#include<bits/stdc++.h>
using namespace std;
#define endl "\n"
typedef long long int ll;
const int MOD = 1e9 + 7;
void Dijkstra(vector<vector<pair<int, ll>>>& adj, vector<ll>& dist, int initial){
int n = (int)adj.size();
vector<bool> vis(n, 0);
dist[initial] = 0;
priority_queue<pair<ll, int>> pq;
pq.push({0, initial});
while(!pq.empty()){
int x = pq.top().second; pq.pop();
if(vis[x]) continue;
vis[x] = 1;
for(auto p : adj[x]){
int node = p.first; ll w = p.second;
if(dist[node] > dist[x] + w){
dist[node] = dist[x] + w;
pq.push({-dist[node], node});
}
}
}
}
void solve(){
int n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v; s--; t--; u--; v--;
vector<vector<pair<int, ll>>> adj(n);
for(int i = 0; i < m; i++){
int a, b, c; cin >> a >> b >> c; a--; b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<ll> distv(n, 1e18);
Dijkstra(adj, distv, v);
vector<ll> distu(n, 1e18);
Dijkstra(adj, distu, u);
vector<ll> distt(n, 1e18);
Dijkstra(adj, distt, t);
vector<ll> dists(n, 1e18);
Dijkstra(adj, dists, s);
ll ans = distv[u];
//Now I should make two more Dijkstras, one with minimum time to u, and the other with minimum time to v.
priority_queue<pair<ll, int>> pq;
vector<ll> mn(n, 1e18);
vector<bool> vis(n, 0);
for(int i = 0; i < n; i++){
if(distt[i] + dists[i] == distt[s]){
mn[i] = distu[i];
pq.push({-mn[i], i});
}
}
while(!pq.empty()){
int x = pq.top().second; pq.pop();
if(vis[x]) continue;
ans = min(ans, mn[x] + distv[x]);
vis[x] = 1;
for(auto p : adj[x]){
int node = p.first; ll w = p.second;
if(dists[node] + distt[x] + w == distt[s] && mn[node] > mn[x]){
mn[node] = mn[x];
pq.push({-mn[node], node});
}
}
}
mn.assign(n, 1e18);
vis.assign(n, 0);
for(int i = 0; i < n; i++){
if(distt[i] + dists[i] == distt[s]){
mn[i] = distv[i];
pq.push({-mn[i], i});
}
}
while(!pq.empty()){
int x = pq.top().second; pq.pop();
if(vis[x]) continue;
ans = min(ans, mn[x] + distu[x]);
vis[x] = 1;
for(auto p : adj[x]){
int node = p.first; ll w = p.second;
if(dists[node] + distt[x] + w == distt[s] && mn[node] > mn[x]){
mn[node] = mn[x];
pq.push({-mn[node], node});
}
}
}
cout << ans << endl;
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
//~ int tt; cin >> tt;
int tt = 1;
for(int t = 1; t <= tt; t++){
solve();
}
}
