#include <bits/stdc++.h>
#define pb push_back
#define int long long
using namespace std;
const int MAX_N = 1e5;
vector<pair<int, int>> adj[MAX_N];
vector<int> dijkstra(int n, int s) {
vector<int> dist(n, 1e18);
priority_queue<pair<int, int>> pq;
pq.push({0, s});
dist[s] = 0;
while (!pq.empty()) {
int d = -pq.top().first;
int u = pq.top().second;
pq.pop();
if (dist[u] != d) continue;
for (pair<int, int> v: adj[u]) {
if (dist[v.first] > dist[u]+v.second) {
dist[v.first] = dist[u]+v.second;
pq.push({-dist[v.first], v.first});
}
}
}
return dist;
}
vector<pair<int, vector<int>>> dijkstra2(int n, int s) {
vector<pair<int, vector<int>>> dist(n, {1e18, {}});
dist[s] = {0, {s}};
priority_queue<pair<int, int>> pq;
pq.push({0, s});
while (!pq.empty()) {
int d = -pq.top().first;
int u = pq.top().second;
pq.pop();
if (dist[u].first != d) continue;
for (pair<int, int> v: adj[u]) {
if (dist[v.first].first == dist[u].first+v.second) {
dist[v.first].second.push_back(u);
} else if (dist[v.first].first > dist[u].first+v.second) {
dist[v.first] = {dist[u].first+v.second, {u}};
pq.push({-dist[v.first].first, v.first});
}
}
}
return dist;
}
int ans;
vector<int> dist_u, dist_v;
vector<pair<int, vector<int>>> dist;
vector<bool> vis;
vector<int> du, dv;
void calc_camino(int u) {
if (vis[u]) return;
vis[u] = true;
for (int v: dist[u].second) {
calc_camino(v);
int d1 = dist_u[u], d2 = dist_v[u];
d1 = min(du[v], d1);
d2 = min(dv[v], d2);
ans = min(ans, d1+d2);
if (du[u]+dv[u] > d1+d2) {
du[u] = d1;
dv[u] = d2;
}
}
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(NULL);
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
--s; --t; --u; --v;
while (m--) {
int a, b, c;
cin >> a >> b >> c;
--a; --b;
adj[a].pb({b, c});
adj[b].pb({a, c});
}
dist_u = dijkstra(n, u);
dist_v = dijkstra(n, v);
dist = dijkstra2(n, s);
ans = dist_u[v];
vis = vector<bool>(n, false); vis[s] = true;
du = dv = vector<int>(n);
for (int i = 0; i < n; ++i) {
du[i] = dist_u[i];
dv[i] = dist_v[i];
}
calc_camino(t);
cout << ans << endl;
return 0;
}
