#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll C=1e9;
const ll M=2e5;
vector<vector<pair<int,ll>>> adj;
void f(vector<ll> &v,int x){
v[x]=0;
queue<int>q;
q.push(x);
while(!q.empty()){
int i=q.front();
q.pop();
for(pair<int,ll> p:adj[i]){
ll j,c;
tie(j,c)=p;
if(v[j]>v[i]+c){
v[j]=v[i]+c;
q.push(j);
}
}
}
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(0);
ll n,m,s,t,u,v;
cin>>n>>m>>s>>t>>u>>v;
adj=vector<vector<pair<int,ll>>>(n+1);
for(int i=0;i<m;i++){
ll a,b,c;
cin>>a>>b>>c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
vector<ll> du(n+1,C*M);
vector<ll> dv(n+1,C*M);
vector<ll> dt(n+1,C*M);
vector<ll> ds(n+1,C*M);
f(du,u);
f(dv,v);
f(ds,s);
f(dt,t);
ll tot=C*M;
for(int i=1;i<=n;i++){
tot=min(tot,ds[i]+dt[i]);
}
vector<bool> b(n+1);
for(int i=1;i<=n;i++){
b[i]=ds[i]+dt[i]==tot;
}
ll res=M*C;
for(int i=1;i<=n;i++){
if(!b[i]){
continue;
}
queue<int>q;
q.push(i);
vector<ll> d(n+1,C*M);
d[i]=0;
while(!q.empty()){
int j=q.front();
q.pop();
if(!b[j]){
continue;
}
if(d[j]+ds[i]+dt[j]==tot||d[j]+ds[j]+dt[i]==tot){
res=min({res,du[i]+dv[j],du[j]+dv[i]});
}
for(pair<int,ll> p:adj[j]){
ll k,c;
tie(k,c)=p;
if(d[k]>d[j]+c){
d[k]=d[j]+c;
q.push(k);
}
}
}
}
cout<<min(res,du[v]);
}
