#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const int MODVAL = 1000000007;
struct UnionFind
{
vector<int> uf, sz;
int nc;
UnionFind(int N): uf(N), sz(N,1), nc(N)
{ for(int i=0; i<N; ++i) uf[i] = i; }
int size()
{ return nc; }
int Find(int a)
{ return uf[a]==a ? a : uf[a]=Find(uf[a]); }
bool Union(int a, int b)
{
a = Find(a);
b = Find(b);
if( a != b )
{
if( sz[a] >= sz[b] ) swap(a, b);
uf[a] = b;
sz[b] += sz[a];
--nc;
}
return (a!=b);
}
};
struct mint
{
int val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(LL x):val(x%MODVAL) {}
};
mint operator+(mint x, mint y) { return x.val+y.val; }
mint operator-(mint x, mint y) { return x.val-y.val+MODVAL; }
mint operator*(mint x, mint y) { return LL(x.val)*y.val; }
mint POW(mint x, int e) {
mint v = 1;
for(;e;x=x*x,e>>=1)
if(e&1)
v=v*x;
return v;
}
class MagicalGirlLevelTwoDivOne { public:
int theCount(vector <string> palette, int n, int m)
{
if( (n^m)&1 )
return 0;
int H = palette.size();
int W = palette[0].size();
#define key(y,x) (2+(y)*W+(x))
UnionFind uf(W*H+2);
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
{
if( palette[y][x] != '.' )
uf.Union(key(y,x), (palette[y][x]-'0')%2); // 0:even, 1:odd
if( y-n>=0 )
uf.Union(key(y,x), key(y-n,x));
if( x-m>=0 )
uf.Union(key(y,x), key(y,x-m));
}
if( uf.Find(0) == uf.Find(1) )
return 0;
vector< vector<int> > dep(n, vector<int>(m));
vector< vector<int> > stt(n, vector<int>(m));
for(int y=0; y<n; ++y)
for(int x=0; x<m; ++x)
{
for(int yy=y; yy<H; yy+=n)
for(int xx=x; xx<W; xx+=m)
if(palette[yy][xx] == '.')
dep[y][x]++;
int k = uf.Find(key(y,x));
if( k == uf.Find(0) )
stt[y][x] = 0;
else if( k == uf.Find(1) )
stt[y][x] = 1;
else
stt[y][x] = 2;
}
memo.assign(1024*10, -1);
return rec(dep, stt, n, m, 0, 0);
}
vector<int> memo;
int rec(const vector< vector<int> >& dep, const vector< vector<int> >& stt, const int H, const int W,
int y, int status)
{
if( y == H )
if( status == (1<<W)-1 )
return 1;
else
return 0;
int me = status*H+y;
if( memo[me] != -1 )
return memo[me];
mint total;
for(int bits=0; bits<(1<<W); ++bits)
{
mint cur(1);
int odd = 0;
for(int x=0; x<W; ++x)
if( (bits>>x)&1 )
++odd;
int odddep = 0;
int evendep = 0;
if(odd%2 == 0)
goto next;
for(int x=0; x<W; ++x)
if( stt[y][x] != 2 && stt[y][x] != ((bits>>x)&1) )
goto next;
for(int x=0; x<W; ++x)
{
int d = dep[y][x];
(((bits>>x)&1) ? odddep : evendep) += d;
}
cur = cur * POW(5, odddep);
cur = cur * POW(4,evendep);
cur = cur * rec(dep, stt, H, W, y+1, status^bits);
total = total + cur;
next:;
}
return memo[me] = total.val;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, MagicalGirlLevelTwoDivOne().theCount(palette, n, m));}
int main(){
CASE(0)
string palette_[] = {"12",
"2."};
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = 2;
int m = 2;
int _ = 5;
END
CASE(1)
string palette_[] = {"21",
"1."};
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = 2;
int m = 2;
int _ = 4;
END
CASE(2)
string palette_[] = {"...",
"...",
"..."};
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = 1;
int m = 1;
int _ = 1953125;
END
CASE(3)
string palette_[] = {"..58..",
"..47.."};
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = 2;
int m = 3;
int _ = 0;
END
CASE(4)
string palette_[] = {"...1.2.3",
"4.5.6...",
"...7.8.9",
"1.2.3..."};
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = 4;
int m = 4;
int _ = 886073030;
END
CASE(5)
string palette_[] = {"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"....................",
"...................."};
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = 10;
int m = 10;
int _ = 240076532;
END
/*
CASE(6)
string palette_[] = ;
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = ;
int m = ;
int _ = ;
END
CASE(7)
string palette_[] = ;
vector <string> palette(palette_, palette_+sizeof(palette_)/sizeof(*palette_));
int n = ;
int m = ;
int _ = ;
END
*/
}
// END CUT HERE