#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>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;
static const unsigned MODVAL = 1000000009;
struct mint
{
unsigned val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(unsigned x):val(x%MODVAL) {}
mint(LL x):val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x+=y; }
mint operator-(mint x, mint y) { return x-=y; }
mint operator*(mint x, mint y) { return x*=y; }
mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
class CoinsGame { public:
int ways(vector <string> board)
{
map<pair<int,int>,int> ID;
for(int y=0; y<board.size(); ++y)
for(int x=0; x<board[0].size(); ++x)
if(board[y][x]=='.') {
int id = ID.size() + 1;
ID[make_pair(y,x)] = id;
}
vector< vector<int> > G(ID.size()+1);
G[0] = vector<int>(4, 0);
int H = board.size();
int W = board[0].size();
for(int y=0; y<board.size(); ++y)
for(int x=0; x<board[0].size(); ++x)
if(board[y][x]=='.')
{
int dy[]={-1,+1,0,0};
int dx[]={0,0,-1,+1};
for(int d=0; d<4; ++d)
{
int yy=y+dy[d], xx=x+dx[d];
if(yy<0||H<=yy||xx<0||W<=xx) {
// fell
G[ID[make_pair(y,x)]].push_back(0); // 0=fall
}
else if(board[yy][xx]=='#') {
// stop at yy-dy[d], xx-dx[d]
G[ID[make_pair(y,x)]].push_back(ID[make_pair(y,x)]);
}
else {
G[ID[make_pair(y,x)]].push_back(ID[make_pair(yy,xx)]);
}
}
}
return solve(G).val;
}
mint solve(vector< vector<int> >& G)
{
vector< vector<int> > set_buffer;
set<int> active_sets;
set<int> active_splitters;
{
set_buffer.push_back( vector<int>(1,0) );
vector<int> all;
for(int v=1; v<G.size(); ++v)
all.push_back(v);
set_buffer.push_back(all);
active_sets.insert(0);
active_sets.insert(1);
active_splitters.insert(0);
}
while(!active_splitters.empty())
{
const vector<int>& splv = set_buffer[*active_splitters.begin()];
set<int> spl(splv.begin(), splv.end());
active_splitters.erase(active_splitters.begin());
for(int d=0; d<4; ++d)
for(set<int>::iterator it=active_sets.begin(); it!=active_sets.end(); )
{
int ii = *it++;
const vector<int>& cur = set_buffer[ii];
vector<int> t, f;
for(int k=0; k<cur.size(); ++k)
(spl.count(G[cur[k]][d]) ? t : f).push_back(cur[k]);
if(!t.empty() && !f.empty())
{
set_buffer.push_back(t);
set_buffer.push_back(f);
active_sets.insert(set_buffer.size()-2);
active_sets.insert(set_buffer.size()-1);
if(active_splitters.count(ii)) {
active_splitters.insert(set_buffer.size()-2);
active_splitters.insert(set_buffer.size()-1);
} else {
active_splitters.insert(t.size()<f.size() ? set_buffer.size()-2 : set_buffer.size()-1);
}
active_splitters.erase(ii);
active_sets.erase(ii);
}
}
}
vector<int> es;
for(set<int>::iterator it=active_sets.begin(); it!=active_sets.end(); ++it)
if(*it)
es.push_back(set_buffer[*it].size());
/*
for(bool changed=true; changed;)
{
changed=false;
for(int i=0; i<eqs.size(); ++i) if(!eqs[i].second && !dead[i]){
set<int> spl(eqs[i].first.begin(), eqs[i].first.end());
eqs[i].second = true;
for(int k=0; k<eqs.size(); ++k)
for(int d=0; d<4; ++d) if(!dead[k]) {
vector<int> t, f;
for(vector<int>::iterator it=eqs[k].first.begin(); it!=eqs[k].first.end(); ++it)
(spl.count(G[*it][d]) ? t : f).push_back(*it);
if(!t.empty() && !f.empty()) {
if(eqs[k].second) {
eqs.push_back(make_pair(t,t.size()>f.size()));
eqs.push_back(make_pair(f,t.size()<=f.size()));
dead.push_back(false);
dead.push_back(false);
changed = true;
} else {
eqs.push_back(make_pair(t,false));
eqs.push_back(make_pair(f,false));
dead.push_back(false);
dead.push_back(false);
changed = true;
}
dead[k] = true;
}
}
}
}
vector<int> es;
for(int i=1; i<eqs.size(); ++i) if(!dead[i])
es.push_back(eqs[i].first.size());
*/
int sum = accumulate(es.begin(), es.end(), 0);
mint x = POW(2, sum);
for(int i=0; i<es.size(); ++i)
x -= POW(2, es[i])-1;
return x-1;
}
};
// 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(_, CoinsGame().ways(board));}
int main(){
CASE(0)
string board_[] = {".."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 1;
END
CASE(1)
string board_[] = {"##.#",
".###",
"###.",
"#.##"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 11;
END
CASE(2)
string board_[] = {"####",
"#..#",
"#..#",
"####"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 0;
END
CASE(3)
string board_[] = {"#.#.#"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 0;
END
CASE(4)
string board_[] = {"........",
"........",
"........",
"........",
"........",
"........",
"........",
"........"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 688856388;
END
CASE(5)
string board_[] = {"........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................", "........................................"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 150087966;
END
CASE(5)
string board_[] = {"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 150087966;
END
CASE(5)
string board_[] = {"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",
"........................................",};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int _ = 150087966;
END
}
// END CUT HERE