#include <bits/stdc++.h>
using namespace std;
using ll=long long;
constexpr int MAXN=6e5+7;
ll INF=1e18;
vector<pair<int,ll>> graf[MAXN];
pair<pair<int,int>,ll> kraw[MAXN];
ll odl[MAXN];
ll odlA[MAXN];
ll odlB[MAXN];
bool odw[MAXN];
vector<pair<int,ll>> G[MAXN];
int n,m,A,B,C,D;
void wczytanie(){
cin>>n>>m>>A>>B>>C>>D;
int v,u;ll cena;
for (int i=0;i<m;i++){
cin>>v>>u>>cena;
graf[u].push_back({v,cena});
graf[v].push_back({u,cena});
kraw[i]={{u,v},cena};
}
}
void dijkstra_od_S(int S){
for (int i=1;i<=n;i++) odl[i]=INF;
for (int i=1;i<=n;i++) odw[i]=0;
odl[S]=0;
priority_queue<pair<ll,int>> q;
q.push({0,S});
int v;
while (q.size()>0){
v=q.top().second;q.pop();
if (odw[v]) continue;
odw[v]=1;
for (pair<int,ll> u:graf[v]){
if (odl[u.first]>odl[v]+u.second){
odl[u.first]=odl[v]+u.second;
q.push({-odl[u.first],u.first});
}
}
}
}
void stworz_G(){
int v,u;ll cena;
ll OAB=odlA[B];
for (int i=0;i<m;i++){
v=kraw[i].first.first;u=kraw[i].first.second;cena=kraw[i].second;
G[v].push_back({u,cena});
G[u].push_back({v,cena});
G[v+2*n].push_back({u+2*n,cena});
G[u+2*n].push_back({v+2*n,cena});
if (odlA[v]+cena+odlB[u]==OAB || odlB[v]+cena+odlA[u]==OAB){
G[v+n].push_back({u+n,0});
G[u+n].push_back({v+n,0});
}
}
for (int i=1;i<=n;i++){
G[i].push_back({i+n,0});
G[i+n].push_back({i+2*n,0});
}
}
ll solve(){
for (int i=1;i<=3*n;i++) odl[i]=INF;
for (int i=1;i<=3*n;i++) odw[i]=0;
odl[C]=0;
priority_queue<pair<ll,int>> q;
q.push({0,C});
int v;
while (q.size()>0){
v=q.top().second;q.pop();
if (odw[v]) continue;
odw[v]=1;
for (pair<int,ll> u:G[v]){
if (odl[u.first]>odl[v]+u.second){
odl[u.first]=odl[v]+u.second;
q.push({-odl[u.first],u.first});
}
}
}
return min(odl[D],min(odl[D+n],odl[D+2*n]));
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
wczytanie();
dijkstra_od_S(A);
for (int i=1;i<=n;i++) odlA[i]=odl[i];
dijkstra_od_S(B);
for (int i=1;i<=n;i++) odlB[i]=odl[i];
stworz_G();
cout<<solve();
}
