#include <bits/stdc++.h>
using namespace std;
using ll = long long;
void IO(string name = "") {
cin.tie(0)->sync_with_stdio(0);
if (name.size()) {
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
}
}
const int maxN = 1e5;
const ll inf = 2e18;
int N, M, S, T, U, V;
vector<pair<int, int>> adj[maxN];
ll distU[maxN], distV[maxN], distS[maxN], distT[maxN];
void dijkstra(int s, ll dist[maxN]) {
fill(dist, dist+N, inf);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
dist[s] = 0;
pq.push({0, s});
while(pq.size()) {
auto [d, u] = pq.top(); pq.pop();
if(d>dist[u]) continue;
for(auto [v, w] : adj[u]) {
if(dist[u]+w<dist[v]) {
dist[v] = dist[u]+w;
pq.push({dist[v], v});
}
}
}
}
bool visited[maxN];
ll dpU[maxN], dpV[maxN];
void dfs(int u) {
visited[u] = 1;
for(auto [v, w] : adj[u]) {
if(distS[u]+w+distT[v]!=distS[T]) continue;
if(!visited[v]) dfs(v);
if(min(distU[u], dpU[v])+min(distV[u], dpV[v]) < dpU[u]+dpV[u]) {
dpU[u] = min(distU[u], dpU[v]);
dpV[u] = min(distV[u], dpV[v]);
}
}
}
int main() {
// IO("wormsort");
cin >> N >> M >> S >> T >> U >> V;
S--; T--; U--; V--;
for(int i = 0, u, v, w; i < M; i++) {
cin >> u >> v >> w;
u--; v--;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijkstra(U, distU);
dijkstra(V, distV);
dijkstra(S, distS);
dijkstra(T, distT);
fill(dpU, dpU+N, inf);
fill(dpV, dpV+N, inf);
dpU[T] = distU[T];
dpV[T] = distV[T];
dfs(S);
cout << min(dpU[S]+dpV[S], distU[V]) << "\n";
}
