#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 5;
int numNode, numEdge, sour, fin, bonusLen;
long long targetLen;
vector <array <int, 2>> G[N];
int maxWei = 0;
void init(){
cin >> numNode >> numEdge >> sour >> fin >> bonusLen >> targetLen;
for(int i = 1; i <= numEdge; i++){
int u, v, w; cin >> u >> v >> w;
G[u].push_back({v, w}); G[v].push_back({u, w});
maxWei = max(w, maxWei);
}
maxWei = max(maxWei, bonusLen);
maxWei *= 2;
}
namespace sub1{
long long dist1[N], dist2[N];
void dijk(int sour, long long dist[]){
#define bg array <long long, 2>
priority_queue <bg, vector <bg>, greater <bg>> pq;
for(int i = 1; i <= numNode; i++){
dist[i] = 1e18;
}
pq.push({dist[sour] = 0, sour});
while(!pq.empty()){
long long cost = pq.top()[0];
int u = pq.top()[1];
pq.pop();
if(cost > dist[u]) continue;
for(const array <int, 2> it : G[u]){
int v = it[0], w = it[1];
if(dist[v] > cost + w){
dist[v] = cost + w;
pq.push({dist[v], v});
}
}
}
}
void solve(){
dijk(sour, dist1); dijk(fin, dist2);
bool check = dist1[fin] <= targetLen;
if(check){
cout << 1LL * numNode * (numNode - 1) / 2;
return;
}
int ans = 0;
for(int u = 1; u <= numNode; u++){
for(int v = u + 1; v <= numNode; v++){
if(dist1[u] + bonusLen + dist2[v] <= targetLen){
ans++;
}
if(dist1[v] + bonusLen + dist2[u] <= targetLen){
ans++;
}
}
}
cout << ans;
}
}
namespace sub2{
long long dist1[N], dist2[N];
void dijk(int sour, long long dist[]){
#define bg array <long long, 2>
priority_queue <bg, vector <bg>, greater <bg>> pq;
for(int i = 1; i <= numNode; i++){
dist[i] = 1e18;
}
pq.push({dist[sour] = 0, sour});
while(!pq.empty()){
long long cost = pq.top()[0];
int u = pq.top()[1];
pq.pop();
if(cost > dist[u]) continue;
for(const array <int, 2> it : G[u]){
int v = it[0], w = it[1];
if(dist[v] > cost + w){
dist[v] = cost + w;
pq.push({dist[v], v});
}
}
}
}
struct FenwickTree{
int bit[N];
void up(int u, int val){
for(int i = u; i <= 2 * numNode + 3; i+= i&-i) bit[i]+= val;
}
int get(int u){
int sum = 0;
for(int i = u; i; i-= i&-i) sum+= bit[i];
return sum;
}
} fwt;
void solve(){
dijk(sour, dist1); dijk(fin, dist2);
if(dist1[fin] <= targetLen){
cout << 1LL * numNode * (numNode - 1) / 2;
return;
}
targetLen-= bonusLen;
vector <long long> values;
values.push_back(targetLen);
for(int i = 1; i <= numNode; i++){
values.push_back(dist2[i]);
values.push_back(targetLen - dist1[i]);
}
sort(values.begin(), values.end());
values.resize(unique(values.begin(), values.end()) - values.begin());
map <long long, int> pos;
for(int i = 0; i < (int)values.size(); i++) pos[values[i]] = i + 1;
vector <int> sorted;
for(int i = 1; i <= numNode; i++) sorted.push_back(i);
sort(sorted.begin(), sorted.end(), [&](int u, int v){
if(dist1[u] == dist1[v]) return dist2[u] < dist2[v];
else return dist1[u] > dist1[v];
});
long long ans = 0;
for(auto x : sorted){
ans+= fwt.get(pos[targetLen - dist1[x]]);
fwt.up(pos[dist2[x]], 1);
}
cout << ans;
}
}
void process(){
return sub2::solve();
}
signed main(){
ios_base::sync_with_stdio(false); cin.tie(nullptr);
#define taskname "kieuoanh"
if(fopen(taskname".inp", "r")){
freopen(taskname".inp", "r", stdin);
freopen(taskname".out", "w", stdout);
}
init();
process();
return 0;
}
