197afdc1d0 2015-03-26        kinaba: #include <iostream>
197afdc1d0 2015-03-26        kinaba: #include <sstream>
197afdc1d0 2015-03-26        kinaba: #include <iomanip>
197afdc1d0 2015-03-26        kinaba: #include <vector>
197afdc1d0 2015-03-26        kinaba: #include <string>
197afdc1d0 2015-03-26        kinaba: #include <map>
197afdc1d0 2015-03-26        kinaba: #include <set>
197afdc1d0 2015-03-26        kinaba: #include <algorithm>
197afdc1d0 2015-03-26        kinaba: #include <numeric>
197afdc1d0 2015-03-26        kinaba: #include <iterator>
197afdc1d0 2015-03-26        kinaba: #include <functional>
197afdc1d0 2015-03-26        kinaba: #include <complex>
197afdc1d0 2015-03-26        kinaba: #include <queue>
197afdc1d0 2015-03-26        kinaba: #include <stack>
197afdc1d0 2015-03-26        kinaba: #include <cmath>
197afdc1d0 2015-03-26        kinaba: #include <cassert>
197afdc1d0 2015-03-26        kinaba: #include <tuple>
197afdc1d0 2015-03-26        kinaba: using namespace std;
197afdc1d0 2015-03-26        kinaba: typedef long long LL;
197afdc1d0 2015-03-26        kinaba: typedef complex<double> CMP;
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: static const unsigned MODVAL = 1000000007;
197afdc1d0 2015-03-26        kinaba: struct mint
197afdc1d0 2015-03-26        kinaba: {
197afdc1d0 2015-03-26        kinaba: 	unsigned val;
197afdc1d0 2015-03-26        kinaba: 	mint():val(0){}
197afdc1d0 2015-03-26        kinaba: 	mint(int      x):val(x%MODVAL) {}
197afdc1d0 2015-03-26        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
197afdc1d0 2015-03-26        kinaba: 	mint(LL       x):val(x%MODVAL) {}
197afdc1d0 2015-03-26        kinaba: };
197afdc1d0 2015-03-26        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
197afdc1d0 2015-03-26        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
197afdc1d0 2015-03-26        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
197afdc1d0 2015-03-26        kinaba: mint operator+(mint x, mint y) { return x+=y; }
197afdc1d0 2015-03-26        kinaba: mint operator-(mint x, mint y) { return x-=y; }
197afdc1d0 2015-03-26        kinaba: mint operator*(mint x, mint y) { return x*=y; }
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: // nCk :: O(1) time, O(n^2) space.
197afdc1d0 2015-03-26        kinaba: vector< vector<mint> > CP_;
197afdc1d0 2015-03-26        kinaba: mint C(int n, int k) {
197afdc1d0 2015-03-26        kinaba: 	while( CP_.size() <= n ) {
197afdc1d0 2015-03-26        kinaba: 		int nn = CP_.size();
197afdc1d0 2015-03-26        kinaba: 		CP_.push_back(vector<mint>(nn+1,1));
197afdc1d0 2015-03-26        kinaba: 		for(int kk=1; kk<nn; ++kk)
197afdc1d0 2015-03-26        kinaba: 			CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
197afdc1d0 2015-03-26        kinaba: 	}
197afdc1d0 2015-03-26        kinaba: 	return k<0 || n<k ? 0 : CP_[n][k];
197afdc1d0 2015-03-26        kinaba: }
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: typedef tuple<int,int,int> Vec;
197afdc1d0 2015-03-26        kinaba: inline int operator*(Vec v, Vec u) {
197afdc1d0 2015-03-26        kinaba: 	return get<0>(v)*get<0>(u) + get<1>(v)*get<1>(u) + get<2>(v)*get<2>(u);
197afdc1d0 2015-03-26        kinaba: }
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: class RockPaperScissorsMagic { public:
197afdc1d0 2015-03-26        kinaba: 	int count(int W, int L, int T, vector <int> card)
197afdc1d0 2015-03-26        kinaba: 	{
197afdc1d0 2015-03-26        kinaba: 		const int N0 = std::count(card.begin(), card.end(), 0);
197afdc1d0 2015-03-26        kinaba: 		const int N1 = std::count(card.begin(), card.end(), 1);
197afdc1d0 2015-03-26        kinaba: 		const int N2 = std::count(card.begin(), card.end(), 2);
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: 		mint ans = 0;
197afdc1d0 2015-03-26        kinaba: 		for(int x1=0; x1<=N0; ++x1)
197afdc1d0 2015-03-26        kinaba: 		for(int x2=0; x1+x2<=N0; ++x2)
197afdc1d0 2015-03-26        kinaba: 		for(int y1=0; y1<=N1; ++y1)
197afdc1d0 2015-03-26        kinaba: 		for(int y2=0; y1+y2<=N1; ++y2)
197afdc1d0 2015-03-26        kinaba: 		for(int z1=0; z1<=N2; ++z1)
197afdc1d0 2015-03-26        kinaba: 		for(int z2=0; z1+z2<=N2; ++z2) {
197afdc1d0 2015-03-26        kinaba: 			int x3,y3,z3;
197afdc1d0 2015-03-26        kinaba: 			Vec x(x1, x2, x3=N0-x1-x2);
197afdc1d0 2015-03-26        kinaba: 			Vec y(y1, y2, y3=N1-y1-y2);
197afdc1d0 2015-03-26        kinaba: 			Vec z(z1, z2, z3=N2-z1-z2);
197afdc1d0 2015-03-26        kinaba: 			Vec TLW(T,L,W);
197afdc1d0 2015-03-26        kinaba: 			Vec WTL(W,T,L);
197afdc1d0 2015-03-26        kinaba: 			Vec LTW(L,T,W);
197afdc1d0 2015-03-26        kinaba: 			if(TLW*x+WTL*y != TLW*y+WTL*x) continue;
197afdc1d0 2015-03-26        kinaba: 			if(T!=L && x1-x2!=y1-y2) continue;
197afdc1d0 2015-03-26        kinaba: 			if(W!=L && x1-x3!=y1-y3) continue;
