#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>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<double> CMP;

int bitcnt(int x)
{
	int c = 0;
	for(; x; x>>=1)
		c += x&1;
	return c;
}

class TravellingPurchasingMan { public:
	static const int INF = 0x3fffffff;
	struct Store {
		int open;
		int close;
		int shopping;
	};

	int maxStores(int N, vector <string> interestingStores, vector <string> roads)
	{
		vector< vector<int> > d(N, vector<int>(N, INF));
		for(int i=0; i<N; ++i)
			d[i][i] = 0;
		for(int i=0; i<roads.size(); ++i)
		{
			stringstream sin(roads[i]);
			int a, b, len;
			sin >> a >> b >> len;
			d[a][b] = d[b][a] = len;
		}
		for(int k=0; k<N; ++k)
		for(int i=0; i<N; ++i)
		for(int j=0; j<N; ++j)
			d[i][j] = min(d[i][j], d[i][k]+d[k][j]);

		const int M = interestingStores.size();
		vector<Store> s;
		for(int i=0; i<interestingStores.size(); ++i)
		{
			stringstream sin(interestingStores[i]);
			int op,cl,du;
			sin >> op >> cl >> du;
			Store st = {op,cl+1,du}; // [,)
			s.push_back(st);
		}

		vector< pair<int,int> > pop_mask;
		for(int mask=0; mask<(1<<M); ++mask)
			pop_mask.push_back(make_pair(bitcnt(mask), mask));
		sort(pop_mask.begin(), pop_mask.end());

		vector< vector<int> > tbl(M, vector<int>(1<<M, INF));
		for(int u=0; u<M; ++u) {
			int t=0, v=N-1, mask=0;
			int ta = t + d[v][u];
			int to = max(ta, s[u].open);
			if(to < s[u].close) {
				int td = to + s[u].shopping;
				tbl[u][mask|(1<<u)] = min(tbl[u][mask|(1<<u)], td); 
			}
		}

		int best = 0;
		for(int i=0; i<pop_mask.size(); ++i) {
			int mask = pop_mask[i].second;
			for(int v=0; v<M; ++v) if((mask&(1<<v)) && tbl[v][mask]!=INF)
			{
				best = pop_mask[i].first;
				int t = tbl[v][mask];
				for(int u=0; u<M; ++u) if(!(mask&(1<<u))) {
					int ta = t + d[v][u];
					int to = max(ta, s[u].open);
					if(to < s[u].close) {
						int td = to + s[u].shopping;
						tbl[u][mask|(1<<u)] = min(tbl[u][mask|(1<<u)], td); 
					}
				}
			}
		}
		return best;
	}
};

// 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(_, TravellingPurchasingMan().maxStores(N, interestingStores, roads));}
int main(){

CASE(0)
	int N = 3; 
	string interestingStores_[] = {"1 10 10" , "1 55 31", "10 50 100" };
	  vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_)); 
	string roads_[] = {"1 2 10"};
	  vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	int _ = 1; 
END
CASE(1)
	int N = 3; 
	string interestingStores_[] = {"1 10 10" , "1 55 30", "10 50 100" };
	  vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_)); 
	string roads_[] = {"1 2 10"};
	  vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	int _ = 2; 
END
CASE(2)
	int N = 5; 
	string interestingStores_[] = {"0 1000 17"};
	  vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_)); 
	string roads_[] = {"2 3 400", "4 1 500", "4 3 300", "1 0 700", "0 2 400"};
	  vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	int _ = 0; 
END
CASE(3)
// if no wf is done.
	int N = 3; 
	string interestingStores_[] = {"0 100 1"};
	  vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_)); 
    string roads_[] = {"0 1 10", "1 2 10"};
	  vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	int _ = 1; 
END
/*
CASE(4)
	int N = ; 
	string interestingStores_[] = ;
	  vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_)); 
	string roads_[] = ;
	  vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	int _ = ; 
END
*/
}
// END CUT HERE
