f6f3e6962a 2011-04-09        kinaba: #include <iostream>
f6f3e6962a 2011-04-09        kinaba: #include <sstream>
f6f3e6962a 2011-04-09        kinaba: #include <iomanip>
f6f3e6962a 2011-04-09        kinaba: #include <vector>
f6f3e6962a 2011-04-09        kinaba: #include <string>
f6f3e6962a 2011-04-09        kinaba: #include <map>
f6f3e6962a 2011-04-09        kinaba: #include <set>
f6f3e6962a 2011-04-09        kinaba: #include <algorithm>
f6f3e6962a 2011-04-09        kinaba: #include <numeric>
f6f3e6962a 2011-04-09        kinaba: #include <iterator>
f6f3e6962a 2011-04-09        kinaba: #include <functional>
f6f3e6962a 2011-04-09        kinaba: #include <complex>
f6f3e6962a 2011-04-09        kinaba: #include <queue>
f6f3e6962a 2011-04-09        kinaba: #include <stack>
f6f3e6962a 2011-04-09        kinaba: #include <cmath>
f6f3e6962a 2011-04-09        kinaba: #include <cassert>
f6f3e6962a 2011-04-09        kinaba: #include <cstring>
f6f3e6962a 2011-04-09        kinaba: using namespace std;
f6f3e6962a 2011-04-09        kinaba: typedef long long LL;
f6f3e6962a 2011-04-09        kinaba: typedef complex<double> CMP;
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: template<typename T>
f6f3e6962a 2011-04-09        kinaba: struct DP4
f6f3e6962a 2011-04-09        kinaba: {
f6f3e6962a 2011-04-09        kinaba: 	int N1, N2, N3, N4;
f6f3e6962a 2011-04-09        kinaba: 	vector<T> data;
f6f3e6962a 2011-04-09        kinaba: 	DP4(int N1, int N2, int N3, int N4, const T& t = T())
f6f3e6962a 2011-04-09        kinaba: 		: N1(N1), N2(N2), N3(N3), N4(N4), data(N1*N2*N3*N4, t) { assert(data.size()*sizeof(T)<(1<<26)); }
f6f3e6962a 2011-04-09        kinaba: 	T& operator()(int i1, int i2, int i3, int i4)
f6f3e6962a 2011-04-09        kinaba: 		{ return data[ (((i1*N2)+i2)*N3+i3)*N4+i4 ]; }
f6f3e6962a 2011-04-09        kinaba: };
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: static const int MODVAL = 1000000007;
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: class FoxAverageSequence { public:
f6f3e6962a 2011-04-09        kinaba: 	int theCount(vector <int> seq)
f6f3e6962a 2011-04-09        kinaba: 	{
f6f3e6962a 2011-04-09        kinaba: 		const int N = seq.size();
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: 		DP4<LL> dp(N,2,41,40*N+1);
f6f3e6962a 2011-04-09        kinaba: 		for(int b=0; b<=40; ++b)
f6f3e6962a 2011-04-09        kinaba: 			if( seq[0]==-1 || seq[0]==b )
f6f3e6962a 2011-04-09        kinaba: 				dp(0,0,b,b) += 1;
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: 		for(int i=1; i<N; ++i)
f6f3e6962a 2011-04-09        kinaba: 			for(int dn=0; dn<=1; ++dn)
f6f3e6962a 2011-04-09        kinaba: 			for(int  b=0;  b<=40; ++b)
f6f3e6962a 2011-04-09        kinaba: 			for(int  s=0;  s<=40*i; ++s)
f6f3e6962a 2011-04-09        kinaba: 			if( LL v = dp(i-1,dn,b,s) )
f6f3e6962a 2011-04-09        kinaba: 				for(int c=0; c<=min(40,s/i); ++c)
f6f3e6962a 2011-04-09        kinaba: 					if( seq[i]==-1 || seq[i]==c )
f6f3e6962a 2011-04-09        kinaba: 						if( !dn || b<=c )
f6f3e6962a 2011-04-09        kinaba: 							(dp(i,b>c,c,s+c) += v) %= MODVAL;
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: 		LL ans = 0;
f6f3e6962a 2011-04-09        kinaba: 		for(int dn=0; dn<=1; ++dn)
f6f3e6962a 2011-04-09        kinaba: 		for(int  b=0;  b<=40; ++b)
f6f3e6962a 2011-04-09        kinaba: 		for(int  s=0;  s<=40*N; ++s)
f6f3e6962a 2011-04-09        kinaba: 			ans += dp(N-1,dn,b,s);
f6f3e6962a 2011-04-09        kinaba: 		return ans % MODVAL;
f6f3e6962a 2011-04-09        kinaba: 	}
f6f3e6962a 2011-04-09        kinaba: };
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: // BEGIN CUT HERE
f6f3e6962a 2011-04-09        kinaba: #include <ctime>
f6f3e6962a 2011-04-09        kinaba: double start_time; string timer()
f6f3e6962a 2011-04-09        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
f6f3e6962a 2011-04-09        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
f6f3e6962a 2011-04-09        kinaba:  { os << "{ ";
f6f3e6962a 2011-04-09        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
f6f3e6962a 2011-04-09        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
f6f3e6962a 2011-04-09        kinaba: void verify_case(const int& Expected, const int& Received) {
f6f3e6962a 2011-04-09        kinaba:  bool ok = (Expected == Received);
f6f3e6962a 2011-04-09        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
f6f3e6962a 2011-04-09        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
f6f3e6962a 2011-04-09        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
f6f3e6962a 2011-04-09        kinaba: #define END	 verify_case(_, FoxAverageSequence().theCount(seq));}
f6f3e6962a 2011-04-09        kinaba: int main(){
f6f3e6962a 2011-04-09        kinaba: 
f6f3e6962a 2011-04-09        kinaba: CASE(0)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {3, -1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 4;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(1)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {5, 3, -1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 2;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(2)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {-1, 0, 40};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 0;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(3)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {-1, 40, -1, -1, -1, 10, -1, -1, -1, 21, -1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 579347890;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(4)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {-1, 12, 25, 0, 18, -1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 58;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(5)
f6f3e6962a 2011-04-09        kinaba: int seq_[] = {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = -1;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(6)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {-1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 41;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(7)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {-1,-1};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = (41+1)*41/2;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: CASE(8)
f6f3e6962a 2011-04-09        kinaba: 	int seq_[] = {-1,-1,0};
f6f3e6962a 2011-04-09        kinaba: 	  vector <int> seq(seq_, seq_+sizeof(seq_)/sizeof(*seq_));
f6f3e6962a 2011-04-09        kinaba: 	int _ = 81;
f6f3e6962a 2011-04-09        kinaba: END
f6f3e6962a 2011-04-09        kinaba: }
f6f3e6962a 2011-04-09        kinaba: // END CUT HERE