#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
const int MX = 1e5 + 5;
const ll INF = 1e18;
vector<pair<int, int>> g[MX];
vector<ll> d(MX, INF);
vector<int> par(MX, -1), cur_route[MX];
priority_queue<pair<ll, int>> pq;
bool vis[MX];
vector<vector<int>> routes;
set<pair<int, int>> free_route;
int n, m, s, t, us, vs;
void update_route (int u) {
vector<int> ruta = {t};
while (u != -1) {
ruta.push_back(u);
u = par[u];
}
routes.push_back(ruta);
}
void dijkstra (int source) {
d[source] = 0;
pq.push(make_pair(0, source));
cur_route[source].push_back(source);
while (!pq.empty()) {
int u = pq.top().second;
pq.pop();
if (vis[u]) continue;
vis[u] = true;
for (auto v : g[u]) {
if (d[v.first] > d[u] + v.second) {
d[v.first] = d[u] + v.second;
pq.push(make_pair(-d[v.first], v.first));
par[v.first] = u;
if (v.first == t) {
routes.clear();
update_route(u);
}
} else if (v.first == t && d[v.first] == d[u] + v.second) {
update_route(u);
}
}
}
}
ll dijkstra2 (int source, int obj) {
fill(d.begin(), d.end(), INF);
memset(vis, false, sizeof(vis));
d[source] = 0;
pq.push(make_pair(0, source));
while (!pq.empty()) {
int u = pq.top().second;
pq.pop();
if (vis[u]) continue;
vis[u] = true;
for (auto v : g[u]) {
ll travel = d[u] + (free_route.count(make_pair(u, v.first)) ? 0 : v.second);
if (d[v.first] > travel) {
d[v.first] = travel;
pq.push(make_pair(-d[v.first], v.first));
}
}
}
return d[obj];
}
int main () {
//take input
cin >> n >> m >> s >> t >> us >> vs;
for (int i = 0; i < m; i++) {
int u, v, c;
cin >> u >> v >> c;
g[u].push_back(make_pair(v, c));
g[v].push_back(make_pair(u, c));
}
//calcura el commuter pass
dijkstra(s);
//provar todas las rutas possibles
ll sol = INF;
for (auto vec : routes) {
free_route.clear();
for (int i = 0; i < (int) vec.size() - 1; i++) {
free_route.insert(make_pair(vec[i], vec[i + 1]));
free_route.insert(make_pair(vec[i + 1], vec[i]));
}
ll cur = dijkstra2(us, vs);
sol = min(sol, cur);
}
cout << sol << '\n';
}
