#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define ll long long
#define ld long double
#define fr(i,sz) for(i=0;i<sz;i++)
#define fa(i,v) for(auto &i:v)
#define yesno cout<<"YES"<<endl; else cout<<"NO"<<endl;
#define vvl vector<vector<ll> >
#define vl vector<ll>
#define pll pair<ll,ll>
#define vpll vector<pair<ll,ll> >
#define vvpll vector<vector<pair<ll,ll> > >
#define mp make_pair
#define pb push_back
#define rs resize
#define cl(v) v.clear()
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define inf (ll)1e18
#define f1 first
#define f2 second
#define mod (ll)(1e9+7)
ll gcd(ll a, ll b) {if (b > a) {return gcd(b, a);} if (b == 0) {return a;} return gcd(b, a % b);}
int main(){
fastio
int t=1;
// cin>>t;
while(t--){
ll n,m,s,t,u,w,i,ans1=inf,ans=inf;
cin>>n>>m>>s>>t>>u>>w;
vvpll v(n+1);
vvl fromt(n+1), froms(n+1);
while(m--){
ll x,y,z;
cin>>x>>y>>z;
v[x].pb(mp(y,z));
v[y].pb(mp(x,z));
}
vl distu(n+1,inf), distv(n+1,inf), dists(n+1,inf), distt(n+1,inf), newdists(n+1,inf), newdistt(n+1,inf);
priority_queue<pll,vpll,greater<pll> > q;
distu[u]=0;
q.push(mp(0,u));
while(!q.empty()){
ll a=q.top().f2, b=q.top().f1;
q.pop();
if(distu[a]<b) continue;
fa(i,v[a]) if(distu[i.f1]>b+i.f2){
distu[i.f1]=b+i.f2;
q.push(mp(distu[i.f1],i.f1));
}
}
distv[w]=0;
q.push(mp(0,w));
while(!q.empty()){
ll a=q.top().f2, b=q.top().f1;
q.pop();
if(distv[a]<b) continue;
fa(i,v[a]) if(distv[i.f1]>b+i.f2){
distv[i.f1]=b+i.f2;
q.push(mp(distv[i.f1],i.f1));
}
}
dists[s]=0;
q.push(mp(0,s));
while(!q.empty()){
ll a=q.top().f2, b=q.top().f1;
q.pop();
if(dists[a]<b) continue;
fa(i,v[a]) if(dists[i.f1]>b+i.f2){
fromt[i.f1].clear();
fromt[i.f1].pb(a);
dists[i.f1]=b+i.f2;
q.push(mp(dists[i.f1],i.f1));
}
else if(dists[i.f1]==b+i.f2) fromt[i.f1].pb(a);
}
distt[t]=0;
q.push(mp(0,t));
while(!q.empty()){
ll a=q.top().f2, b=q.top().f1;
q.pop();
if(distt[a]<b) continue;
fa(i,v[a]) if(distt[i.f1]>b+i.f2){
froms[i.f1].clear();
froms[i.f1].pb(a);
distt[i.f1]=b+i.f2;
q.push(mp(distt[i.f1],i.f1));
}
else if(distt[i.f1]==b+i.f2) froms[i.f1].pb(a);
}
queue<ll> q1;
ans=distu[w];
q1.push(s);
newdists[s]=distu[s];
ans=min(ans,distv[s]+distu[s]);
while(!q1.empty()){
ll a=q1.front();
q1.pop();
fa(i,froms[a]){
q1.push(i);
newdists[i]=min(newdists[a],distu[i]);
ans=min(ans,newdists[i]+distv[i]);
}
}
q1.push(t);
newdistt[t]=distu[t];
ans=min(ans,distv[t]+distu[t]);
while(!q1.empty()){
ll a=q1.front();
q1.pop();
fa(i,fromt[a]){
q1.push(i);
newdistt[i]=min(newdistt[a],distu[i]);
ans=min(ans,newdistt[i]+distv[i]);
}
}
cout<<ans;
// fr(i,n) cout<<distu[i+1]<<' ';
// fr(i,n) cout<<distv[i+1]<<' ';
}
}
