/**
* author : Lăng Trọng Đạt
* created: 17-01-2024
**/
#include <bits/stdc++.h>
using namespace std;
#ifndef LANG_DAT
#define db(...) ;
#endif // LANG_DAT
#define int long long
#define mp make_pair
#define f first
#define s second
#define pb push_back
#define all(v) (v).begin(), (v).end()
using pii = pair<int, int>;
using vi = vector<int>;
#define FOR(i, a, b) for (int (i) = a; (i) <= (b); i++)
void mx(int& a, int b) { if (b > a) a = b; }
void mi(int& a, int b) { if (b < a) a = b; }
#define si(x) (int)(x.size())
const int INF = 1e18;
const int MOD = 1e9 + 7;
const int MAXN = 1e5 + 5;
int du[MAXN], dv[MAXN]; // minimum distance from node u, v to other node
int ans = 0, n;
vector<pii> adj[MAXN];
void dijkstra1(int source, int* dist) {
priority_queue<vi> pq; // {cost from source, node}
pq.push({0, source});
while (si(pq)) {
vi x = pq.top(); pq.pop();
if (dist[x[1]] == -1) {
dist[x[1]] = -x[0];
for (pii p : adj[x[1]]) {
pq.push({x[0] - p.s, p.f});
}
}
}
}
void dijkstra2(int from, int to) {
vector<vi> nxt(n + 1), prv(n + 1); // DAG generate from dijkstra
priority_queue<vi> pq; // {cost from source, node, prev_node}
vi dist(n + 1, -1);
pq.push({0, from, 0});
while (si(pq)) {
vi x = pq.top(); pq.pop();
if (dist[x[1]] == -1) {
dist[x[1]] = -x[0];
nxt[x[2]].pb(x[1]);
prv[x[1]].pb(x[2]);
for (pii p : adj[x[1]]) {
pq.push({x[0] - p.s, p.f, x[1]});
}
} else if (-x[0] == dist[x[1]]) {
nxt[x[2]].pb(x[1]);
prv[x[1]].pb(x[2]);
}
}
set<int> not_use; // set of node which is not part of any minimum part from node s to t
/// remove node from DAG to ensure that only node t have out_deg is 0
vi in_deg(n + 1), out_deg(n + 1);
vi q;
FOR(i, 1, n) {
if (si(nxt[i]) == 0 && i != to) q.pb(i);
out_deg[i] = si(nxt[i]);
}
db(out_deg)
db(prv)
while (si(q)) {
int x = q.back(); q.pop_back();
not_use.insert(x);
for (int u : prv[x]) {
if (--out_deg[u] == 0)
q.pb(u);
}
}
// db(out_deg)
FOR(i, 1, n) {
for (int u : nxt[i]) in_deg[u]++;
}
FOR(i, 1, n) {
if (in_deg[i] == 0) q.pb(i);
db(i, nxt[i])
}
db(not_use)
// db(nxt)
// using topological sort
vi dp(n + 1, INF); // dp[i]: minimum from u to node i
while (si(q)) {
int x = q.back(); q.pop_back();
if (not_use.count(x)) continue;
mi(dp[x], du[x]);
mi(ans, dv[x] + dp[x]);
db(ans, x, dv[x], dp[x])
for (int u : nxt[x]) {
mi(dp[u], dp[x]);
if (--in_deg[u] == 0) {
q.push_back(u);
}
}
}
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
if (fopen("hi.inp", "r")) {
freopen("hi.inp", "r", stdin);
// freopen("hi.out", "w", stdout);
}
memset(du, -1, sizeof(du));
memset(dv, -1, sizeof(dv));
int m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
int a, b, c;
while (cin >> a >> b >> c) {
adj[a].pb({b, c});
adj[b].pb({a, c});
}
dijkstra1(v, dv);
dijkstra1(u, du);
// FOR(i, 1, n) {
// db(i, du[i], dv[i]);
// }
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
swap(u, v);
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans;
}
