#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;
template<typename T>
struct DP3
{
int N1, N2, N3;
vector<T> data;
DP3(int N1, int N2, int N3, const T& t = T())
: N1(N1), N2(N2), N3(N3), data(N1*N2*N3, t) { assert(data.size()*sizeof(T)<(1<<26)); }
T& operator()(int i1, int i2, int i3)
{ return data[ ((i1*N2)+i2)*N3+i3 ]; }
void swap(DP3& rhs)
{ data.swap(rhs.data); }
};
class RectangleAvoidingColoring { public:
long long count(vector <string> board)
{
int H = board.size();
int W = board[0].size();
// o????
// o????
// xooxo
// xoxoo
// xxooo
if( H>=5 && W>=5 )
return 0;
if( H >= 5 )
transpose(board, H, W);
// H <= 4
int BADPAT = H*(H-1)/2;
DP3<LL> dp(1<<BADPAT, 1<<BADPAT, W+1);
dp(0,0,0) = 1;
for(int i=0; i<W; ++i)
for(int BlackBad=0; BlackBad<(1<<BADPAT); BlackBad++)
for(int WhiteBad=0; WhiteBad<(1<<BADPAT); WhiteBad++)
{
for(int pat=0; pat<(1<<H); ++pat) {
int bbb = bb(pat,H);
int wbb = wb(pat,H);
if( possible(pat, board, i, H) && !(bbb&BlackBad) && !(wbb&WhiteBad) )
dp(BlackBad|bbb,WhiteBad|wbb,i+1) += dp(BlackBad,WhiteBad,i);
}
}
LL sum = 0;
for(int BlackBad=0; BlackBad<(1<<BADPAT); BlackBad++)
for(int WhiteBad=0; WhiteBad<(1<<BADPAT); WhiteBad++)
sum += dp(BlackBad,WhiteBad,W);
return sum;
}
bool possible(int pat, const vector<string>& board, int i, int H)
{
for(int y=0; y<H; ++y) {
if( board[y][i]=='B' && !(pat&(1<<y))) return false;
if( board[y][i]=='W' && (pat&(1<<y))) return false;
}
return true;
}
int bb(int pat,int H)
{
int mask = 0, idx=0;
for(int i=0; i<H; ++i)
for(int j=i+1; j<H; ++j,++idx)
if(pat & (1<<i))
if(pat & (1<<j))
mask |= (1<<idx);
return mask;
}
int wb(int pat,int H)
{
int mask = 0, idx=0;
for(int i=0; i<H; ++i)
for(int j=i+1; j<H; ++j,++idx)
if(!(pat & (1<<i)))
if(!(pat & (1<<j)))
mask |= (1<<idx);
return mask;
}
void transpose(vector<string>& b, int& H, int& W)
{
vector<string> bb(W);
for(int x=0; x<W; ++x)
for(int y=0; y<H; ++y)
bb[x] += b[y][x];
swap(H, W);
b = bb;
}
};
// 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 long long& Expected, const long long& 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(_, RectangleAvoidingColoring().count(board));}
int main(){
CASE(0)
string board_[] = {"??",
"??"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = 14LL;
END
CASE(1)
string board_[] = {"B?",
"?B"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = 3LL;
END
CASE(2)
string board_[] = {"WW",
"WW"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = 0LL;
END
CASE(3)
string board_[] = {"??B??",
"W???W",
"??B??"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = 12LL;
END
CASE(4)
string board_[] = {"??",
"W?",
"W?",
"?W",
"W?"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = 16LL;
END
/*
CASE(5)
string board_[] = {};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = LL;
END
CASE(6)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
long long _ = LL;
END
*/
}
// END CUT HERE