#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define fi first
#define se second
vector<vector<pair<ll, ll>>> graf;
void dijkstra(int s, vector<ll>& dist) {
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
dist[s] = 0;
pq.push({0, s});
while (!pq.empty()) {
ll dl = pq.top().first;
ll wi = pq.top().second;
pq.pop();
if (dl > dist[wi]) continue;
dist[wi] = dl;
for (pair<ll, ll> p : graf[wi]) {
ll waga = p.second;
ll i = p.first;
if (dl + waga < dist[i]) {
dist[i] = dl + waga;
pq.push({dist[i], i});
}
}
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
ll n, m, w1, w2, c, s, t, u, v;
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
graf.resize(n + 1);
for (int i = 0; i < m; i++) {
cin >> w1 >> w2 >> c;
graf[w1].push_back({w2, c});
graf[w2].push_back({w1, c});
}
priority_queue<pair<ll, pair<ll, ll>>, vector<pair<ll, pair<ll, ll>>>, greater<pair<ll, pair<ll, ll>>>> pqsolve;
vector<ll> dists(n + 1, 1e18);
vector<ll> distt(n + 1, 1e18);
vector<ll> distu(n + 1, 1e18);
vector<ll> distv(n + 1, 1e18);
dijkstra(s, dists);
dijkstra(t, distt);
dijkstra(u, distu);
dijkstra(v, distv);
ll odl = dists[t];
vector<vector<pair<ll, ll>>> dagst(n + 1), dagts(n + 1);
vector<ll> bilansst(n + 1), bilansts(n + 1, 0), dpst(n + 1, 1e18), dpts(n + 1, 1e18), wdag(n + 1, 1e18);
for (int wi = 1; wi <= n; wi++) {
if (distt[wi] + dists[wi] == odl) {
wdag[wi] = 1;
for (pair<ll, ll> p : graf[wi]) {
ll waga = p.second;
ll i = p.first;
if (dists[i] + distt[wi] + waga == odl) {
dagst[wi].pb({i, waga});
dagts[i].pb({wi, waga});
bilansst[wi]++;
bilansts[i]++;
}
}
}
}
// dp z s do t
queue<int> q;
dpst[s] = distu[s];
q.push(s);
while (!q.empty()) {
int wi = q.front();
q.pop();
dpst[wi] = distu[wi];
for (pair<ll, ll> p : dagst[wi]) {
ll waga = p.second;
ll i = p.first;
dpst[wi] = min(dpst[i], dpst[wi]);
}
for (pair<ll, ll> p : dagts[wi]) {
ll waga = p.second;
ll i = p.first;
bilansst[i]--;
if (bilansst[i] == 0) q.push(i);
}
}
// dp z t do s
dpts[t] = distu[t];
q.push(t);
while (!q.empty()) {
int wi = q.front();
q.pop();
dpts[wi] = distu[wi];
for (pair<ll, ll> p : dagts[wi]) {
ll waga = p.second;
ll i = p.first;
dpts[wi] = min(dpts[i], dpts[wi]);
}
for (pair<ll, ll> p : dagst[wi]) {
ll waga = p.second;
ll i = p.first;
bilansts[i]--;
if (bilansts[i] == 0) q.push(i);
}
}
// wyniki
ll wynik = distu[v];
for (int i = 1; i <= n; i++) {
if (wdag[i] == 1) {
wynik = min(wynik, min(dpst[i], dpts[i]) + distv[i]);
}
}
cout << wynik << endl;
}
