#include<bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define f first
#define s second
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pb push_back
#define epb emplace_back
using namespace std;
const int NMAX = 1e5 + 1;
vector <vector <pll> > g(NMAX);
ll d[NMAX][4];
vector <vector <int> > p(NMAX);
void Dijkstra(int n, int s, int ind){
d[s][ind] = 0;
priority_queue <pll> q;
q.push({0, s});
vector <bool> used(n + 1);
while(!q.empty()){
int v = q.top().s;
q.pop();
if(used[v]) continue;
used[v] = true;
for(auto x : g[v]){
int to = x.f;
ll l = x.s;
if(d[to][ind] > d[v][ind] + l){
d[to][ind] = d[v][ind] + l;
q.push({-d[to][ind], to});
if(!ind){
p[to].clear();
p[to].pb(v);
}
}
else{
if(d[to][ind] == d[v][ind] + l){
if(!ind) p[to].pb(v);
}
}
}
}
}
vector <vector <int> > G(NMAX);
stack <int> st;
vector <bool> used(NMAX, false);
void dfs(int v){
used[v] = true;
for(int to : G[v]){
if(used[to]) continue;
dfs(to);
}
st.push(v);
}
int main(){
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int x, y; cin >> x >> y;
for(int i = 1; i <= m; i++){
int u, v;
ll c;
cin >> u >> v >> c;
g[u].pb({v, c});
g[v].pb({u, c});
}
for(int i = 1; i <= n; i++){
for(int j = 0; j < 4; j++) d[i][j] = 1e18;
}
Dijkstra(n, s, 0);
Dijkstra(n, t, 1);
Dijkstra(n, x, 2);
Dijkstra(n, y, 3);
for(int i = 1; i <= n; i++){
for(int to : p[i]) G[to].pb(i);
}
dfs(s);
ll ans[n + 1];
for(int i = 1; i <= n; i++){
ans[i] = 1e18;
}
ll res = 1e18;
while(!st.empty()){
int v = st.top();
st.pop();
if(d[t][0] != d[v][0] + d[v][1]) continue;
ans[v] = min(d[v][2], ans[v]);
res = min(res, ans[v] + d[v][3]);
for(int to : G[v]){
ans[to] = min(ans[to], ans[v]);
}
}
cout << res;
return 0;
}
