#include<bits/stdc++.h>
#define fi first
#define se second
using namespace std;
using ll=long long;
const ll inf=1e18;
const int N=1e5;
int n,m,S,T,U,V;
vector<pair<int,ll>>g[N+5];
ll d[4][N+5];
void dji(int start,int type){
for(int i=1;i<=n;++i)
d[type][i]=inf;
d[type][start]=0;
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>>pq;
pq.push({0,start});
// cout<<type<<' '<<start<<"->\n";
while(!pq.empty()){
pair<ll,int>t=pq.top();
pq.pop();
ll w=t.fi;
int u=t.se;
// cout<<u<<','<<w<<'\n';
if(d[type][u]!=w) continue;
for(pair<int,ll>i:g[u]){
ll _w=w+i.se;
if(d[type][i.fi]>_w){
d[type][i.fi]=_w;
pq.push({_w,i.fi});
}
}
}
}
int deg[N+5];
ll Dist_V[N+5],Dist_U[N+5];
vector<int>adj[N+5];
void sol(){
for(int i=1;i<=n;++i){
// cout<<i<<','<<d[0][i]<<":\n";
for(pair<int,ll>j:g[i]){
// cout<<j.fi<<' '<<d[1][j.fi]<<' '<<j.se<<'\n';
if(d[0][i]+j.se+d[1][j.fi]==d[0][T])
{
// cout<<i<<' '<<j.fi<<'\n';
adj[j.fi].push_back(i);
deg[i]++;
}
}
}
queue<int>qe;
for(int i=1;i<=n;++i){
if(!deg[i]){
qe.push(i);
}
Dist_V[i]=d[3][i];
Dist_U[i]=d[2][i];
}
ll ans=inf;
while(!qe.empty()){
int t=qe.front();
// cout<<t<<'.'<<Dist_V[t]<<'\n';
ans=min(ans,Dist_V[t]+d[2][t]);
ans=min(ans,Dist_U[t]+d[3][t]);
qe.pop();
for(int j:adj[t]){
Dist_V[j]=min(Dist_V[j],Dist_V[t]);
Dist_U[j]=min(Dist_U[j],Dist_U[t]);
if(!--deg[j]) qe.push(j);
}
}
cout<<ans;
}
int main(){
ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin>>n>>m;
cin>>S>>T;
cin>>U>>V;
for(int i=1;i<=m;++i){
int x,y;
ll w;
cin>>x>>y>>w;
g[x].push_back({y,w});
g[y].push_back({x,w});
}
dji(S,0);
dji(T,1);
dji(U,2);
dji(V,3);
sol();
return 0;
}
