1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
const double EPS = 1e-9;
const int INF = 2; // it doesn't actually have to be infinity or a big number
//~ https://cp-algorithms.com/linear_algebra/linear-system-gauss.html#implementation
int gauss (vector < vector<double> > a, vector<double> & ans) {
    int n = (int) a.size();
    int m = (int) a[0].size() - 1;

    vector<int> where (m, -1);
    for (int col=0, row=0; col<m && row<n; ++col) {
        int sel = row;
        for (int i=row; i<n; ++i)
            if (abs (a[i][col]) > abs (a[sel][col]))
                sel = i;
        if (abs (a[sel][col]) < EPS)
            continue;
        for (int i=col; i<=m; ++i)
            swap (a[sel][i], a[row][i]);
        where[col] = row;

        for (int i=0; i<n; ++i)
            if (i != row) {
                double c = a[i][col] / a[row][col];
                for (int j=col; j<=m; ++j)
                    a[i][j] -= a[row][j] * c;
            }
        ++row;
    }

    ans.assign (m, 0);
    for (int i=0; i<m; ++i)
        if (where[i] != -1)
            ans[i] = a[where[i]][m] / a[where[i]][i];
    for (int i=0; i<n; ++i) {
        double sum = 0;
        for (int j=0; j<m; ++j)
            sum += ans[j] * a[i][j];
        if (abs (sum - a[i][m]) > EPS)
            return 0;
    }

    for (int i=0; i<m; ++i)
        if (where[i] == -1)
            return INF;
    return 1;
}
unordered_map<ull, int>mapa;
void gen(int i, int mx, int p, ull m)
{
	if (!p)
	{
		//~ cout<<mapa.size()<<" "<<bitset<5>(m)<<"\n";
		mapa[m]=mapa.size();
		return;
	}
	gen(i+1, mx, p-1, m|(1ull<<i));
	if (mx-i-1>=p) gen(i+1, mx, p, m);
}
int main()
{
	//~ vector<vector<double>>v={{1, 1, 3}, {1, -1, -1}};
	//~ vector<double>odp;
	//~ gauss(v, odp);
	//~ cout<<odp[0]<<" "<<odp[1];
	//~ return 0;
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	int n, m, p=0, npos=0; cin>>n>>m;
	ull lmsk=0;
	for (int qq=0; qq<2; qq++)
	{
		for (int i=0; i<n; i++)
		{
			for (int j=0; j<m; j++)
			{
				char c; cin>>c;
				if (c=='O')
				{
					p+=!qq;
					lmsk|=(1ull<<(i*m+j))*qq;
					npos+=(qq? 1 : -1)*((i+j)&1);
				}
			}
		}
	}
	if (npos)
	{
		cout<<"0\n";
		return 0;
	}
	gen(0, n*m, p, 0);
	vector<vector<double>>sys(mapa.size()+1, vector<double>(mapa.size()+1, 0));
	for (int i=0; i<(int)mapa.size(); i++) sys[i][i]=-1, sys.back()[i]=1;
	sys.back().back()=2;
	for (auto i : mapa)
	{
		ull msk=i.first;
		//~ cout<<"XD "<<i.first<<" "<<i.second<<"\n";
		vector<ull>pol;
		for (int j=0; j<n*m; j++)
		{
			if (msk&(1ull<<j))
			{
				ull b=1ull<<j;
				msk^=b;
				if (j-m>=0 && !(msk&(b>>m))) pol.push_back(msk^(b>>m));
				if (j+m<n*m && !(msk&(b<<m))) pol.push_back(msk^(b<<m));
				if (j%m!=0 && !(msk&(b>>1))) pol.push_back(msk^(b>>1));
				if (j%m!=m-1 && !(msk&(b<<1))) pol.push_back(msk^(b<<1));
				msk^=b;
			}
		}
		
		//~ for (auto j : pol)
		//~ {
			//~ cout<<i.second<<" "<<bitset<5>(msk)<<" "<<bitset<5>(j)<<"\n";
		//~ }
		//~ cout<<"\n";

		double k=pol.size();
		for (auto j : pol)
		{
			sys[mapa[j]][i.second]=1./k;
		}
	}
	vector<double>ans;
	//~ for (auto i : sys)
	//~ {
		//~ for (auto j : i)
		//~ {
			//~ cout<<fixed<<setprecision(1)<<j<<" ";
		//~ }
		//~ cout<<"\n";
	//~ }
	gauss(sys, ans);
	//~ for (auto i : ans) cout<<fixed<<setprecision(3)<<i<<"\n";
	cout<<fixed<<setprecision(13)<<ans[mapa[lmsk]]<<"\n";
}