#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define pii pair<ll,ll>
#define mp make_pair
#define f first
#define s second
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
int main() {
ios::sync_with_stdio(false); cin.tie(0);
int n, m; cin >> n >> m;
int s, t, u, v; cin >> s >> t >> u >> v;
int a, b, c;
vector<vector<pii>> adj(n);
F0R(i,m) {
cin >> a >> b >> c;
adj[--a].pb({--b,c}); adj[b].pb({a,c});
}
vector<ll> dist_s(n,LLONG_MAX), dist_u(n,LLONG_MAX),dist_v(n,LLONG_MAX);
dist_s[--s] = dist_u[--u] = dist_v[--v] = 0; t--;
auto dijkstra = [&](vector<ll>& ret, int start)->void {
priority_queue<pii,vector<pii>,greater<pii>> pq;
pq.push({0,start});
while (pq.size()) {
pii cur = pq.top(); pq.pop();
if (cur.f > ret[cur.s]) {continue;}
for (pii x : adj[cur.s]) {
if (cur.f+x.s < ret[x.f]) {
pq.push({ret[x.f]=cur.f+x.s,x.f});
}
}
}
};
dijkstra(dist_s,s); dijkstra(dist_u,u); dijkstra(dist_v,v);
ll ans = dist_u[v];
vector<pii> ret(n+1,{-1,-1});
auto dfs = [&](auto&& dfs, int cur)->void {
//vis[cur] = true;
ret[cur] = {dist_u[cur],dist_v[cur]};
//pii mn = {dist_u[cur],dist_v[cur]};
for (pii x : adj[cur]) {
if (dist_s[x.f] == dist_s[cur]-x.s) {
if (ret[x.f] == ret[n]) {dfs(dfs,x.f);}
ret[cur].f = min(ret[cur].f,ret[x.f].f);
ret[cur].s = min(ret[cur].s,ret[x.f].s);
}
}
ans = min(ans,dist_u[cur]+ret[cur].s);
ans = min(ans,dist_v[cur]+ret[cur].f);
//cout << cur+1 << ' ' << mn.f << ' ' << mn.s << '\n';
//return mn;
};
dfs(dfs,t); cout << ans << '\n';
}
