982758e5e4 2011-11-29        kinaba: #include <iostream>
982758e5e4 2011-11-29        kinaba: #include <sstream>
982758e5e4 2011-11-29        kinaba: #include <iomanip>
982758e5e4 2011-11-29        kinaba: #include <vector>
982758e5e4 2011-11-29        kinaba: #include <string>
982758e5e4 2011-11-29        kinaba: #include <map>
982758e5e4 2011-11-29        kinaba: #include <set>
982758e5e4 2011-11-29        kinaba: #include <algorithm>
982758e5e4 2011-11-29        kinaba: #include <numeric>
982758e5e4 2011-11-29        kinaba: #include <iterator>
982758e5e4 2011-11-29        kinaba: #include <functional>
982758e5e4 2011-11-29        kinaba: #include <complex>
982758e5e4 2011-11-29        kinaba: #include <queue>
982758e5e4 2011-11-29        kinaba: #include <stack>
982758e5e4 2011-11-29        kinaba: #include <cmath>
982758e5e4 2011-11-29        kinaba: #include <cassert>
982758e5e4 2011-11-29        kinaba: #include <cstring>
982758e5e4 2011-11-29        kinaba: #ifdef __GNUC__
982758e5e4 2011-11-29        kinaba: #include <ext/hash_map>
982758e5e4 2011-11-29        kinaba: #define unordered_map __gnu_cxx::hash_map
982758e5e4 2011-11-29        kinaba: #else
982758e5e4 2011-11-29        kinaba: #include <unordered_map>
982758e5e4 2011-11-29        kinaba: #endif
982758e5e4 2011-11-29        kinaba: using namespace std;
982758e5e4 2011-11-29        kinaba: typedef long long LL;
982758e5e4 2011-11-29        kinaba: typedef complex<double> CMP;
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: static const int MODVAL = 1000000009; // must be prime for op/
982758e5e4 2011-11-29        kinaba: struct mint
982758e5e4 2011-11-29        kinaba: {
982758e5e4 2011-11-29        kinaba: 	int val;
982758e5e4 2011-11-29        kinaba: 	mint():val(0){}
982758e5e4 2011-11-29        kinaba: 	mint(int    x):val(x%MODVAL) {} // x>=0
982758e5e4 2011-11-29        kinaba: 	mint(size_t x):val(x%MODVAL) {} // x>=0
982758e5e4 2011-11-29        kinaba: 	mint(LL     x):val(x%MODVAL) {} // x>=0
982758e5e4 2011-11-29        kinaba: };
982758e5e4 2011-11-29        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
982758e5e4 2011-11-29        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
982758e5e4 2011-11-29        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
982758e5e4 2011-11-29        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
982758e5e4 2011-11-29        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
982758e5e4 2011-11-29        kinaba: mint operator+(mint x, mint y) { return x+=y; }
982758e5e4 2011-11-29        kinaba: mint operator-(mint x, mint y) { return x-=y; }
982758e5e4 2011-11-29        kinaba: mint operator*(mint x, mint y) { return x*=y; }
982758e5e4 2011-11-29        kinaba: mint operator/(mint x, mint y) { return x/=y; }
982758e5e4 2011-11-29        kinaba: vector<mint> FAC_(1,1);
982758e5e4 2011-11-29        kinaba: mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*FAC_.size() ); return FAC_[n]; }
982758e5e4 2011-11-29        kinaba: mint C(LL n, LL k) { return k<0 || n<k ? 0 : FAC(n) / (FAC(k) * FAC(n-k)); }
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: class AxonometricProjection { public:
982758e5e4 2011-11-29        kinaba: 	int howManyWays(vector <int> left, vector <int> front)
982758e5e4 2011-11-29        kinaba: 	{
982758e5e4 2011-11-29        kinaba: 		mint ans = 1;
982758e5e4 2011-11-29        kinaba: 		sort(left.begin(), left.end());
982758e5e4 2011-11-29        kinaba: 		sort(front.begin(), front.end());
982758e5e4 2011-11-29        kinaba: 		ans *= perm(left);
982758e5e4 2011-11-29        kinaba: 		ans *= perm(front);
982758e5e4 2011-11-29        kinaba: 		for(int i=0, k=0; i<left.size() || k<front.size(); )
982758e5e4 2011-11-29        kinaba: 		{
982758e5e4 2011-11-29        kinaba: 			if( k<front.size() && (i==left.size() || front[k]<left[i]) )
982758e5e4 2011-11-29        kinaba: 			{
982758e5e4 2011-11-29        kinaba: 				// advance k
982758e5e4 2011-11-29        kinaba: 				int h = front[k];
982758e5e4 2011-11-29        kinaba: 				int len = 0;
982758e5e4 2011-11-29        kinaba: 				while( k!=front.size() && front[k]==h )
982758e5e4 2011-11-29        kinaba: 					++k, ++len;
982758e5e4 2011-11-29        kinaba: 				ans *= choose(h, len);
982758e5e4 2011-11-29        kinaba: 			}
982758e5e4 2011-11-29        kinaba: 			else if( i<left.size() && (k==front.size() || left[i]<front[k]) )
982758e5e4 2011-11-29        kinaba: 			{
982758e5e4 2011-11-29        kinaba: 				// advance i
982758e5e4 2011-11-29        kinaba: 				int h = left[i];
982758e5e4 2011-11-29        kinaba: 				int len = 0;
982758e5e4 2011-11-29        kinaba: 				while( i!=left.size() && left[i]==h )
982758e5e4 2011-11-29        kinaba: 					++i, ++len;
982758e5e4 2011-11-29        kinaba: 				ans *= choose(h, len);
982758e5e4 2011-11-29        kinaba: 			}
982758e5e4 2011-11-29        kinaba: 			else
982758e5e4 2011-11-29        kinaba: 			{
982758e5e4 2011-11-29        kinaba: 				// both
982758e5e4 2011-11-29        kinaba: 				int h = left[i];
982758e5e4 2011-11-29        kinaba: 				assert( h == front[k] );
982758e5e4 2011-11-29        kinaba: 				int len1 = 0, len2 = 0;
982758e5e4 2011-11-29        kinaba: 				while( i!=left.size() && left[i]==h )
