#include<bits/stdc++.h>
#define int long long
using namespace std;
#define all(x) x.begin(), x.end()
const int maxiN = 2e5;
struct edge{
int voisin;
int weight;
};
struct node{
int id;
int weight;
};
bool operator<(node const&a, node const&b){
return a.weight > b. weight;
}
vector<edge> links[maxiN];
int n;
const int MAX_W = 1e18;
vector<int> djistra(int source){
vector<int> re(n, MAX_W);
priority_queue<node> pq;
pq.push({source, 0});
while(!pq.empty()){
auto act = pq.top();
pq.pop();
if(re[act.id] != MAX_W)continue;
re[act.id] = act.weight;
for(auto e:links[act.id])
pq.push({e.voisin, e.weight+act.weight});
}
return re;
}
void dbg(vector<int> v){
for(int &i:v){
cout << i << ' ' ;
}
cout<<endl;
}
signed main(){
ios::sync_with_stdio(false);cin.tie(0);
int m;
cin>>n>>m;
int D,F,len,limit;
cin>>D>>F>>len>>limit;
D--;
F--;
for(int i = 0 ; i< m ; i++){
int a,b,w;
cin>>a>>b>>w;
a--;b--;
links[a].push_back({b, w});
links[b].push_back({a, w});
}
vector<int> dD = djistra(D);
vector<int> dF = djistra(F);
vector<pair<int,int>> distId;
for(int i = 0 ; i < n ; i++){
distId.push_back({dF[i], i});
}
int ans2 = 0;
for(int i = 0 ; i< n ; i++){
for(int j = 0;j<n;j++){
if(i!=j)
if(dD[i]+len+dF[j]<=limit){
ans2++;}
}
}
if(dD[F] <= limit){
cout << 1LL*n*(n-1)/2<<endl;
return 0;
}
sort(distId.begin(), distId.end());
int ans = 0;
for(int i = 0 ; i < n ; i++){
auto it = upper_bound(all(distId),make_pair(limit-len-dD[i],MAX_W));
ans += (int)(it-distId.begin());
}
cout << ans << endl;
}
