#include<bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define int long long
//#define int double
typedef pair<int,int> pii;
typedef vector<pii> vii;
typedef vector<int> vi;
typedef vector<bool> vb;
#define FOR(i,a) for(int i=0;i<(a);i++)
#define FORE(i,a,b) for(int i=(a);i<(b);i++)
#define all(x) x.begin(),x.end()
#define fi first
#define se second
#define pb push_back
#define sp <<" "<<
#define cont(x) for(auto el:x) cout<<el<<' ';cout<<endl;
#define contp(x) for(auto el:x) cout<<el.fi<<'-'<<el.se<<' ';cout<<endl;
#define DEBUG(x) cout<<#x sp x<<endl;
#define carp(x,y) ((x%MOD)*(y%MOD))%MOD
#define topla(x,y) ((x%MOD)+(y%MOD))%MOD
#define mid (l+r)/2
const int MAXN=1e5+5;
const int MOD=1e9+7;
const int INF=1e18;
int n,m,s,t,u,v;
vii adj[MAXN];
pii tut[MAXN];
void dij(int bas,bool f){
set<pii> s;
s.insert({0,bas});
if(f) tut[bas].fi=0;
else tut[bas].se=0;
while(!s.empty()){
auto el=*s.begin();
s.erase(el);
int nd=el.se;
for(auto [kom,cost]:adj[nd]){
if(f){ //u
if(tut[kom].fi>tut[nd].fi+cost){
if(s.count({tut[kom].fi,kom})) s.erase({tut[kom].fi,kom});
tut[kom].fi=tut[nd].fi+cost;
s.insert({tut[kom].fi,kom});
}
}
else{ //v
if(tut[kom].se>tut[nd].se+cost){
if(s.count({tut[kom].se,kom})) s.erase({tut[kom].se,kom});
tut[kom].se=tut[nd].se+cost;
s.insert({tut[kom].se,kom});
}
}
}
}
}
pii tut2[MAXN]; //s'den başlayıp bana gelen min pathtteki
//{u'ya en yakın, v'ye en yakın mesafe}
int dd[MAXN];
int p[MAXN];
void dij2(int bas){
set<pii> s;
s.insert({0,bas});
dd[bas]=0;
while(!s.empty()){
auto el=*s.begin();
s.erase(el);
int nd=el.se;
for(auto [kom,cost]:adj[nd]){
if(dd[kom]>dd[nd]+cost){
if(s.count({dd[kom],kom})) s.erase({dd[kom],kom});
p[kom]=nd;
dd[kom]=dd[nd]+cost;
s.insert({dd[kom],kom});
tut2[kom].fi=min(tut[kom].fi,tut2[nd].fi);
tut2[kom].se=min(tut[kom].se,tut2[nd].se);
}
else if(dd[kom]==dd[nd]+cost){
int bir=min(tut2[nd].fi,tut[kom].fi);
int iki=min(tut2[nd].se,tut[kom].se);
if(bir+iki<tut2[kom].fi+tut2[kom].se){
p[kom]=nd;
tut2[kom].fi=bir;
tut2[kom].se=iki;
s.insert({dd[kom],kom});
}
}
}
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
FOR(i,m){
int a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
FORE(i,1,n+1) tut[i].fi=tut[i].se=dd[i]=tut2[i].fi=tut2[i].se=INF;
//u ve v'den herkese sp bul
dij(u,true);
dij(v,false);
//FORE(i,1,n+1) cout<<"here" sp i sp tut[i].fi sp tut[i].se<<endl;
dij2(s);
vb mark(n+1,false);
int x=t;
while(x!=s){
mark[x]=true;
x=p[x];
}
mark[s]=true;
int ans=0;
if(!mark[u] and !mark[v]){
ans=min(tut[u].se,tut2[t].fi+tut2[t].se);
}
else if(!mark[v]){
ans=tut2[t].se;
}
else if(!mark[u]){
ans=tut2[t].fi;
}
cout<<ans<<endl;
}
