#include <bits/stdc++.h>
using namespace std;
#define int long long
#define inf 0x3F3F3F3F3F3F3F3F
const int MXN = 1e5 + 5;
vector<array<int, 2>> adj[MXN];
vector<int> par[MXN], g[MXN], o;
int dist[2][MXN], d[MXN], mn[2][MXN], used[MXN];
void dijk(int s, int* dist) {
for (int i = 0; i < MXN; i++) dist[i] = inf;
priority_queue<array<int, 2>, vector<array<int, 2>>, greater<array<int, 2>>> pq;
dist[s] = 0;
pq.push({0, s});
while (!pq.empty()) {
auto [w, a] = pq.top();
pq.pop();
if (w > dist[a]) continue;
for (const array<int, 2> &v : adj[a]) {
if (dist[v[0]] > w + v[1]) {
dist[v[0]] = w + v[1];
pq.push({dist[v[0]], v[0]});
}
}
}
}
void build(int a) {
used[a] = 1;
for (int &v : par[a]) {
g[v].push_back(a);
if (used[v]) continue;
build(v);
}
}
void tp(int a) {
used[a] = 1;
for (int &v : g[a]) {
if (used[v]) continue;
tp(v);
}
o.push_back(a);
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(nullptr);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
while (m--) {
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijk(u, dist[0]), dijk(v, dist[1]);
for (int i = 0; i < MXN; i++) d[i] = mn[0][i] = mn[1][i] = inf;
priority_queue<array<int, 2>, vector<array<int, 2>>, greater<array<int, 2>>> pq;
d[s] = 0;
pq.push({0, s});
while (!pq.empty()) {
auto [w, a] = pq.top();
pq.pop();
if (w > d[a]) continue;
for (const array<int, 2> &v : adj[a]) {
if (d[v[0]] > w + v[1]) {
d[v[0]] = w + v[1];
par[v[0]].clear();
par[v[0]].push_back(a);
pq.push({d[v[0]], v[0]});
}
else if (d[v[0]] == w + v[1]) par[v[0]].push_back(a);
}
}
build(t);
fill(used + 1, used + n + 1, 0);
tp(s);
reverse(o.begin(), o.end());
int res = inf;
for (int x : o) {
for (int j = 0; j < 2; j++) {
mn[j][x] = min(mn[j][x], dist[j][x]);
res = min(res, mn[j][x] + dist[j ^ 1][x]);
}
for (int v : g[x]) {
for (int j = 0; j < 2; j++) mn[j][v] = min(mn[j][v], mn[j][x]);
}
}
cout << min(dist[0][v], res) << '\n';
}
