#include "bits/stdc++.h"
// #pragma GCC optimize("Ofast,unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,mmx,avx,avx2")
using namespace std;
using ll = long long;

// Source: Aeren (modified from tourist?)
template<typename T>
struct Z_p{
    using Type = typename decay<decltype(T::value)>::type;
    static vector<Type> MOD_INV;
    constexpr Z_p(): value(){ }
    template<typename U> Z_p(const U &x){ value = normalize(x); }
    template<typename U> static Type normalize(const U &x){
        Type v;
        if(-mod() <= x && x < mod()) v = static_cast<Type>(x);
        else v = static_cast<Type>(x % mod());
        if(v < 0) v += mod();
        return v;
    }
    const Type& operator()() const{ return value; }
    template<typename U> explicit operator U() const{ return static_cast<U>(value); }
    constexpr static Type mod(){ return T::value; }
    Z_p &operator+=(const Z_p &otr){ if((value += otr.value) >= mod()) value -= mod(); return *this; }
    Z_p &operator-=(const Z_p &otr){ if((value -= otr.value) < 0) value += mod(); return *this; }
    template<typename U> Z_p &operator+=(const U &otr){ return *this += Z_p(otr); }
    template<typename U> Z_p &operator-=(const U &otr){ return *this -= Z_p(otr); }
    Z_p &operator++(){ return *this += 1; }
    Z_p &operator--(){ return *this -= 1; }
    Z_p operator++(int){ Z_p result(*this); *this += 1; return result; }
    Z_p operator--(int){ Z_p result(*this); *this -= 1; return result; }
    Z_p operator-() const{ return Z_p(-value); }
    template<typename U = T>
    typename enable_if<is_same<typename Z_p<U>::Type, int>::value, Z_p>::type &operator*=(const Z_p& rhs){
        #ifdef _WIN32
        uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
        uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
        asm(
            "divl %4; \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (mod())
        );
        value = m;
        #else
        value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
        #endif
        return *this;
    }
    template<typename U = T>
    typename enable_if<is_same<typename Z_p<U>::Type, int64_t>::value, Z_p>::type &operator*=(const Z_p &rhs){
        int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
        value = normalize(value * rhs.value - q * mod());
        return *this;
    }
    template<typename U = T>
    typename enable_if<!is_integral<typename Z_p<U>::Type>::value, Z_p>::type &operator*=(const Z_p &rhs){
        value = normalize(value * rhs.value);
        return *this;
    }
    template<typename U>
    Z_p &operator^=(U e){
        if(e < 0) *this = 1 / *this, e = -e;
        Z_p res = 1;
        for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
        return *this = res;
    }
    template<typename U>
    Z_p operator^(U e) const{
        return Z_p(*this) ^= e;
    }
    Z_p &operator/=(const Z_p &otr){
        Type a = otr.value, m = mod(), u = 0, v = 1;
        if(a < (int)MOD_INV.size()) return *this *= MOD_INV[a];
        while(a){
            Type t = m / a;
            m -= t * a; swap(a, m);
            u -= t * v; swap(u, v);
        }
        assert(m == 1);
        return *this *= u;
    }
    template<typename U> friend const Z_p<U> &abs(const Z_p<U> &v){ return v; }
    Type value;
};
template<typename T> bool operator==(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value == rhs.value; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator==(const Z_p<T>& lhs, U rhs){ return lhs == Z_p<T>(rhs); }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator==(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) == rhs; }
template<typename T> bool operator!=(const Z_p<T> &lhs, const Z_p<T> &rhs){ return !(lhs == rhs); }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator!=(const Z_p<T> &lhs, U rhs){ return !(lhs == rhs); }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator!=(U lhs, const Z_p<T> &rhs){ return !(lhs == rhs); }
template<typename T> bool operator<(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value < rhs.value; }
template<typename T> bool operator>(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value > rhs.value; }
template<typename T> bool operator<=(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value <= rhs.value; }
template<typename T> bool operator>=(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value >= rhs.value; }
template<typename T> Z_p<T> operator+(const Z_p<T> &lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) += rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator+(const Z_p<T> &lhs, U rhs){ return Z_p<T>(lhs) += rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator+(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) += rhs; }
template<typename T> Z_p<T> operator-(const Z_p<T> &lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) -= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator-(const Z_p<T>& lhs, U rhs){ return Z_p<T>(lhs) -= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator-(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) -= rhs; }
template<typename T> Z_p<T> operator*(const Z_p<T> &lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) *= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator*(const Z_p<T>& lhs, U rhs){ return Z_p<T>(lhs) *= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator*(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) *= rhs; }
template<typename T> Z_p<T> operator/(const Z_p<T> &lhs, const Z_p<T> &rhs) { return Z_p<T>(lhs) /= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator/(const Z_p<T>& lhs, U rhs) { return Z_p<T>(lhs) /= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator/(U lhs, const Z_p<T> &rhs) { return Z_p<T>(lhs) /= rhs; }
template<typename T> istream &operator>>(istream &in, Z_p<T> &number){
    typename common_type<typename Z_p<T>::Type, int64_t>::type x;
    in >> x;
    number.value = Z_p<T>::normalize(x);
    return in;
}
template<typename T> ostream &operator<<(ostream &out, const Z_p<T> &number){ return out << number(); }

