#include "bits/stdc++.h"
using namespace std;
#define int long long
#define endl '\n'
#define sz(x) (int)(x.size())
#define ff first
#define ss second
#define m_p make_pair
#define INF LLONG_MAX
#define OO LLONG_MAX
using vi=vector<int>;
using vvi=vector<vi>;
using pii=pair<int,int>;
template<typename T> using inverse_pq = priority_queue<T,vector<T>, greater<T> >;
template<typename T=int> void cin_vector(vector<T> &v) {for(int& i : v) cin>>i;}
vvi void_vector=vvi();
void djikstra(vector<vector<pii> >& g, vi& dist, int start, int end=-1, vvi& dag=void_vector){
inverse_pq<pii> pq;
vvi father(g.size());
vector<bool> mark(g.size(),false);
pq.push({0,start});
dist[start]=0;
while(!pq.empty()){
int top=pq.top().ss; pq.pop();
if(mark[top]) continue;
mark[top]=true;
for(auto i : g[top]){
int d=i.ss+dist[top];
if(d==dist[i.ff]){
father[i.ff].push_back(top);
}else if(d<dist[i.ff]){
vector<int> aux(1,top);
dist[i.ff]=d;
father[i.ff].swap(aux);
pq.push({d,i.ff});
}
}
}
if(end!=-1){
queue<int> q;
vector<bool> v(dag.size(), false);
q.push(end);
v[end]=true;
while(!q.empty()){
int top=q.front(); q.pop();
for(int i : father[top]){
dag[i].push_back(top);
if(!v[i]){
q.push(i);
v[i]=true;
}
}
}
}
}
void dfs(vvi& g, vi& distu, vi& distv, vector<pair<int,pii>>& nemo, int start){
int a=distu[start]; int b=distv[start];
nemo[start].ss.ff=a; nemo[start].ss.ss=b;
nemo[start].ff=a+b;
for(int i : g[start]){
if(nemo[i].ff==INF){
dfs(g, distu, distv,nemo, i);
}
nemo[start].ff=min(nemo[start].ff, min(a+nemo[i].ss.ss,b+nemo[i].ss.ff));
nemo[start].ss.ff=min(nemo[start].ss.ff,nemo[i].ss.ff);
nemo[start].ss.ss=min(nemo[start].ss.ss,nemo[i].ss.ss);
}
}
int32_t main(){
ios_base::sync_with_stdio(false); cin.tie(0);
int n,m;
cin>>n>>m;
int s,t,u,v;
cin>>s>>t>>u>>v;
vector<vector<pii> > g(n+1);
while(m--){
int a,b,w;
cin>>a>>b>>w;
g[a].push_back(m_p(b,w));
g[b].push_back(m_p(a,w));
}
vi dist(n+1, INF), distu(n+1, INF), distv(n+1, INF);
vvi dag(n+1);
djikstra(g,distu, u);
djikstra(g,distv, v);
djikstra(g,dist, s, t, dag);
vector<pair<int,pii>> nemo(n+1,m_p(INF,m_p(INF,INF)));
dfs(dag, distu, distv, nemo, s) ;
int ans=INF;
for(auto i : nemo) ans=min(ans,i.ff);
cout<<min(distu[v], ans)<<endl;
return 0;
}
