#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ld long double
#define fi first
#define se second
#define pb push_back
#define pii pair<int,int>
#define piii pair<pair<int,int>,pair<int,int>>
#define pip pair<int,pair<int,int>>
vector<pii>adj[100005];
int dis[100005];
int disu[100005], disv[100005];
vector<int>bef[100005];
bool vis[100005];
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
int n, m; cin >> n >> m;
int s,t; cin >> s >> t;
int u,v; cin >> u >> v;
for(int i = 1; i <= m; i++){
int x, y, w; cin >> x >> y >> w;
adj[x].pb({y,w});
adj[y].pb({x,w});
}
priority_queue<pii, vector<pii>, greater<pii>>pq;
pq.push({0,u});
for(int i = 1; i <= n; i++)disu[i] = 1e18;
disu[u] = 0;
while(!pq.empty()){
int jarak = pq.top().fi, node = pq.top().se;
pq.pop();
if(jarak != disu[node])continue;
for(auto it : adj[node]){
int curr = jarak + it.se;
if(curr < disu[it.fi]){
disu[it.fi] = curr;
pq.push({curr, it.fi});
}
}
}
pq.push({0,v});
for(int i = 1; i <= n; i++)disv[i] = 1e18;
disv[v] = 0;
while(!pq.empty()){
int jarak = pq.top().fi, node = pq.top().se;
pq.pop();
if(jarak != disv[node])continue;
for(auto it : adj[node]){
int curr = jarak + it.se;
if(curr < disv[it.fi]){
disv[it.fi] = curr;
pq.push({curr, it.fi});
}
}
}
for(int i = 1; i <= n; i++)dis[i] = 1e18;
dis[s] = 0;
priority_queue<pip,vector<pip>,greater<pip>>peq;
peq.push({0,{s, -1}});
while(!peq.empty()){
int jarak = peq.top().fi, node = peq.top().se.fi, par = peq.top().se.se;
peq.pop();
if(jarak != dis[node])continue;
if(par != -1){
bef[node].pb(par);
}
//cout << "here >> " << node << " " << disu[node] << " " << disv[node] << endl;
if(node == t)break;
for(auto it : adj[node]){
int curr = jarak + it.se;
if(curr <= dis[it.fi]){
dis[it.fi] = curr;
peq.push({curr, {it.fi, node}});
}
}
}
while(!peq.empty()){
int jarak = peq.top().fi, node = peq.top().se.fi, par = peq.top().se.se;
peq.pop();
if(node == t && jarak == dis[t] && par != -1){
bef[node].pb(par);
}
}
priority_queue<piii, vector<piii>, greater<piii>>q;
q.push({{disu[t] + disv[t], t}, {disu[t],disv[t]}});
for(int i = 1; i <= n; i++)dis[i] = 1e18;
dis[t] = disu[t] + disv[t];
int ans = disu[v];
// for(auto it : bef[t]){
// cout << "here >> " << it << endl;
// }
//cout << "here >> " << q.top().fi.se << endl;
while(!q.empty()){
int node = q.top().fi.se, jarak = q.top().fi.fi, valu = q.top().se.fi, valv = q.top().se.se;
//cout << "here >> " << node << endl;
q.pop();
if(jarak != dis[node])continue;
if(node == s){
//cout << "here" << endl;
ans = min(ans, jarak);
continue;
}
for(auto it : bef[node]){
//cout << "here1 >> " << it << endl;
int curr = min(jarak, min(valu, disu[it]) + min(valv, disv[it]));
if(curr < dis[it]){
//cout << "here >> " << it << endl;
dis[it] = curr;
q.push({{curr, it}, {min(valu, disu[it]), min(valv, disv[it])}});
}
}
}
cout << ans << endl;
}
