#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pli = pair<ll, int>;
const ll inf = 1e18;
const int N = 100100;
int n, m, S, T, U, V;
vector<pli> adj[N];
ll ans;
bool vis[N];
ll distU[N];
ll distV[N];
ll dist[N];
ll dpU[N];
ll dpV[N];
void dijkstra(int source, ll dist[N]) {
priority_queue<pli, vector<pli>, greater<pli>> pq;
for (int i = 1; i <= n; ++i) {
dist[i] = inf;
vis[i] = false;
}
dist[source] = 0;
pq.emplace(0, source);
while (!pq.empty()) {
int a = pq.top().second;
pq.pop();
if (vis[a]) continue;
vis[a] = true;
for (pli to : adj[a]) {
ll alt = dist[a] + to.first;
int b = to.second;
if (alt < dist[b]) {
dist[b] = alt;
pq.emplace(alt, b);
}
}
}
}
void dijkstra2() {
priority_queue<pli, vector<pli>, greater<pli>> pq;
for (int i = 1; i <= n; ++i) {
dist[i] = inf;
vis[i] = false;
}
dist[S] = 0;
dpU[S] = distU[S];
dpV[S] = distV[S];
pq.emplace(0, S);
while (!pq.empty()) {
int a = pq.top().second;
pq.pop();
if (vis[a]) continue;
vis[a] = true;
for (pli to : adj[a]) {
ll alt = dist[a] + to.first;
int b = to.second;
if (alt < dist[b]) {
dist[b] = alt;
dpU[b] = min(distU[b], dpU[a]);
dpV[b] = min(distV[b], dpV[a]);
pq.emplace(alt, b);
} else if (alt == dist[b]) {
ll potU = min(distU[b], dpU[a]);
ll potV = min(distV[b], dpV[a]);
if (potU + potV <= dpU[b] + dpV[b]) {
dpU[b] = potU;
dpV[b] = potV;
}
}
}
}
ans = min(ans, dpU[T] + dpV[T]);
}
int main() {
cin.tie(0)->sync_with_stdio(false);
// #ifndef _DEBUG
// freopen("piepie.in", "r", stdin);
// freopen("piepie.out", "w", stdout);
// #endif
cin >> n >> m >> S >> T >> U >> V;
for (int i = 0; i < m; ++i) {
int a, b, w;
cin >> a >> b >> w;
adj[a].emplace_back(w, b);
adj[b].emplace_back(w, a);
}
dijkstra(U, distU);
dijkstra(V, distV);
ans = distV[U];
for (int i = 0; i < 2; ++i) {
dijkstra2();
swap(S, T);
}
cout << ans << '\n';
}
