#include<bits/stdc++.h>
#define int long long
#define pii pair<int, int>
#define ppi pair<pii, int>
#define pu push_back
#define fi first
#define se second
using namespace std;
const int maxn = 1e5;
const int inf = 1e15;
int n, m, s, t, u, v;
int a[maxn+5], b[maxn+5], c[maxn+5], du[maxn+5], dv[maxn+5], ds[maxn+5], dt[maxn+5];
vector<pii> adj[maxn+5];
priority_queue<ppi, vector<ppi>, greater<ppi>> p;
priority_queue<pii, vector<pii>, greater<pii>> q;
signed main() {
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i=1; i<=m; i++) {
cin >> a[i] >> b[i] >> c[i];
adj[a[i]].pu({b[i], c[i]});
adj[b[i]].pu({a[i], c[i]});
}
for (int i=1; i<=n; i++) {
du[i] = dv[i] = ds[i] = dt[i] = inf;
}
// dijkstra u to all nodes and v to all nodes
du[u] = 0;
q.push({0, u});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
if (dis > du[now]) continue;
for (auto i: adj[now]) {
if (dis + i.se >= du[i.fi]) continue;
du[i.fi] = dis + i.se;
q.push({du[i.fi], i.fi});
}
}
dv[v] = 0;
q.push({0, v});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
if (dis > dv[now]) continue;
for (auto i: adj[now]) {
if (dis + i.se >= dv[i.fi]) continue;
dv[i.fi] = dis + i.se;
q.push({dv[i.fi], i.fi});
}
}
// do the same for nodes s and t
ds[s] = 0;
q.push({0, s});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
if (dis > ds[now]) continue;
for (auto i: adj[now]) {
if (dis + i.se >= ds[i.fi]) continue;
ds[i.fi] = dis + i.se;
q.push({ds[i.fi], i.fi});
}
}
dt[t] = 0;
q.push({0, t});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
if (dis > dt[now]) continue;
for (auto i: adj[now]) {
if (dis + i.se >= dt[i.fi]) continue;
dt[i.fi] = dis + i.se;
q.push({dt[i.fi], i.fi});
}
}
// update
q.push({0, t});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
for (auto i: adj[now]) {
if (dis + i.se > dt[i.fi] || ds[i.fi] + dt[i.fi] > ds[t]) continue;
// cout << i.fi << " to " << now << " is an edge in a shortest path from s-t" << endl;
dv[i.fi] = min(dv[i.fi], dv[now]);
dv[now] = min(dv[now], dv[i.fi]);
q.push({dt[i.fi], i.fi});
}
}
// for (int i=1; i<=n; i++) {
// cout << "dv[" << i << "]: " << dv[i] << endl;
// }
int ans = du[v];
for (int i=1; i<=n; i++) {
if (ds[i] + dt[i] > ds[t]) continue;
ans = min(ans, du[i] + dv[i]);
}
cout << ans << endl;
return 0;
}