/*
using ModType = int;
struct VarMod{ static ModType value; };
ModType VarMod::value;
ModType &mod = VarMod::value;
using Zp = Z_p<VarMod>;
*/

// constexpr int mod = 1e9 + 7; // 1000000007
constexpr int mod = (119 << 23) + 1; // 998244353
// constexpr int mod = 1e9 + 9; // 1000000009
using Zp = Z_p<integral_constant<decay<decltype(mod)>::type, mod>>;

template<typename T> vector<typename Z_p<T>::Type> Z_p<T>::MOD_INV;
template<typename T = integral_constant<decay<decltype(mod)>::type, mod>>
void precalc_inverse(int SZ){
    auto &inv = Z_p<T>::MOD_INV;
    if(inv.empty()) inv.assign(2, 1);
    for(; inv.size() <= SZ; ) inv.push_back((mod - 1LL * mod / (int)inv.size() * inv[mod % (int)inv.size()]) % mod);
}

template<typename T>
vector<T> precalc_power(T base, int SZ){
    vector<T> res(SZ + 1, 1);
    for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
    return res;
}

int main()
{
    ios::sync_with_stdio(0); cin.tie(0);
    mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

    int n, m; cin >> n >> m;
    vector<string> v(n);
    Zp two(2), three(3), minus(-1);
    int tot = 0;
    for (int i = 0; i < n; ++i) {
        cin >> v[i];
        tot += count(begin(v[i]), end(v[i]), 'o');
    }
    Zp ans = 0;
    auto ways = [&] (int c) {
        if (c <= 1) return Zp(0);
        Zp ret = two^(tot-c);
        --c;
        ret /= 9;
        ret *= (two^c)*(3*c+1) - (minus^c);
        return ret;
    };
    for (int i = 0; i < n; ++i) {
        int ct = 0;
        for (int j = 0; j < m; ++j) {
            if (v[i][j] == 'o') ++ct;
            else {
                ans += ways(ct);
                ct = 0;
            }
        }
        ans += ways(ct);
    }
    for (int i = 0; i < m; ++i) {
        int ct = 0;
        for (int j = 0; j < n; ++j) {
            if (v[j][i] == 'o') ++ct;
            else {
                ans += ways(ct);
                ct = 0;
            }
        }
        ans += ways(ct);
    }
    cout << ans;
}
### Prompt

Your challenge is to write 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"
// #pragma GCC optimize("Ofast,unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,mmx,avx,avx2")
using namespace std;
using ll = long long;

