#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define int ll
using P = pair<int, int>;
#define all(x) x.begin(), x.end()
#define rep(i, l, n) for (int i = l; i < (n); ++i)
#define sz(x) (int)x.size()
const char nl = '\n';
const int mod = 998244353;
const int inf = 1e14+100;
const int NMAX = 1e5+10;
priority_queue<P, vector<P>, greater<P>> pq;
vector<P> g[NMAX];
void dij(vector<int> &d, int src) {
for (auto &i: d)i = inf;
d[src] = 0, pq.push(P(0, src));
while (!pq.empty()) {
auto [dis, node] = pq.top(); pq.pop();
if (d[node] != dis)continue;
for (auto [son, weight]: g[node])
if (dis+weight < d[son])
d[son] = dis+weight,
pq.push(P(d[son], son));
}
}
void solve() {
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
rep(i, 0, m) {
int a, b, w; cin >> a >> b >> w;
g[a].push_back(P(b, w));
g[b].push_back(P(a, w));
}
vector<int> dag[n+1], ds(n+1), dt(n+1), du(n+1), dv(n+1);
dij(ds, s), dij(du, u);
dij(dt, t), dij(dv, v);
rep(i, 1, n+1)
for (auto [son, w]: g[i])
if (ds[i]+dt[son]+w == ds[t])dag[i].push_back(son);
int res = du[v];
vector<int> dp1(n+1, inf), dp2(n+1, inf);
dp1[s] = du[s], dp2[s] = dv[s];
queue<int> q; q.push(s);
while (!q.empty()) {
int nd = q.front(); q.pop();
res = min(res, dp1[nd]+dv[nd]);
res = min(res, dp2[nd]+du[nd]);
for (auto son: dag[nd])
dp1[son] = min(du[son], dp1[nd]),
dp2[son] = min(dv[son], dp2[nd]),
q.push(son);
}
cout << res << nl;
}
int32_t main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
//int t; cin >> t;
//while(t--)
solve();
return 0;
}
