#include <bits/stdc++.h>
using namespace std;
using ll = long long;
static const int MAXN = 100000 + 5;
vector<pair<int,ll>> adj[MAXN];
ll odS[MAXN];
bool visited[MAXN], onSP[MAXN];
void dijkstra_from_T(int T) {
fill(odS, odS+MAXN, LLONG_MAX);
memset(visited, 0, sizeof(visited));
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
odS[T] = 0;
pq.push({0, T});
while (!pq.empty()) {
auto [d, v] = pq.top(); pq.pop();
if (visited[v]) continue;
visited[v] = true;
for (auto [u, w] : adj[v]) {
if (odS[u] > d + w) {
odS[u] = d + w;
pq.push({odS[u], u});
}
}
}
}
void dfs_mark_SP(int v, int T) {
// we assume onSP[v] is already set true by the caller
if (v == T) return;
for (auto [u, w] : adj[v]) {
if (!onSP[u] && odS[v] - w == odS[u]) {
onSP[u] = true;
dfs_mark_SP(u, T);
}
}
}
ll minMoney(int start, int goal) {
memset(visited, 0, sizeof(visited));
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
pq.push({0, start});
while (!pq.empty()) {
auto [cost, v] = pq.top(); pq.pop();
if (visited[v]) continue;
visited[v] = true;
if (v == goal) return cost;
for (auto [u, w] : adj[v]) {
ll extra = (onSP[v] && onSP[u]) ? 0 : w;
pq.push({cost + extra, u});
}
}
return -1; // unreachable
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, S, T, pocetok, kraj;
cin >> n >> m >> S >> T >> pocetok >> kraj;
for (int i = 1; i <= n; i++) {
adj[i].clear();
onSP[i] = false;
}
for (int i = 0; i < m; i++) {
int a, b; ll c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
// 1) get distances *to* T
dijkstra_from_T(T);
// 2) mark all nodes on *some* S→T shortest path
onSP[S] = true;
dfs_mark_SP(S, T);
// 3) find min “extra‐money” from pocetok to kraj
cout << minMoney(pocetok, kraj) << "\n";
return 0;
}
