#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;
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);
}
};
class HexagonPuzzle { public:
int theCount(vector <string> board)
{
vector< pair<int,int> > id2pos;
map<pair<int,int>, int> pos2id;
int N = board.size();
for(int i=0; i<N; ++i)
for(int k=0; k<=i; ++k) {
id2pos.push_back( make_pair(i,k) );
pos2id[make_pair(i,k)] = id2pos.size()-1;
}
int M = id2pos.size();
UnionFind uf(M);
for(int i=0; i<N; ++i)
for(int k=0; k<=i; ++k)
if( board[i][k] == '.' )
{
if( i+1<N && board[i+1][k]=='.' && board[i+1][k+1]=='.' )
{
int a = pos2id[ make_pair(i,k) ];
int b = pos2id[ make_pair(i+1,k) ];
int c = pos2id[ make_pair(i+1,k+1) ];
uf.Union(a,b);
uf.Union(b,c);
}
if( i+1<N && k+1<=i && board[i][k+1]=='.' && board[i+1][k+1]=='.' )
{
int a = pos2id[ make_pair(i,k) ];
int b = pos2id[ make_pair(i,k+1) ];
int c = pos2id[ make_pair(i+1,k+1) ];
uf.Union(a,b);
uf.Union(b,c);
}
}
map<int, int> sc;
for(int i=0; i<N; ++i)
for(int k=0; k<=i; ++k)
if( board[i][k] == '.' )
{
int a = pos2id[ make_pair(i,k) ];
int ra = uf.Find(a);
sc[ra] = uf.sz[ra];
}
static const int MODVAL = 1000000007;
LL result = 1;
for(map<int,int>::iterator it=sc.begin(); it!=sc.end(); ++it)
{
int n = it->second;
LL r = 1;
for(int i=3; i<=n; ++i)
r = (r*i)%MODVAL;
result = (result * r) % MODVAL;
}
return int(result);
}
};
// 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(_, HexagonPuzzle().theCount(board));}
int main(){
CASE(0)
string board_[] = {".",
".X",
"X..",
".X.X"}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 3;
END
CASE(1)
string board_[] = {"X"}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 1;
END
CASE(2)
string board_[] = {".",
"..",
"...",
".X.."}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 20160;
END
CASE(3)
string board_[] = {".",
"..",
"XXX",
"..X.",
".X..X",
"XXXX..",
"..X.X.X",
"..X.XX.."}
;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 108;
END
CASE(4)
string board_[] = {".",
"..",
"...",
"....",
".....",
"......",
".......",
"........"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 261547992;
END
/*
CASE(5)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = ;
END
CASE(6)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = ;
END
*/
}
// END CUT HERE