#include <bits/stdc++.h>
#define ll long long
using namespace std;
void dijkstra(ll s, ll n, vector<vector<pair<ll,ll>>>& adj, vector<ll>& dist) {
dist.assign(n, 1e18);
dist[s] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto [d,u] = pq.top();
pq.pop();
if (d>dist[u]) continue;
for (auto [v,w] : adj[u]) {
if (dist[v]>dist[u]+w) {
dist[v] = dist[u]+w;
pq.push({dist[v], v});
}
}
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
ll n,m;
cin >> n >> m;
ll s,t,u1,v1;
cin >> s >> t >> u1 >> v1;
s--; t--; u1--; v1--;
vector<vector<pair<ll,ll>>> adj(n);
for (int i=0; i<m; i++) {
ll u,v,c;
cin >> u >> v >> c;
u--; v--;
adj[u].push_back({v,c});
adj[v].push_back({u,c});
}
vector<ll> dists, distt, distu, distv;
dijkstra(s, n, adj, dists);
dijkstra(t, n, adj, distt);
dijkstra(u1, n, adj, distu);
dijkstra(v1, n, adj, distv);
vector<vector<ll>> adj1(n);
vector<ll> deg(n);
for (int u=0; u<n; u++) {
for (auto [v,w] : adj[u]) {
if (dists[u]+w+distt[v]==dists[t]) {
adj1[u].push_back(v);
deg[v]++;
}
}
}
vector<ll> topo;
queue<ll> q;
for (int i=0; i<n; i++) {
if (deg[i]==0) q.push(i);
}
while(!q.empty()) {
ll u = q.front();
q.pop();
topo.push_back(u);
for (auto v : adj1[u]) {
if (--deg[v]==0) q.push(v);
}
}
vector<ll> dp1 = distu, dp2 = distv;
ll res = distu[v1];
for (auto u : topo) {
for (auto v : adj1[u]) {
dp1[v] = min(dp1[v], dp1[u]);
dp2[v] = min(dp2[v], dp2[u]);
}
}
for (int i=0; i<n; i++) {
if (dists[i]+distt[i]==dists[t]) {
res = min({res, dp1[i]+distv[i], dp2[i]+distu[i]});
}
}
cout << res;
}
