#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int, int> pii;
typedef pair<int, pii> pip;
typedef pair<pii, int> ppi;
typedef pair<pii, pii> ppp;
const int LLINF = 2e18 + 10;
const int MAXN = 2e5 + 10;
int n;
vector<pii> adj[MAXN];
vector<int> dijkstra(int s) {
vector<int> dist(n + 1, LLINF);
vector<int> mrk(n + 1, false);
priority_queue<pii> pq;
dist[s] = 0;
pq.push({0, s});
while (!pq.empty()) {
int v = pq.top().second;
pq.pop();
if (mrk[v]) continue;
mrk[v] = true;
for (auto [w, c]: adj[v]) {
if (!mrk[w] && dist[w] >= dist[v] + c) {
dist[w] = dist[v] + c;
pq.push({-dist[w], w});
}
}
}
return dist;
}
int dc[4][MAXN];
bool mrkc[4][MAXN];
priority_queue<pip> pqc;
void relax_edge(int tv, int v, int tw, int w, int c) {
if (!mrkc[tw][w] && dc[tw][w] > dc[tv][v] + c) {
dc[tw][w] = dc[tv][v] + c;
pqc.push({-dc[tw][w], {tw, w}});
}
}
int commuter_pass(int s, int tt) {
for (int i = 1; i <= n; i++) {
dc[0][i] = dc[1][i] = dc[2][i] = dc[3][i] = LLINF;
}
dc[0][s] = 0;
pqc.push({0, {0, s}});
while (!pqc.empty()) {
auto p = pqc.top();
int v = p.second.second, t = p.second.first;
pqc.pop();
if (mrkc[t][v]) continue;
mrkc[t][v] = true;
for (auto [w, c]: adj[v]) {
if (c < 0) {
if (c == -1 && (t == 0 || t == 1)) {
relax_edge(t, v, 1, w, 0);
}
if (c == -2 && (t == 0 || t == 2)) {
relax_edge(t, v, 2, w, 0);
}
} else {
relax_edge(t, v, t, w, c);
if (t == 1 || t == 2) {
relax_edge(t, v, 3, w, c);
}
}
}
}
return min({ dc[0][tt], dc[1][tt], dc[2][tt], dc[3][tt] });
}
void solve() {
int m, house, school, book_u, book_v;
cin >> n >> m >> house >> school >> book_u >> book_v;
vector<ppi> edges;
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
edges.push_back({{a, b}, c});
}
vector<int> dh = dijkstra(house);
vector<int> ds = dijkstra(school);
for (auto &e: edges) {
int a = e.first.first, b = e.first.second, c = e.second;
if (dh[a] + c + ds[b] == dh[school]) {
adj[a].push_back({b, -1});
adj[b].push_back({a, -2});
}
if (dh[b] + c + ds[a] == dh[school]) {
adj[a].push_back({b, -2});
adj[b].push_back({a, -1});
}
}
cout << commuter_pass(book_u, book_v) << endl;
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
solve();
return 0;
}
