#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define endl "\n";
#define vec vector<ll>
#define vecvec vector<vector<ll>>
using namespace std;
/*#define FileName ""
string Ghhhh = ".in";
string Ghhhhh = ".out";
ifstream Girdi(FileName + Ghhhh);
ofstream Cikti(FileName + Ghhhhh);
#define cin Girdi
#define cout */
const ll INF = 1e15;
ll n,m,s,t,u,v;
vector<vector<pair<ll,ll>>> adj;
vector<vector<ll>> dist,dp;
vector<ll> ds;
inline void dijkstra(ll start,ll k){
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> pq;
pq.push({0,start});
dist[k][start] = 0;
while(!pq.empty()){
ll node = pq.top().second;
pq.pop();
for(auto it : adj[node]){
if(dist[k][it.first] > dist[k][node] + it.second){
dist[k][it.first] = dist[k][node] + it.second;
pq.push({dist[k][it.first],it.first});
}
}
}
}
inline ll dijkstra2(ll start, ll end){
fill(ds.begin(),ds.end(),INF);
fill(dp[0].begin(),dp[0].end(),INF);
fill(dp[1].begin(),dp[1].end(),INF);
priority_queue<pair<ll,pair<ll,ll>>, vector<pair<ll,pair<ll,ll>>>, greater<pair<ll,pair<ll,ll>>>> pq;
pq.push({0,{start,0}});
while(!pq.empty()){
ll node = pq.top().second.first;
ll parent = pq.top().second.second;
ll distt = pq.top().first;
pq.pop();
if(ds[node] == INF){
ds[node] = distt;
for(auto go : adj[node]){
pq.push({ds[node] + go.second,{go.first,node}});
}
}
if(ds[node] != distt) continue;
if(min(dp[0][parent],dist[0][node]) + min(dp[1][parent],dist[1][node]) <= (dp[0][node] + dp[1][node])){
dp[0][node] = min(dp[0][parent],dist[0][node]);
dp[1][node] = min(dp[1][parent],dist[1][node]);
}
}
return dp[1][end] + dp[0][end];
}
inline void solve(){
cin >> n >> m >> s >> t >> u >> v;
adj.resize(n+1);
dist.resize(2,vector<ll>(n+1,INF));
dp.resize(2,vector<ll>(n+1));
ds.resize(n+1);
while(m--){
ll a,b,w;
cin >> a >> b >> w;
adj[a].pb({b,w});
adj[b].pb({a,w});
}
dijkstra(u,0);
dijkstra(v,1);
cout << min(min(dijkstra2(t,s),dijkstra2(s,t)),dist[0][v]) << endl;
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
ll t = 1;
//cin >> t;
while(t--){
solve();
}
}
