#ifndef Local
#pragma GCC optimize("O3,unroll-loops")
const int lim=1e5+500;
#else
const int lim=3e3+3;
#endif
#include "bits/stdc++.h"
using namespace std;
#define int int64_t
#define pb push_back
const int mod=998244353;
//const int mod=(1ll<<61)-1;
using pii=pair<int,int>;
vector<pii>v[lim];
int n,m;
inline void dj(int s,int*dist){
for(int i=1;i<=n;i++)dist[i]=LLONG_MAX;
dist[s]=0;
priority_queue<pii,vector<pii>,greater<pii>>pq;
pq.push({0,s});
while(pq.size()){
auto [tm,now]=pq.top();
pq.pop();
if(tm^dist[now])continue;
for(auto [j,c]:v[now]){
if(dist[now]+c<dist[j]){
dist[j]=dist[now]+c;
pq.push({dist[j],j});
}
}
}
}
inline void solve(){
cin>>n>>m;
int s,t;
cin>>s>>t;
int a,b;
cin>>a>>b;
for(int i=0;i<m;i++){
int x,y,c;
cin>>x>>y>>c;
v[x].pb({y,c});
v[y].pb({x,c});
}
int dist[n+1],lead[n+1];
for(int i=0;i<=n;i++){
dist[i]=LLONG_MAX;
lead[i]=0;
}
dist[s]=lead[s]=0;
priority_queue<pii,vector<pii>,greater<pii>>pq;
pq.push({0,s});
while(pq.size()){
auto [tm,now]=pq.top();
pq.pop();
if(tm^dist[now])continue;
for(auto [j,c]:v[now]){
if(dist[now]+c<dist[j]){
dist[j]=dist[now]+c;
pq.push({dist[j],j});
lead[j]=1;
}else if(dist[now]+c==dist[j]){
lead[j]++;
}
}
}
int dista[n+1],distb[n+1],distT[n+1];
dj(a,dista);
dj(b,distb);
dj(t,distT);
int ans=dista[b],dpa[n+1],dpb[n+1];
for(int i=0;i<=n;i++){
dpa[i]=dpb[i]=LLONG_MAX;
}
dpa[s]=distb[s];
dpb[s]=dista[s];
queue<int>q;
q.push(s);
while(q.size()){
int now=q.front();
q.pop();
dpa[now]=min(dpa[now],distb[now]);
dpb[now]=min(dpb[now],dista[now]);
ans=min(ans,dpa[now]+dista[now]);
ans=min(ans,dpb[now]+distb[now]);
for(auto [j,c]:v[now]){
if(dist[now]+c+distT[j]==dist[t]){
dpa[j]=min(dpa[j],dpa[now]);
dpb[j]=min(dpb[j],dpb[now]);
if(!(--lead[j])){
q.push(j);
}
}
}
}
cout<<ans<<"\n";
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
#ifdef Local
freopen(".in","r",stdin);
freopen(".out","w",stdout);
#else
#endif
int t=1;
//cin>>t;
while (t--)
{
solve();
}
}
