#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = 4e18;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
s--; t--; u--; v--; // 0-indexed
vector<vector<tuple<int,int,ll>>> g(n);
for (int i = 0; i < m; i++) {
int a, b; ll c;
cin >> a >> b >> c;
a--; b--;
g[a].emplace_back(b, i, c);
g[b].emplace_back(a, i, c);
}
auto dijkstra = [&](int start) -> vector<ll> {
vector<ll> dist(n, INF);
dist[start] = 0;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
pq.emplace(0, start);
while (!pq.empty()) {
auto [d, x] = pq.top(); pq.pop();
if (d > dist[x]) continue;
for (auto [y, _, c] : g[x]) {
if (dist[y] > dist[x] + c) {
dist[y] = dist[x] + c;
pq.emplace(dist[y], y);
}
}
}
return dist;
};
auto ds = dijkstra(s);
auto dt = dijkstra(t);
auto du = dijkstra(u);
auto dv = dijkstra(v);
ll dist_st = ds[t];
ll ans = du[v];
// Перебор всех рёбер как кандидатов на покрытие
for (int x = 0; x < n; x++) {
for (auto [y, _, c] : g[x]) {
// Проверяем, лежит ли ребро (x,y) на КОП s-t
if (ds[x] + c + dt[y] == dist_st || ds[y] + c + dt[x] == dist_st) {
ll cost = du[x] + c + dv[y];
if (cost < ans) ans = cost;
ll cost2 = du[y] + c + dv[x];
if (cost2 < ans) ans = cost2;
}
}
}
cout << ans << '\n';
}
