// #pragma GCC optimize("Ofast,unroll-loops")
// #pragma GCC target("avx,avx2,fma")

#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ull unsigned long long
#define dd double
#define ld long double
#define sl(n) scanf("%lld", &n)
#define si(n) scanf("%d", &n)
#define sd(n) scanf("%lf", &n)
#define pll pair <ll, ll>
#define pii pair <int, int>
#define mp make_pair
#define pb push_back
#define all(v) v.begin(), v.end()
#define inf (1LL << 61)
#define loop(i, start, stop, inc) for(ll i = start; i <= stop; i += inc)
#define for1(i, stop) for(ll i = 1; i <= stop; ++i)
#define for0(i, stop) for(ll i = 0; i < stop; ++i)
#define rep1(i, start) for(ll i = start; i >= 1; --i)
#define rep0(i, start) for(ll i = (start-1); i >= 0; --i)
#define ms(n, i) memset(n, i, sizeof(n))
#define casep(n) printf("Case %lld:", ++n)
#define pn printf("\n")
#define pf printf
#define EL '\n'
#define fastio std::ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);

// === Debug macro starts here ===
#ifndef ONLINE_JUDGE
#define DEBUG
#define SYS_COL system("COLOR")
#endif

int recur_depth = 0;
#ifdef DEBUG
#define dbg(x) {++recur_depth; auto x_=x; --recur_depth; SYS_COL; cerr<<string(recur_depth, '\t')<<"\e[91m"<<__func__<<":"<<__LINE__<<"\t"<<#x<<" = "<<x_<<"\e[39m"<<endl;}
template<typename Ostream, typename Cont>
typename enable_if<is_same<Ostream,ostream>::value, Ostream&>::type operator<<(Ostream& os,  const Cont& v){
	os<<"[";
	for(auto& x:v){os<<x<<", ";}
	return os<<"]";
}
template<typename Ostream, typename ...Ts>
Ostream& operator<<(Ostream& os,  const pair<Ts...>& p){
	return os<<"{"<<p.first<<", "<<p.second<<"}";
}
#else
#define dbg(x)
#endif
// === Debug macro ends here ===

#define ff first
#define ss second

const ll sz = 3e5 + 10, mod = 998244353;
vector <ll> dp[sz], way[sz];
vector <char> mat[sz];
ll n, m;

ll way1(ll r, ll c)
{
    if(r > n)
        return 1;

    ll &ret = way[r][c];
    if(ret != -1)
        return ret;

    if(c == m) {
        if(mat[r][c] != 'o')
            return ret = way1(r+1, 1);
        return ret = (2*way1(r+1, 1)) % mod;
    }

    ret = way1(r, c+1);
    if(mat[r][c] == 'o') ret = (2*ret) % mod;

    return ret;
}

ll way2(ll r, ll c)
{
    if(c > m)
        return 1;

    ll &ret = way[r][c];
    if(ret != -1)
        return ret;

    if(r == n) {
        if(mat[r][c] != 'o')
            return ret = way2(1, c+1);
        return ret = (2*way2(1, c+1)) % mod;
    }

    ret = way2(r+1, c);
    if(mat[r][c] == 'o') ret = (2*ret) % mod;

    return ret;
}

ll solve1(ll r, ll c)
{
    if(r > n)
        return 0;

    ll &ret = dp[r][c];
    if(ret != -1)
        return ret;

    ret = 0;
    if(c == m) {
        ret = solve1(r+1, 1);

        if(mat[r][c] == 'o')
            ret = 2*ret;

        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(mat[r][c] == 'o') ret = solve1(r, c+1);

    if(mat[r][c] != 'o' || mat[r][c+1] != 'o') {
        ret += solve1(r, c+1);
        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(c+1 == m) {
        ret += way1(r+1, 1) +solve1(r+1, 1);
        ret += solve1(r+1, 1);
    }
    else {
        ret += way1(r,c+2) + solve1(r, c+2);
        ret += solve1(r, c+2);
    }

    ret %= mod;
    //cerr << r << " " << c << " || " << ret << endl;
    return ret;
}

ll solve2(ll r, ll c)
{
    if(c > m)
        return 0;

    ll &ret = dp[r][c];
    if(ret != -1)
        return ret;

    ret = 0;
    if(r == n) {
        ret = solve2(1, c+1);

        if(mat[r][c] == 'o')
            ret = 2*ret;

        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(mat[r][c] == 'o') ret = solve2(r+1, c);

    if(mat[r][c] != 'o' || mat[r+1][c] != 'o') {
        ret += solve2(r+1, c);
        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(r+1==n) {
        ret += way2(1, c+1) + solve2(1, c+1);
        ret += solve2(1, c+1);
    }
    else {
        ret += way2(r+2, c) + solve2(r+2, c);
        ret += solve2(r+2, c);
    }

    ret %= mod;
    return ret;
}

int main()
{
    cin >> n >> m;

    for1(i, n) {
        dp[i].resize(m+2, -1);
        way[i].resize(m+2, -1);
        mat[i].resize(m+2);
    }

    for1(i, n) {
        for1(j, m) {
            scanf(" %c", &mat[i][j]);
        }
    }

    ll ans1 = solve1(1, 1);
    //dbg(ans1);

    for1(i, n)
        for1(j, m)
            dp[i][j] = way[i][j] = -1;

    ll ans2 = solve2(1, 1);
    //dbg(ans2);

    cout << (ans1+ans2) % mod << EL;

    return 0;
}


### Prompt

Create a solution in CPP for 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
// #pragma GCC optimize("Ofast,unroll-loops")
// #pragma GCC target("avx,avx2,fma")

