#include <iostream>
#include <vector>
#include <queue>
using namespace std;
typedef long long ll;
typedef pair<ll, int> pli;
const ll INF = 1e18;
int main() {
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t;
cin >> u >> v;
vector<vector<pair<int, ll>>> graph(n + 1);
for (int i = 0; i < m; i++) {
int a, b;
ll c;
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
// Compute shortest paths
auto dijkstra = [&](int start, vector<ll>& dist) {
dist.assign(n + 1, INF);
dist[start] = 0;
priority_queue<pli, vector<pli>, greater<pli>> pq;
pq.push({0, start});
while (!pq.empty()) {
auto [d, node] = pq.top(); pq.pop();
if (d > dist[node]) continue;
for (auto [next, cost] : graph[node]) {
if (dist[node] + cost < dist[next]) {
dist[next] = dist[node] + cost;
pq.push({dist[next], next});
}
}
}
};
vector<ll> dist_s(n + 1), dist_t(n + 1), dist_u(n + 1), dist_v(n + 1);
dijkstra(s, dist_s);
dijkstra(t, dist_t);
dijkstra(u, dist_u);
dijkstra(v, dist_v);
ll answer = dist_u[v]; // Direct cost without commuter pass
// For each pair of nodes, consider them as part of the commuter pass route
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
// Skip if unreachable
if (dist_s[i] == INF || dist_t[j] == INF) continue;
// Cost of commuter pass S→i→j→T
ll pass_cost = dist_s[i] + dist_t[j];
// Cost from U to V when going through i and j
// (assuming those edges are covered by the pass)
if (dist_u[i] != INF && dist_v[j] != INF) {
answer = min(answer, dist_u[i] + dist_v[j]);
}
// Also consider the reverse direction
if (dist_u[j] != INF && dist_v[i] != INF) {
answer = min(answer, dist_u[j] + dist_v[i]);
}
}
}
cout << answer << endl;
return 0;
}
