#include <bits/stdc++.h>
using namespace std ;
#define int long long
typedef long long ll ;
typedef pair<int, int> ii ;
typedef vector<int> vi ;
typedef vector<ii> vii ;
#define fi first
#define se second
#define pb push_back
#define endl '\n'
#define all(a) a.begin(),a.end()
#define FOR(i,a,b) for(int i(a) ; i <= (int)(b) ; i++)
#define FORD(i,a,b) for(int i(a) ; i >= (int)(b) ; i--)
#define FORN(i,a,b) for(int i(a) ; i < (int)b ; i++)
#define sz(a) (int)a.size()
#define MASK(a) (1ll << (i))
#define BIT(mask,i) ((mask>>i)&1)
template<class X, class Y> bool maxi(X &x, const Y &y) {return (x < y ? x = y, 1 : 0) ;}
template<class X, class Y> bool mini(X &x, const Y &y) {return (x > y ? x = y, 1 : 0) ;}
const int MAXN = 3e5 + 5 ;
const int mod = 1e9 + 7 ;
const ll inf = 1e18 ;
const int oo = 2e9 ;
int n , m , S , T , U , V ;
vii g[MAXN] ;
int dist[MAXN][4] ;
int best[MAXN][4] ;
int ans ;
void init() {
cin >> n >> m ;
cin >> S >> T ;
cin >> U >> V ;
FOR(i,1,m) {
int u , v , w ; cin >> u >> v >> w ;
g[u].pb(ii(v,w)) ; g[v].pb(ii(u,w)) ;
}
}
void dijkstra(int st,int type) {
FOR(i,1,n) dist[i][type] = inf ;
dist[st][type] = 0 ;
priority_queue<ii,vector<ii>,greater<ii>> pq ;
pq.push({0 , st}) ;
while(!pq.empty()) {
int u = pq.top().se ;
int c = pq.top().fi ;
pq.pop() ;
if(c > dist[u][type]) continue ;
for(auto [v,w] : g[u]) {
if(mini(dist[v][type],c+w)) {
pq.push({c + w , v}) ;
}
}
}
}
void dfs(int u) {
best[u][0] = dist[u][1] ;
best[u][1] = dist[u][2] ;
for(auto [v,w] : g[u]) {
if( (dist[v][0] + w) != dist[u][0]) continue ;
dfs(v) ;
mini(best[u][0],best[v][0]) ;
mini(best[u][1],best[v][1]) ;
}
mini(ans,best[u][0] + dist[u][2]) ;
mini(ans,best[u][1] + dist[u][1]) ;
}
void solve() {
dijkstra(S,0) ;
dijkstra(U,1) ;
dijkstra(V,2) ;
ans = dist[V][1] ;
dfs(T) ;
cout << ans ;
}
signed main() {
#define task "bus"
ios_base::sync_with_stdio(0) ; cin.tie(0) ; cout.tie(0) ;
if(fopen(task".inp","r")) {
freopen(task".inp","r",stdin) ; freopen(task".out","w",stdout) ;
}
init() ; solve() ;
cerr << "TIME : " << clock() * 0.001 << "s" << endl ;
return 0 ;
}
