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
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
using ULL=unsigned long long;
#define FOR(i,l,r) for(int i=(l);i<=(r);++i)
#define REP(i,n) FOR(i,0,(n)-1)
#define ssize(x) int(x.size())
template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<'('<<p.first<<", "<<p.second<<')';}
template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<'{';int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<'}';}
#ifdef DEBUG
#define debug(x...) cerr<<"["#x"]: ",[](auto...$){((cerr<<$<<"; "),...)<<'\n';}(x)
#else
#define debug(...) {}
#endif

int main() {
	cin.tie(0)->sync_with_stdio(0);
	int n, m;
	cin >> n >> m;
	int sum = 0, pio = 0;
	vector t(n, vector (m, 'a'));
	REP (i, n)
		REP (j, m) {
			cin >> t[i][j];
			if (t[i][j] == 'O')
				sum ^= (i & 1) ^ (j & 1);
		}

	vector tt(n, vector (m, 'a'));
	REP (i, n) {
		REP (j, m) {
			cin >> tt[i][j];
			if (tt[i][j] == 'O') {
				++pio;
				sum ^= (i & 1) ^ (j & 1);
			}
		}
	}

	if (sum) {
		cout << 0 << endl;
		return 0;
	}

	int moves = 0;
	REP (i, n)
		REP (j, m - 1)
			if (tt[i][j] != tt[i][j + 1])
				++moves;

	REP (i, n - 1)
		REP (j, m)
			if (tt[i][j] != tt[i + 1][j])
				++moves;

	int max_moves = pio * 4;
	vector dp(n, vector (max_moves + 1 + m + m, vector (pio + 1 + m, vector (1 << m, 0ll))));

	auto zlicz = [&](int mask) {
		int ret = 0;
		REP (i, m - 1)
			ret += (((mask >> i) & 1) != 0) != (((mask >> (i + 1)) & 1) != 0);
		return ret;
	};

	auto dolicz = [&](int mask, int msk) {
		return __builtin_popcount(mask ^ msk);
	};

	auto ile = [&](int mask) {
		return __builtin_popcount(mask);
	};

	REP (i, 1 << m)
		dp[0][zlicz(i)][ile(i)][i] = 1;

	REP (i, n - 1)
		REP (has, pio + 1)
			REP (g, has * 4 + 1)
				REP (mask, 1 << m) {
					if (dp[i][g][has][mask] == 0)
						continue;
					REP (nmask, 1 << m)
						dp[i + 1][g + zlicz(nmask) + dolicz(mask, nmask)][has + ile(nmask)][nmask] +=
																				dp[i][g][has][mask];
				}

	LL rum = 0;
	REP (i, max_moves + 1)
		REP (mask, 1 << m)
			rum += dp[n - 1][i][pio][mask] * i;
	rum /= 2;
	debug(moves, rum);

	cout << setprecision(15) << fixed << (double)moves / (double)rum << endl;
}