#include <bits/stdc++.h>
#define vec vector
#define long int64_t
using namespace std;
int N;
vec<vec<array<int, 2>>> rails;
vec<long> dijkstra(int source) {
vec<long> cost(N, 1e18);
cost[source] = 0;
auto cmp = [&](const int& u, const int& v) {
return cost[u] != cost[v] ? cost[u] < cost[v] : u < v;
};
set<int, decltype(cmp)> s(cmp);
s.insert(source);
while (!s.empty()) {
int u = *s.begin();
s.erase(s.begin());
for (auto [v, c] : rails[u]) {
if (c + cost[u] < cost[v]) {
s.erase(v);
cost[v] = c + cost[u];
s.insert(v);
}
}
}
return cost;
}
vec<long> ucost, vcost;
int S, T;
long dpdijkstra(bool change) {
if (change) { swap(S, T); }
vec<long> uclose(N, 1e18), vclose(N, 1e18);
vec<long> cost(N, 1e18);
cost[S] = 0;
auto cmp = [&](const int& u, const int& v) {
return cost[u] != cost[v] ? cost[u] < cost[v] : u < v;
};
set<int, decltype(cmp)> s(cmp);
s.insert(S);
while (!s.empty()) {
int u = *s.begin();
s.erase(s.begin());
for (auto [v, c] : rails[u]) {
if (c + cost[u] > cost[v]) { continue; }
if (c + cost[u] < cost[v]) {
s.erase(v);
cost[v] = c + cost[u];
s.insert(v);
}
uclose[v] = min(ucost[v], uclose[u]);
vclose[v] = min(vcost[v], vclose[u]);
}
}
return uclose[T] + vclose[T];
}
int main() {
cin.tie(0) -> sync_with_stdio(0);
int M; cin >> N >> M;
cin >> S >> T; S--; T--;
int U, V; cin >> U >> V; U--; V--;
rails.resize(N);
for (int i = 0; i < M; i++) {
int u, v, c; cin >> u >> v >> c; u--; v--;
rails[u].push_back({v, c});
rails[v].push_back({u, c});
}
ucost = dijkstra(U), vcost = dijkstra(V);
long ans = ucost[V];
ans = min(ans, dpdijkstra(false));
ans = min(ans, dpdijkstra(true));
cout << ans << endl;
}
