#include <bits/stdc++.h>
using namespace std ;
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define int long long
#define ld long double
#define f(i,a,b) for(int i=a;i<b;++i)
#define endl '\n'
#define debug cout<<"\n========================================\n";
#define err1(a) cout<<#a<<" "<<a<<endl;
#define err2(a,b) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<endl;
#define err3(a,b,c) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<" "<<#c<<" "<<c<<endl;
#define err4(a,b,c,d) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<" "<<#c<<" "<<c<<" "<<#d<<" "<<d<<endl;
#define PQ priority_queue
#define LB lower_bound
#define UB upper_bound
#define fr first
#define sc second
#define all(a) (a).begin(),(a).end()
#define allr(a) (a).rbegin(),(a).rend()
#define show(a) {for(auto xyz:a)cout<<xyz<<" ";cout<<endl;}
#define sz(x) (int)(x).size()
const int INF = 1e16 ;
vector<int> Dijkstra(int n,int src,vector< vector< array<int,2> > > &g){
PQ<array<int,2> > q ;
vector<int> dis(n, INF) ;
dis[src] = 0 ;
q.push({-dis[src],src}) ;
while(sz(q)){
int i = q.top()[1], k = -q.top()[0] ;
q.pop() ;
if( k != dis[i] ){
continue ;
}
for(auto [j,w]:g[i]){
if( dis[j] > dis[i] + w ){
dis[j] = dis[i] + w ;
q.push({-dis[j],j}) ;
}
}
}
return dis ;
}
signed main(){
fastio;
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V ;
--S, --T, --U, --V;
vector< vector< array<int,2> > > g(N) ;
f(i,0,M){
int a, b, c; cin >> a >> b >> c ;
--a, --b;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
vector<int> disV = Dijkstra(N,V,g), disS = Dijkstra(N,S,g), disT = Dijkstra(N,T,g), disU = Dijkstra(N,U,g) ;
vector<int> ComDisV = disV, ComDisV2 = disV ;
int MinDis = disT[S] ;
vector< vector<int> > next(N), next2(N) ;
f(i,0,N){
for(auto [j, w]:g[i]){
//does i->j works during S->T
if( disS[i] + w + disT[j] == MinDis){
next[i].push_back(j) ;
}
//does i->j works during T->S
if( disT[i] + w + disS[j] == MinDis){
next2[i].push_back(j) ;
}
}
}
PQ<array<int,2> > q ;
f(i,0,N){
if( sz(next[i]) ){
q.push({-ComDisV[i], i}) ;
}
}
while(sz(q)){
int i = q.top()[1] , d = -q.top()[0] ;
q.pop() ;
if(d != ComDisV[i]){
continue ;
}
for(auto j:next[i]){
if(ComDisV[j] > ComDisV[i]){
ComDisV[j] = ComDisV[i] ;
q.push({-ComDisV[j], j}) ;
}
}
}
assert(sz(q) == 0) ;
f(i,0,N){
if( sz(next2[i]) ){
q.push({-ComDisV2[i], i}) ;
}
}
while(sz(q)){
int i = q.top()[1] , d = -q.top()[0] ;
q.pop() ;
if(d != ComDisV2[i]){
continue ;
}
for(auto j:next2[i]){
if(ComDisV2[j] > ComDisV2[i]){
ComDisV2[j] = ComDisV2[i] ;
q.push({-ComDisV2[j], j}) ;
}
}
}
int ans = INF ;
f(i,0,N){
ans = min(ans, disU[i] + ComDisV2[i] ) ;
ans = min(ans, disU[i] + ComDisV[i] ) ;
}
cout << ans ;
}
