#include <bits/stdc++.h> //Logm
using namespace std;
#define int long long
#define II pair<int,int>
#define fi first
#define se second
template<class X, class Y> bool mini(X& x, const Y y) {
if (x > y) return x = y, 1;
return 0;
}
const int N = 1e5+5;
int n, m;
int S, T, U, V;
vector<II> adj[N];
vector<II> trace[N];
map<II, bool> dag;
int f[N];
void dijkstra1(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});
trace[v.se].push_back(II(v.fi, u.se));
}
else if (f[v.se] == f[u.se] + v.fi) {
trace[v.se].push_back(II(v.fi, u.se));
}
}
}
}
vector<II> adj2[N];
void dijkstra2(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: adj2[u.se]) {
if (mini(f[v.se], f[u.se] + v.fi)) {
q.push({f[v.se], v.se});
}
}
}
}
bool vis[N];
void dfs1(int u) {
vis[u] = 1;
for (II x: trace[u]) {
int v = x.se, w = x.fi;
dag[II(v, u)] = 1;
if (!vis[v])
dfs1(v);
}
}
void dfs2(int u) {
vis[u] = 1;
for (II x: trace[u]) {
int v = x.se, w = x.fi;
dag[II(u, v)] = 1;
if (!vis[v])
dfs2(v);
}
}
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;
while (m--) {
int u, v, c; cin >> u >> v >> c;
adj[u].push_back(II(c, v));
adj[v].push_back(II(c, u));
}
dijkstra1(S);
dfs1(T);
// for (auto x: dag) {
// cout << x.fi.fi << ' ' << x.fi.se << '\n';
// }
for (int u = 1; u <= n; ++u) {
for (II x: adj[u]) {
int v = x.se, w = x.fi;
if (dag[II(u, v)]) {
adj2[u].push_back(II(0, v));
}
else adj2[u].push_back(II(w, v));
}
}
dijkstra2(U);
int ans = f[V];
dag.clear();
memset(vis, 0, sizeof vis);
dfs2(T);
for (int i = 1; i <= n; ++i) adj2[i].clear();
// for (auto x: dag) {
// cout << x.fi.fi << ' ' << x.fi.se << '\n';
// }
for (int u = 1; u <= n; ++u) {
for (II x: adj[u]) {
int v = x.se, w = x.fi;
if (dag[II(u, v)]) {
adj2[u].push_back(II(0, v));
}
else adj2[u].push_back(II(w, v));
}
}
dijkstra2(U);
cout << f[V];
return 0;
}
