#include <bits/stdc++.h>
// include <ext/pb_ds/assoc_container.hpp>
// include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
using namespace std;
#define all(x) x.begin(), x.end()
#define pb push_back
// define ordered_set tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update>
#define mpr make_pair
#define ln '\n'
void IO(string name){freopen((name+".in").c_str(),"r",stdin); freopen((name+".out").c_str(),"w",stdout);}
#define int long long
bool chmin(int &x, int y){
bool flag = false;
if ( x > y ){
x = y; flag |= true;
}
return flag;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n, m; cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
--s, --t, --u, --v;
vector <pair<int,int>> g[n];
for ( int i = 1; i <= m; i++ ){
int x, y, w; cin >> x >> y >> w;
g[--x].pb({--y, w});
g[y].pb({x, w});
}
const int inf = 1e17+1;
auto F = [&](int st){
vector <int> dis(n, inf);
dis[st] = 0;
priority_queue <pair<int,int>> q;
q.push({0, st});
while ( !q.empty() ){
auto [val, cur] = q.top();
q.pop(); val = -val;
if ( val != dis[cur] ) continue;
for ( auto [to, w]: g[cur] ){
if ( chmin(dis[to], val+w) ){
q.push({-dis[to], to});
}
}
}
return dis;
};
auto S = F(s), T = F(t), U = F(u), V = F(v);
vector <pair<int,int>> _list;
for ( int i = 0; i < n; i++ ){
if ( S[i]+T[i] == S[t] ){
_list.pb({T[i], i});
}
}
sort(all(_list), greater <pair<int,int>> ());
vector <int> dpU(n, inf), dpV(n, inf);
int Mn = U[v];
for ( auto [val, it]: _list ){
dpU[it] = U[it];
dpV[it] = V[it];
for ( auto [to, w]: g[it] ){
if ( T[it]+w == T[to] ){
chmin(dpU[it], dpU[to]);
chmin(dpV[it], dpV[to]);
}
}
chmin(Mn, dpU[it]+V[it]);
chmin(Mn, dpV[it]+U[it]);
}
cout << Mn;
cout << '\n';
}
