#include <bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
//using namespace __gnu_pbds;
bool YES(bool f){ if(f) cout << "Yes\n" ; else cout << "No\n" ; return f ; }
void YES(){YES(1);}
void NO(){YES(0);}
void fopn(string name){freopen((name+".in").c_str(),"r",stdin); freopen((name+".out").c_str(),"w",stdout);}
//#define ordered_set tree<int, null_type,less_equal<int>, rb_tree_tag,tree_order_statistics_node_update>
#define ios ios_base::sync_with_stdio(0) ; cin.tie(0) ; cout.tie(0);
#define int long long
#define ld long double
#define pii pair <int , int>
#define all(x) x.begin() , x.end()
#define ff first
#define ss second
#define endl '\n'
const int N = 2e5 + 5 ;
const int inf = 1e16 ;
const int mod = 1e9 + 8 ;
const double eps = 1e-8 ;
int binpow( int a , int b ){
if ( b == 0 ) return 1 ;
int x = binpow ( a , b/2 ) ;
if ( !(b%2) ) return (x*x) ;
return (x*x*a) ;
}
template <class T>
bool chmax( T& x , const T& y ){
bool f = 0 ;
if ( x < y ) x = y , f = 1 ;
return f ;
}
template <class T>
bool chmin( T &x , const T &y ){
bool f = 0 ;
if ( x > y ) x = y , f = 1 ;
return f ;
}
//code
int n , m , a , b , c , d , ans = inf ;
vector <pii> g[N] ;
int dis[N][4] ;
void djikstra( int s , int f ){
set <pii> q ;
q.insert({0,s}) ;
for ( int i = 1 ; i <= n ; i ++ ) dis[i][f] = inf ;
dis[s][f] = 0 ;
while ( !q.empty() ){
int v = q.begin()->ss ;
q.erase(q.begin()) ;
for ( auto to : g[v] ){
if ( dis[to.ff][f] > dis[v][f]+to.ss ){
q.erase({dis[to.ff][f],to.ff}) ;
dis[to.ff][f] = dis[v][f] + to.ss ;
q.insert({dis[to.ff][f],to.ff}) ;
}
}
}
}
void bfs ( int s , int b ){
for ( int i = 1 ; i <= n ; i ++ ) dis[i][3] = inf ;
dis[s][3] = 0 ;
set <pair < int , pair <int , pii>>> q ;
q.insert({0,{s,{dis[s][1],dis[s][2]}}}) ;
while ( !q.empty() ){
int v = q.begin()->ss.ff ;
int ma = q.begin()->ss.ss.ff ;
int mb = q.begin()->ss.ss.ss ;
q.erase(q.begin()) ;
if ( v == b ){
chmin ( ans , ma + mb ) ;
continue ;
}
for ( auto to : g[v] ){
if ( dis[to.ff][3] > dis[v][3] + to.ss || ( dis[to.ff][3] == dis[v][3] + to.ss && ( dis[to.ff][1] < ma || dis[to.ff][2] < mb ) ) ){
q.erase({dis[to.ff][3],{to.ff,{min(ma,dis[to.ff][1]),min(mb,dis[to.ff][2])}}}) ;
dis[to.ff][3] = dis[v][3] + to.ss ;
q.insert({dis[to.ff][3],{to.ff,{min(ma,dis[to.ff][1]),min(mb,dis[to.ff][2])}}}) ;
}
}
}
}
void solve(){
cin >> n >> m >> a >> b >> c >> d ;
for ( int i = 0 ; i < m ; i ++ ){
int x , y , c ; cin >> x >> y >> c ;
g[x].push_back({y,c}) ;
g[y].push_back({x,c}) ;
}
djikstra( a , 0 ) ;
djikstra( c , 1 ) ;
djikstra( d , 2 ) ;
bfs(a,b) ; bfs(b,a) ; chmin ( ans , dis[d][1] ) ;
cout << ans ;
}
signed main(){
ios ;
int t = 1 ;
//cin >> t ;
while ( t -- ) solve() ;
}