// Source: Aeren (modified from tourist?)
template<typename T>
struct Z_p{
    using Type = typename decay<decltype(T::value)>::type;
    static vector<Type> MOD_INV;
    constexpr Z_p(): value(){ }
    template<typename U> Z_p(const U &x){ value = normalize(x); }
    template<typename U> static Type normalize(const U &x){
        Type v;
        if(-mod() <= x && x < mod()) v = static_cast<Type>(x);
        else v = static_cast<Type>(x % mod());
        if(v < 0) v += mod();
        return v;
    }
    const Type& operator()() const{ return value; }
    template<typename U> explicit operator U() const{ return static_cast<U>(value); }
    constexpr static Type mod(){ return T::value; }
    Z_p &operator+=(const Z_p &otr){ if((value += otr.value) >= mod()) value -= mod(); return *this; }
    Z_p &operator-=(const Z_p &otr){ if((value -= otr.value) < 0) value += mod(); return *this; }
    template<typename U> Z_p &operator+=(const U &otr){ return *this += Z_p(otr); }
    template<typename U> Z_p &operator-=(const U &otr){ return *this -= Z_p(otr); }
    Z_p &operator++(){ return *this += 1; }
    Z_p &operator--(){ return *this -= 1; }
    Z_p operator++(int){ Z_p result(*this); *this += 1; return result; }
    Z_p operator--(int){ Z_p result(*this); *this -= 1; return result; }
    Z_p operator-() const{ return Z_p(-value); }
    template<typename U = T>
    typename enable_if<is_same<typename Z_p<U>::Type, int>::value, Z_p>::type &operator*=(const Z_p& rhs){
        #ifdef _WIN32
        uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
        uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
        asm(
            "divl %4; \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (mod())
        );
        value = m;
        #else
        value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
        #endif
        return *this;
    }
    template<typename U = T>
    typename enable_if<is_same<typename Z_p<U>::Type, int64_t>::value, Z_p>::type &operator*=(const Z_p &rhs){
        int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
        value = normalize(value * rhs.value - q * mod());
        return *this;
    }
    template<typename U = T>
    typename enable_if<!is_integral<typename Z_p<U>::Type>::value, Z_p>::type &operator*=(const Z_p &rhs){
        value = normalize(value * rhs.value);
        return *this;
    }
    template<typename U>
    Z_p &operator^=(U e){
        if(e < 0) *this = 1 / *this, e = -e;
        Z_p res = 1;
        for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
        return *this = res;
    }
    template<typename U>
    Z_p operator^(U e) const{
        return Z_p(*this) ^= e;
    }
    Z_p &operator/=(const Z_p &otr){
        Type a = otr.value, m = mod(), u = 0, v = 1;
        if(a < (int)MOD_INV.size()) return *this *= MOD_INV[a];
        while(a){
            Type t = m / a;
            m -= t * a; swap(a, m);
            u -= t * v; swap(u, v);
        }
        assert(m == 1);
        return *this *= u;
    }
    template<typename U> friend const Z_p<U> &abs(const Z_p<U> &v){ return v; }
    Type value;
};
template<typename T> bool operator==(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value == rhs.value; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator==(const Z_p<T>& lhs, U rhs){ return lhs == Z_p<T>(rhs); }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator==(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) == rhs; }
template<typename T> bool operator!=(const Z_p<T> &lhs, const Z_p<T> &rhs){ return !(lhs == rhs); }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator!=(const Z_p<T> &lhs, U rhs){ return !(lhs == rhs); }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> bool operator!=(U lhs, const Z_p<T> &rhs){ return !(lhs == rhs); }
template<typename T> bool operator<(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value < rhs.value; }
template<typename T> bool operator>(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value > rhs.value; }
template<typename T> bool operator<=(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value <= rhs.value; }
template<typename T> bool operator>=(const Z_p<T> &lhs, const Z_p<T> &rhs){ return lhs.value >= rhs.value; }
template<typename T> Z_p<T> operator+(const Z_p<T> &lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) += rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator+(const Z_p<T> &lhs, U rhs){ return Z_p<T>(lhs) += rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator+(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) += rhs; }
template<typename T> Z_p<T> operator-(const Z_p<T> &lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) -= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator-(const Z_p<T>& lhs, U rhs){ return Z_p<T>(lhs) -= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator-(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) -= rhs; }
template<typename T> Z_p<T> operator*(const Z_p<T> &lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) *= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator*(const Z_p<T>& lhs, U rhs){ return Z_p<T>(lhs) *= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator*(U lhs, const Z_p<T> &rhs){ return Z_p<T>(lhs) *= rhs; }
template<typename T> Z_p<T> operator/(const Z_p<T> &lhs, const Z_p<T> &rhs) { return Z_p<T>(lhs) /= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator/(const Z_p<T>& lhs, U rhs) { return Z_p<T>(lhs) /= rhs; }
template<typename T, typename U, typename enable_if<is_integral<U>::value>::type* = nullptr> Z_p<T> operator/(U lhs, const Z_p<T> &rhs) { return Z_p<T>(lhs) /= rhs; }
template<typename T> istream &operator>>(istream &in, Z_p<T> &number){
    typename common_type<typename Z_p<T>::Type, int64_t>::type x;
    in >> x;
    number.value = Z_p<T>::normalize(x);
    return in;
}
template<typename T> ostream &operator<<(ostream &out, const Z_p<T> &number){ return out << number(); }

