#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 2e5 + 5;
int n, m, s, t, u, v, f[N], se[N], mn[N], mn2[N], ans[N], dist[N];
vector<pair<int, int>> adj[N];
void path(int s, int dist[]) {
dist[s] = 0;
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.push({0, s});
while (pq.size()) {
int p = pq.top().first, u = pq.top().second;
pq.pop();
if (p != dist[u]) continue;
for (auto&x : adj[u]) {
int v = x.first, c = x.second;
if (dist[v] <= dist[u] + c) continue;
dist[v] = dist[u] + c;
pq.push({dist[v], v});
}
}
}
void solve() {
for (int i = 1; i <= n; i++) dist[i] = mn[i] = mn2[i] = ans[i] = 1e18;
dist[s] = 0;
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.push({0, s});
while (pq.size()) {
int p = pq.top().first, u = pq.top().second;
pq.pop();
if (p != dist[u]) continue;
mn[u] = min(mn[u], f[u]);
mn2[u] = min(mn2[u], se[u]);
for (auto&x : adj[u]) {
int v = x.first, c = x.second;
if (dist[v] + c == dist[u]) {
mn[u] = min(mn[u], mn[v]);
mn2[u] = min(mn2[u], mn2[v]);
ans[u] = min(ans[u], ans[v]);
} else if (dist[v] > dist[u] + c) {
dist[v] = dist[u] + c;
pq.push({dist[v], v});
}
}
ans[u] = min({ans[u], se[u] + mn[u], f[u] + mn2[u]});
}
cout << min({ans[t], f[v]}) << '\n';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1;i <= m; i++) {
int u, v, c;
cin >> u >> v >> c;
adj[u].push_back({v, c});
adj[v].push_back({u, c});
}
for (int i = 1;i <= n; i++) f[i] = se[i] = 1e18;
path(u, f);
path(v, se);
solve();
return 0;
}
