#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
#define pasha ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define int long long
#define ff first
#define ss second
#define pb push_back
#define all(v) begin(v), end(v)
using namespace std;
// mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
constexpr int N = 1e+5 + 5, oo = 2e+18;
vector<pair<int, int>> adj[N];
vector<pair<int, int>> dag[N];
int dist[N];
int par[N];
bool used[N];
int dp[N];
bool h = false;
int s, t;
int a, b;
map<pair<int, int>, bool> mark;
void dijkstra(int a) {
priority_queue<pair<int, int>> pq;
dist[a] = 0;
pq.push({0, a});
while (!pq.empty()) {
auto [d, u] = pq.top();
d = -d;
pq.pop();
if (dist[u] < d) {
continue;
}
for (auto &[v, w] : (!h ? adj[u] : dag[u])) {
if (dist[u] + w < dist[v]) {
dist[v] = dist[u] + w;
par[v] = u;
pq.push({-dist[v], v});
}
}
}
}
void dfs1(int u) {
// cout << u << ' ';
if (u == b) return;
used[u] = true;
for (auto &[v, w] : adj[u]) {
if (used[v]) continue;
if (!mark[{u, v}]) mark[{u, v}] = true;
dfs1(v);
}
}
void _() {
int n, m; cin >> n >> m;
cin >> s >> t;
cin >> a >> b;
vector<array<int, 3>> e;
for (int i = 0; i < m; ++i) {
int u, v, w; cin >> u >> v >> w;
e.pb({u, v, w});
adj[u].pb({v, w}), adj[v].pb({u, w});
}
for (int i = 1; i <= n; ++i) {
par[i] = -1;
dist[i] = oo;
}
dijkstra(s);
vector<int> f;
int node = t;
while (par[node] != -1) {
f.pb(node);
node = par[node];
}
f.pb(s);
reverse(all(f));
map<pair<int, int>, bool> special;
for (int i = 1; i < f.size(); ++i) {
mark[{f[i - 1], f[i]}] = true;
special[{f[i - 1], f[i]}] = true;
special[{f[i], f[i - 1]}] = true;
}
dfs1(s);
// return;
for (auto &[u, v, w] : e) {
if (special[{u, v}]) w = 0;
if (mark[{u, v}]) dag[u].pb({v, w});
else dag[v].pb({u, w});
}
for (int i = 1; i <= n; ++i) {
par[i] = -1;
dist[i] = oo;
}
h = true;
dijkstra(a);
cout << dist[b] << '\n';
}
signed main() {
pasha
int t = 1;
// cin >> t;
for (int cs = 1; cs <= t; ++cs) {
_();
// cout << '\n';
}
}
