#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e18;
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
vector<vector<pair<int, long long>>> adj(n);
for (int i = 0; i < m; i++){
int a, b;
long long c;
cin >> a >> b >> c;
a--; b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
auto dijkstra1 = [&](int start) -> vector<long long> {
vector<long long> dist(n, INF);
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
dist[start] = 0;
pq.push({0, start});
while (!pq.empty()) {
long long d = pq.top().first;
int curr = pq.top().second;
pq.pop();
if (d != dist[curr]) continue;
for (auto [next, cost] : adj[curr]) {
if (dist[next] > d + cost) {
dist[next] = d + cost;
pq.push({dist[next], next});
}
}
}
return dist;
};
vector<long long> du = dijkstra1(u);
vector<long long> dv = dijkstra1(v);
auto dijkstra2 = [&](int start, int end) -> long long {
vector<long long> dist(n, INF);
vector<long long> dp0(n, INF), dp1(n, INF);
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
dist[start] = 0;
dp0[start] = du[start];
dp1[start] = dv[start];
pq.push({0, start});
while (!pq.empty()) {
long long d = pq.top().first;
int curr = pq.top().second;
pq.pop();
if (d > dist[curr]) continue;
for (auto [next, cost] : adj[curr]) {
long long new_d = d + cost;
if (new_d < dist[next]) {
dist[next] = new_d;
dp0[next] = min(du[next], dp0[curr]);
dp1[next] = min(dv[next], dp1[curr]);
pq.push({new_d, next});
} else if (new_d == dist[next]) {
long long cand0 = min(du[next], dp0[curr]);
long long cand1 = min(dv[next], dp1[curr]);
if (cand0 + cand1 < dp0[next] + dp1[next]) {
dp0[next] = cand0;
dp1[next] = cand1;
pq.push({new_d, next});
}
}
}
}
return dp0[end] + dp1[end];
};
long long ans = du[v];
ans = min(ans, dijkstra2(s, t));
ans = min(ans, dijkstra2(t, s));
cout << ans << endl;
return 0;
}