/*
using ModType = int;
struct VarMod{ static ModType value; };
ModType VarMod::value;
ModType &mod = VarMod::value;
using Zp = Z_p<VarMod>;
*/

// constexpr int mod = 1e9 + 7; // 1000000007
constexpr int mod = (119 << 23) + 1; // 998244353
// constexpr int mod = 1e9 + 9; // 1000000009
using Zp = Z_p<integral_constant<decay<decltype(mod)>::type, mod>>;

template<typename T> vector<typename Z_p<T>::Type> Z_p<T>::MOD_INV;
template<typename T = integral_constant<decay<decltype(mod)>::type, mod>>
void precalc_inverse(int SZ){
    auto &inv = Z_p<T>::MOD_INV;
    if(inv.empty()) inv.assign(2, 1);
    for(; inv.size() <= SZ; ) inv.push_back((mod - 1LL * mod / (int)inv.size() * inv[mod % (int)inv.size()]) % mod);
}

template<typename T>
vector<T> precalc_power(T base, int SZ){
    vector<T> res(SZ + 1, 1);
    for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
    return res;
}

int main()
{
    ios::sync_with_stdio(0); cin.tie(0);
    mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

    int n, m; cin >> n >> m;
    vector<string> v(n);
    Zp two(2), three(3), minus(-1);
    int tot = 0;
    for (int i = 0; i < n; ++i) {
        cin >> v[i];
        tot += count(begin(v[i]), end(v[i]), 'o');
    }
    Zp ans = 0;
    auto ways = [&] (int c) {
        if (c <= 1) return Zp(0);
        Zp ret = two^(tot-c);
        --c;
        ret /= 9;
        ret *= (two^c)*(3*c+1) - (minus^c);
        return ret;
    };
    for (int i = 0; i < n; ++i) {
        int ct = 0;
        for (int j = 0; j < m; ++j) {
            if (v[i][j] == 'o') ++ct;
            else {
                ans += ways(ct);
                ct = 0;
            }
        }
        ans += ways(ct);
    }
    for (int i = 0; i < m; ++i) {
        int ct = 0;
        for (int j = 0; j < n; ++j) {
            if (v[j][i] == 'o') ++ct;
            else {
                ans += ways(ct);
                ct = 0;
            }
        }
        ans += ways(ct);
    }
    cout << ans;
}
```