#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 LL MODVAL = 1234567891;
struct UnionFind
{
vector<int> uf, sz, cyc;
int nc;
bool operator<(const UnionFind& rhs) const {
if( nc != rhs.nc ) return nc < rhs.nc;
if( uf != rhs.uf ) return uf < rhs.uf;
if( sz != rhs.sz ) return sz < rhs.sz;
return cyc < rhs.cyc;
}
UnionFind(int N): uf(N), sz(N,1), cyc(N), 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]); }
int 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];
cyc[b] += cyc[a];
--nc;
}
else
cyc[a] ++;
return cyc[a];
}
};
class TheCitiesAndRoadsDivOne { public:
int find(vector <string> map)
{
int N = map.size();
UnionFind uf(N);
for(int i=0; i<N; ++i)
for(int j=i+1; j<N; ++j)
if( map[i][j]=='Y' )
if( uf.Union(i, j) >= 2 )
return 0;
return rec(uf, 0, 1, N, map);
}
map< pair<UnionFind,int>, int > memo;
int rec(UnionFind& uf, int i, int j , int N, vector<string>& map)
{
if( i == N )
return uf.nc==1 ? 1 : 0;
if( j == N )
return rec(uf, i+1, i+2, N, map);
pair<UnionFind,int> key(uf, i*N+j);
if( memo.count(key) )
return memo[key];
LL cnt = rec(uf, i, j+1, N, map);
if( map[i][j] == 'N' )
{
UnionFind uf2(uf);
if( uf2.Union(i,j) < 2 )
cnt = (cnt + rec(uf2,i,j+1,N,map)) % MODVAL;
}
return memo[key] = (int)cnt;
}
};
// 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(_, TheCitiesAndRoadsDivOne().find(map));}
int main(){
CASE(0)
string map_[] = {"NN",
"NN"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 1;
END
CASE(1)
string map_[] = {"NNY",
"NNN",
"YNN"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 3;
END
CASE(2)
string map_[] = {"NY",
"YN"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 1;
END
CASE(3)
string map_[] = {"NYNN",
"YNNN",
"NNNY",
"NNYN"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 10;
END
CASE(4)
string map_[] = {"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN",
"NNNNNNNNNNNN"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 1137797187;
END
CASE(5)
string map_[] = {"N"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 1;
END
CASE(6)
string map_[] = {"NYYNN",
"YNYNN",
"YYNNN",
"NNNNY",
"NNNYN"};
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = 6;
END
/*
CASE(7)
string map_[] = ;
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = ;
END
CASE(8)
string map_[] = ;
vector <string> map(map_, map_+sizeof(map_)/sizeof(*map_));
int _ = ;
END
*/
}
// END CUT HERE