn(i, 1, N-1) {
		forn(j, 0, 2) {
			dp[i] += sum[i][j];
		}
	}
    int n, m;
	cin >> n >> m;
	a.rsz(n, vec<int>(m, 0));
	b.rsz(m, vec<int>(n, 0));
	forn(i, 0, n-1) {
		forn(j, 0, m-1) {
			char c;
			cin >> c;
			if (c == 'o') {
				a[i][j] = b[j][i] = 1;
				w++;
			}
		}
	}
	mi ans = sol(a) + sol(b);
	out(ans);
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
#endif
	start_timer();
	Solve();
	return 0;
}

```