982758e5e4 2011-11-29        kinaba: 					++i, ++len1;
982758e5e4 2011-11-29        kinaba: 				while( k!=front.size() && front[k]==h )
982758e5e4 2011-11-29        kinaba: 					++k, ++len2;
982758e5e4 2011-11-29        kinaba: 				ans *= choose2(h, len1, len2);
982758e5e4 2011-11-29        kinaba: 			}
982758e5e4 2011-11-29        kinaba: 		}
982758e5e4 2011-11-29        kinaba: 		return ans.val;
982758e5e4 2011-11-29        kinaba: 	}
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: 	mint perm(const vector<int>& x)
982758e5e4 2011-11-29        kinaba: 	{
982758e5e4 2011-11-29        kinaba: 		map<int,int> cat;
982758e5e4 2011-11-29        kinaba: 		for(int i=0; i<x.size(); ++i)
982758e5e4 2011-11-29        kinaba: 			cat[x[i]]++;
982758e5e4 2011-11-29        kinaba: 		mint r = FAC(x.size());
982758e5e4 2011-11-29        kinaba: 		for(map<int,int>::iterator it=cat.begin(); it!=cat.end(); ++it)
982758e5e4 2011-11-29        kinaba: 			r /= FAC(it->second);
982758e5e4 2011-11-29        kinaba: 		return r;
982758e5e4 2011-11-29        kinaba: 	}
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: 	mint choose(int h, int n)
982758e5e4 2011-11-29        kinaba: 	{
982758e5e4 2011-11-29        kinaba: 		mint r = 0;
982758e5e4 2011-11-29        kinaba: 		for(int k=1; k<=n; ++k)
982758e5e4 2011-11-29        kinaba: 			r += C(n, k) * POW(h, n-k);
982758e5e4 2011-11-29        kinaba: 		return r;
982758e5e4 2011-11-29        kinaba: 	}
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: 	mint choose2(int h, int n1, int n2)
982758e5e4 2011-11-29        kinaba: 	{
982758e5e4 2011-11-29        kinaba: 		return POW(2, n1+n2) + h * choose(h,n1) * choose(h,n2);
982758e5e4 2011-11-29        kinaba: 	}
982758e5e4 2011-11-29        kinaba: };
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: // BEGIN CUT HERE
982758e5e4 2011-11-29        kinaba: #include <ctime>
982758e5e4 2011-11-29        kinaba: double start_time; string timer()
982758e5e4 2011-11-29        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
982758e5e4 2011-11-29        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
982758e5e4 2011-11-29        kinaba:  { os << "{ ";
982758e5e4 2011-11-29        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
982758e5e4 2011-11-29        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
982758e5e4 2011-11-29        kinaba: void verify_case(const int& Expected, const int& Received) {
982758e5e4 2011-11-29        kinaba:  bool ok = (Expected == Received);
982758e5e4 2011-11-29        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
982758e5e4 2011-11-29        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
982758e5e4 2011-11-29        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
982758e5e4 2011-11-29        kinaba: #define END	 verify_case(_, AxonometricProjection().howManyWays(heightsOfLeftView, heightsOfFrontView));}
982758e5e4 2011-11-29        kinaba: int main(){
982758e5e4 2011-11-29        kinaba: 
982758e5e4 2011-11-29        kinaba: CASE(0)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = {1,1};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = {1,1};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = 7;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: CASE(1)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = {50,50,50,50,524};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = {524,524};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = 104060401;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: CASE(2)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = {1,2,3,4,5,6,7,8,9,10};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = {1,2,3,4,5,6,7,8,9,10,11};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = 0;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: CASE(3)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = {5,2,4,1};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = {5,2,4,0,1};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = 429287;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: CASE(4)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = {5,2,4,52,24,524};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = {0,4,20,24,500,504,520,524};
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = 97065655;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: /*
982758e5e4 2011-11-29        kinaba: CASE(5)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = ;
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = ;
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = ;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: CASE(6)
982758e5e4 2011-11-29        kinaba: 	int heightsOfLeftView_[] = ;
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfLeftView(heightsOfLeftView_, heightsOfLeftView_+sizeof(heightsOfLeftView_)/sizeof(*heightsOfLeftView_));
982758e5e4 2011-11-29        kinaba: 	int heightsOfFrontView_[] = ;
982758e5e4 2011-11-29        kinaba: 	  vector <int> heightsOfFrontView(heightsOfFrontView_, heightsOfFrontView_+sizeof(heightsOfFrontView_)/sizeof(*heightsOfFrontView_));
982758e5e4 2011-11-29        kinaba: 	int _ = ;
982758e5e4 2011-11-29        kinaba: END
982758e5e4 2011-11-29        kinaba: */
982758e5e4 2011-11-29        kinaba: }
982758e5e4 2011-11-29        kinaba: // END CUT HERE