#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], mn1[MXN], mn2[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] = mn1[i] = mn2[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) {
mn1[x] = min(mn1[x], dist[0][x]);
mn2[x] = min(mn2[x], dist[1][x]);
res = min(res, mn1[x] + dist[1][x]);
res = min(res, mn2[x] + dist[0][x]);
for (int v : g[x])
{
mn1[v] = min(mn1[v], mn1[x]);
mn2[v] = min(mn2[v], mn2[x]);
}
// mn[x] = min(mn[x], dist[0][x]);
// res = min(res, mn[x] + dist[1][x]);
// for (int v : g[x]) mn[v] = min(mn[v], mn[x]);
}
cout << min(dist[0][v], res) << '\n';
}
