#include "bits/stdc++.h"
using namespace std;
#define int long long
const int N = 1e6 + 5;
#define II pair<int,int>
#define fi first
#define se second
int n, m;
int s, t, U, V;
int f[N], f2[N];
vector<II> adj[N], adj2[N];
map<II, bool> mp;
// Utility function to update minimum values
template<class X, class Y> bool mini(X& x, const Y y) {
if (x > y) return x = y, 1;
return 0;
}
// Dijkstra to find shortest paths from a node
void dijkstra(int node) {
memset(f, 0x3f, sizeof f);
priority_queue<II, vector<II>, greater<II>> q;
q.push({0, node});
f[node] = 0;
while (!q.empty()) {
II u = q.top(); q.pop();
if (u.fi != f[u.se]) continue;
for (II v : adj[u.se]) {
if (mini(f[v.se], f[u.se] + v.fi)) {
q.push({f[v.se], v.se});
mp[{u.se, v.se}] = 1;
}
if (f[v.se] == f[u.se] + v.fi) {
mp[{u.se, v.se}] = 1;
}
}
}
}
// Second Dijkstra on modified graph (zero-cost edges for shortest path edges)
void dijkstra2(int node) {
memset(f2, 0x3f, sizeof f2);
priority_queue<II, vector<II>, greater<II>> q;
q.push({0, node});
f2[node] = 0;
while (!q.empty()) {
II u = q.top(); q.pop();
if (u.fi != f2[u.se]) continue;
for (II v : adj2[u.se]) {
if (mini(f2[v.se], f2[u.se] + v.fi)) {
q.push({f2[v.se], v.se});
}
}
}
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
if (fopen("_ab.inp", "r")) {
freopen("_ab.inp", "r", stdin);
freopen("_ab.out", "w", stdout);
}
cin >> n >> m;
cin >> s >> t >> U >> V;
for (int i = 1; i <= m; i++) {
int u, v, c; cin >> u >> v >> c;
adj[u].push_back({c, v});
adj[v].push_back({c, u});
}
// Step 1: Find shortest paths from S
dijkstra(s);
// Step 2: Construct adj2 for zero-cost edges on the shortest path
for (int i = 1; i <= n; i++) {
for (II j : adj[i]) {
if (mp[{i, j.se}]) {
adj2[i].push_back({0, j.se});
} else {
adj2[i].push_back(j);
}
}
}
// Step 3: Find shortest paths from U using modified graph
dijkstra2(U);
cout << f2[V] << '\n';
return 0;
}