197afdc1d0 2015-03-26        kinaba: 			if(TLW*x+WTL*z != TLW*z+WTL*x) continue;
197afdc1d0 2015-03-26        kinaba: 			if(T!=L && x1-x2!=z1-z2) continue;
197afdc1d0 2015-03-26        kinaba: 			if(W!=L && x1-x3!=z1-z3) continue;
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: 			ans += C(N0, x1) * C(N0-x1, x2)
197afdc1d0 2015-03-26        kinaba: 				* C(N1, y1) * C(N1-y1, y2)
197afdc1d0 2015-03-26        kinaba: 				* C(N2, z1) * C(N2-z1, z2);
197afdc1d0 2015-03-26        kinaba: 		}
197afdc1d0 2015-03-26        kinaba: 		return ans.val;
197afdc1d0 2015-03-26        kinaba: 	}
197afdc1d0 2015-03-26        kinaba: };
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: // BEGIN CUT HERE
197afdc1d0 2015-03-26        kinaba: #include <ctime>
197afdc1d0 2015-03-26        kinaba: double start_time; string timer()
197afdc1d0 2015-03-26        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
197afdc1d0 2015-03-26        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
197afdc1d0 2015-03-26        kinaba:  { os << "{ ";
197afdc1d0 2015-03-26        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
197afdc1d0 2015-03-26        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
197afdc1d0 2015-03-26        kinaba: void verify_case(const int& Expected, const int& Received) {
197afdc1d0 2015-03-26        kinaba:  bool ok = (Expected == Received);
197afdc1d0 2015-03-26        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
197afdc1d0 2015-03-26        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
197afdc1d0 2015-03-26        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
197afdc1d0 2015-03-26        kinaba: #define END	 verify_case(_, RockPaperScissorsMagic().count(win, lose, tie, card));}
197afdc1d0 2015-03-26        kinaba: int main(){
197afdc1d0 2015-03-26        kinaba: 
197afdc1d0 2015-03-26        kinaba: CASE(0)
197afdc1d0 2015-03-26        kinaba: 	int win = 2;
197afdc1d0 2015-03-26        kinaba: 	int lose = 0;
197afdc1d0 2015-03-26        kinaba: 	int tie = 1;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = {0,1,2};
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = 3;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: CASE(1)
197afdc1d0 2015-03-26        kinaba: 	int win = 2;
197afdc1d0 2015-03-26        kinaba: 	int lose = 0;
197afdc1d0 2015-03-26        kinaba: 	int tie = 1;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = {0,0,0};
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = 6;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: CASE(2)
197afdc1d0 2015-03-26        kinaba: 	int win = 0;
197afdc1d0 2015-03-26        kinaba: 	int lose = 0;
197afdc1d0 2015-03-26        kinaba: 	int tie = 0;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = {1,0,2,2,2,0};
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = 729;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: CASE(3)
197afdc1d0 2015-03-26        kinaba: 	int win = 514;
197afdc1d0 2015-03-26        kinaba: 	int lose = 451;
197afdc1d0 2015-03-26        kinaba: 	int tie = 145;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = {0,0,0,0,0,1,1,1,1,1,1,2,2,2};
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = 0;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: CASE(4)
197afdc1d0 2015-03-26        kinaba: 	int win = 3;
197afdc1d0 2015-03-26        kinaba: 	int lose = 6;
197afdc1d0 2015-03-26        kinaba: 	int tie = 9;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = {0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2};
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = 2336040;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: CASE(5)
197afdc1d0 2015-03-26        kinaba: 	int win = 514;
197afdc1d0 2015-03-26        kinaba: 	int lose = 451;
197afdc1d0 2015-03-26        kinaba: 	int tie = 145;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = {0,0,0,1,1,1,1,1,1,2,2,2,2,2,2};
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = 116100;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: /*
197afdc1d0 2015-03-26        kinaba: CASE(6)
197afdc1d0 2015-03-26        kinaba: 	int win = ;
197afdc1d0 2015-03-26        kinaba: 	int lose = ;
197afdc1d0 2015-03-26        kinaba: 	int tie = ;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = ;
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = ;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: CASE(7)
197afdc1d0 2015-03-26        kinaba: 	int win = ;
197afdc1d0 2015-03-26        kinaba: 	int lose = ;
197afdc1d0 2015-03-26        kinaba: 	int tie = ;
197afdc1d0 2015-03-26        kinaba: 	int card_[] = ;
197afdc1d0 2015-03-26        kinaba: 	  vector <int> card(card_, card_+sizeof(card_)/sizeof(*card_));
197afdc1d0 2015-03-26        kinaba: 	int _ = ;
197afdc1d0 2015-03-26        kinaba: END
197afdc1d0 2015-03-26        kinaba: */
197afdc1d0 2015-03-26        kinaba: }
197afdc1d0 2015-03-26        kinaba: // END CUT HERE