#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pli pair<ll, int>
#define fi first
#define se second
ll MAX = 1e18;
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
vector<vector<pli>> g (n+1);
for (int i = 0; i < m; i++) {
int a, b;
ll c;
cin >> a >> b >> c;
g[a].push_back({c, b});
g[b].push_back({c, a});
}
vector<ll> lu(n+1, -1), lv(n+1, -1), ls(n+1, -1);
priority_queue<pli, vector<pli>, greater<pli>> pq;
pq.push({0, u});
while (!pq.empty()) {
pli x = pq.top();
pq.pop();
if (lu[x.se] != -1) continue;
lu[x.se] = x.fi;
for (pli y : g[x.se]) {
if (lu[y.se] == -1) {
pq.push({x.fi+y.fi, y.se});
}
}
}
pq.push({0, v});
while (!pq.empty()) {
pli x = pq.top();
pq.pop();
if (lv[x.se] != -1) continue;
lv[x.se] = x.fi;
for (pli y : g[x.se]) {
if (lv[y.se] == -1) {
pq.push({x.fi+y.fi, y.se});
}
}
}
pq.push({0, s});
while (!pq.empty()) {
pli x = pq.top();
pq.pop();
if (ls[x.se] != -1) continue;
ls[x.se] = x.fi;
for (pli y : g[x.se]) {
if (ls[y.se] == -1) {
pq.push({x.fi+y.fi, y.se});
}
}
}
vector<vector<int>> G (n+1);
vector<int> topo (1, s), k (n+1, 0);
for (int i = 1; i < n+1; i++) {
for (pli j : g[i]) {
if (ls[i]+j.fi == ls[j.se]) G[i].push_back(j.se), k[j.se]++;
}
}
queue<int> q;
q.push(s);
while (!q.empty()) {
int x = q.front(); q.pop();
for (int i : G[x]) {
k[i]--;
if (!k[i]) topo.push_back(i), q.push(i);
}
}
vector<ll> mu(n+1, MAX), mv(n+1, MAX);
mu[s] = lu[s];
mv[s] = lv[s];
vector<ll> score(n+1, MAX);
score[s] = mu[s]+mv[s];
for (int i : topo) {
score[i] = min ({score[i], mu[i]+lv[i], mv[i]+lu[i]});
for (int x : G[i]) {
score[x] = min(score[i], score[x]);
mu[x] = min({mu[x], mu[i], lu[x]});
mv[x] = min({mv[x], mv[i], lv[x]});
}
}
cout << min(score[t], lu[v]) << '\n';
}