#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ull unsigned long long
#define dd double
#define ld long double
#define sl(n) scanf("%lld", &n)
#define si(n) scanf("%d", &n)
#define sd(n) scanf("%lf", &n)
#define pll pair <ll, ll>
#define pii pair <int, int>
#define mp make_pair
#define pb push_back
#define all(v) v.begin(), v.end()
#define inf (1LL << 61)
#define loop(i, start, stop, inc) for(ll i = start; i <= stop; i += inc)
#define for1(i, stop) for(ll i = 1; i <= stop; ++i)
#define for0(i, stop) for(ll i = 0; i < stop; ++i)
#define rep1(i, start) for(ll i = start; i >= 1; --i)
#define rep0(i, start) for(ll i = (start-1); i >= 0; --i)
#define ms(n, i) memset(n, i, sizeof(n))
#define casep(n) printf("Case %lld:", ++n)
#define pn printf("\n")
#define pf printf
#define EL '\n'
#define fastio std::ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);

// === Debug macro starts here ===
#ifndef ONLINE_JUDGE
#define DEBUG
#define SYS_COL system("COLOR")
#endif

int recur_depth = 0;
#ifdef DEBUG
#define dbg(x) {++recur_depth; auto x_=x; --recur_depth; SYS_COL; cerr<<string(recur_depth, '\t')<<"\e[91m"<<__func__<<":"<<__LINE__<<"\t"<<#x<<" = "<<x_<<"\e[39m"<<endl;}
template<typename Ostream, typename Cont>
typename enable_if<is_same<Ostream,ostream>::value, Ostream&>::type operator<<(Ostream& os,  const Cont& v){
	os<<"[";
	for(auto& x:v){os<<x<<", ";}
	return os<<"]";
}
template<typename Ostream, typename ...Ts>
Ostream& operator<<(Ostream& os,  const pair<Ts...>& p){
	return os<<"{"<<p.first<<", "<<p.second<<"}";
}
#else
#define dbg(x)
#endif
// === Debug macro ends here ===

#define ff first
#define ss second

const ll sz = 3e5 + 10, mod = 998244353;
vector <ll> dp[sz], way[sz];
vector <char> mat[sz];
ll n, m;

ll way1(ll r, ll c)
{
    if(r > n)
        return 1;

    ll &ret = way[r][c];
    if(ret != -1)
        return ret;

    if(c == m) {
        if(mat[r][c] != 'o')
            return ret = way1(r+1, 1);
        return ret = (2*way1(r+1, 1)) % mod;
    }

    ret = way1(r, c+1);
    if(mat[r][c] == 'o') ret = (2*ret) % mod;

    return ret;
}

ll way2(ll r, ll c)
{
    if(c > m)
        return 1;

    ll &ret = way[r][c];
    if(ret != -1)
        return ret;

    if(r == n) {
        if(mat[r][c] != 'o')
            return ret = way2(1, c+1);
        return ret = (2*way2(1, c+1)) % mod;
    }

    ret = way2(r+1, c);
    if(mat[r][c] == 'o') ret = (2*ret) % mod;

    return ret;
}

ll solve1(ll r, ll c)
{
    if(r > n)
        return 0;

    ll &ret = dp[r][c];
    if(ret != -1)
        return ret;

    ret = 0;
    if(c == m) {
        ret = solve1(r+1, 1);

        if(mat[r][c] == 'o')
            ret = 2*ret;

        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(mat[r][c] == 'o') ret = solve1(r, c+1);

    if(mat[r][c] != 'o' || mat[r][c+1] != 'o') {
        ret += solve1(r, c+1);
        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(c+1 == m) {
        ret += way1(r+1, 1) +solve1(r+1, 1);
        ret += solve1(r+1, 1);
    }
    else {
        ret += way1(r,c+2) + solve1(r, c+2);
        ret += solve1(r, c+2);
    }

    ret %= mod;
    //cerr << r << " " << c << " || " << ret << endl;
    return ret;
}

ll solve2(ll r, ll c)
{
    if(c > m)
        return 0;

    ll &ret = dp[r][c];
    if(ret != -1)
        return ret;

    ret = 0;
    if(r == n) {
        ret = solve2(1, c+1);

        if(mat[r][c] == 'o')
            ret = 2*ret;

        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(mat[r][c] == 'o') ret = solve2(r+1, c);

    if(mat[r][c] != 'o' || mat[r+1][c] != 'o') {
        ret += solve2(r+1, c);
        if(ret >= mod) ret -= mod;
        return ret;
    }

    if(r+1==n) {
        ret += way2(1, c+1) + solve2(1, c+1);
        ret += solve2(1, c+1);
    }
    else {
        ret += way2(r+2, c) + solve2(r+2, c);
        ret += solve2(r+2, c);
    }

    ret %= mod;
    return ret;
}

int main()
{
    cin >> n >> m;

    for1(i, n) {
        dp[i].resize(m+2, -1);
        way[i].resize(m+2, -1);
        mat[i].resize(m+2);
    }

    for1(i, n) {
        for1(j, m) {
            scanf(" %c", &mat[i][j]);
        }
    }

    ll ans1 = solve1(1, 1);
    //dbg(ans1);

    for1(i, n)
        for1(j, m)
            dp[i][j] = way[i][j] = -1;

    ll ans2 = solve2(1, 1);
    //dbg(ans2);

    cout << (ans1+ans2) % mod << EL;

    return 0;
}


```