#include <bits/stdc++.h>
#define s second
#define f first
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
vector<vector<P>> adj;
ll ans = 1e18;
void dijkstra(vector<ll> &dist, int node) {
dist[node] = 0;
priority_queue<P, vector<P>, greater<P>> pq;
pq.push({0, node});
while (!pq.empty()) {
P u = pq.top(); pq.pop();
if (u.f != dist[u.s]) continue;
for (P j: adj[u.s]) {
if (dist[u.s]+j.s < dist[j.f]) {
pq.push({dist[j.f] = dist[u.s]+j.s, j.f});
}
}
}
}
void BFS(ll t, ll S, vector<ll> &distU, vector<ll> &distV, vector<ll> &diSt) {
ll sPath = diSt[t];
//cout << "SPATH: " << sPath;
queue<pair<P, P>> pq;
pq.push({{t, sPath}, {distU[t], distV[t]}}); // <node, pathlengthremaining>, <minudist, minvdist>
while (!pq.empty()) {
//cout << "HERE";
pair<P, P> n = pq.front(); pq.pop();
if (n.f.f == S) {
//cout << "HERE: " << n.s.f << " " << n.s.s << "\n";
ans = min(ans, n.s.f + n.s.s); continue;
}
for (P u: adj[n.f.f]) {
if (n.f.s - u.s == diSt[u.f]) {
ll nu = min(n.s.f, distU[u.f]);
ll nv = min(n.s.s, distV[u.f]);
pq.push({{u.f, n.f.s - u.s}, {nu, nv}});
}
}
}
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
ll n,m; cin >> n >> m;
ll S, t; cin >> S >> t;
ll u, v; cin >> u >> v;
adj.resize(n+1);
for (int i = 0; i < m; i++) {
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<ll> diSt(n+1, 1e18);
dijkstra(diSt, S);
vector<ll> distU(n+1, 1e18);
vector<ll> distV(n+1, 1e18);
dijkstra(distU, u);
dijkstra(distV, v);
//cout << distU[t] << " " << distV[t] << '\n';
BFS(t, S, distU, distV, diSt);
cout << min(ans, distU[v]);
}
