#include <bits/stdc++.h>
#define endl "\n"
#define int long long
#define pii pair<int,int>
#define piii pair<int,pii>
#define fi first
#define se second
using namespace std;
const int maxn = 2e5+10;
const int INF = 1e18;
int n,m,s,t,u,v;
vector<pii> a[maxn];
vector<int> b[maxn];
int dist[maxn],du[maxn],dv[maxn];
bool valid[maxn];
piii dp[maxn];
void dijkstra(int s, int dist[]){
for (int i=1; i<=n; i++){
dist[i] = INF;
}
priority_queue<pii,vector<pii>,greater<pii>> pq;
dist[s] = 0;
pq.push({0,s});
while (!pq.empty()){
int u = pq.top().se;
int d = pq.top().fi;
pq.pop();
for (auto in:a[u]){
int v = in.fi;
int delta = in.se;
if (dist[v] > d+delta){
dist[v] = d+delta;
pq.push({d+delta,v});
}
}
}
}
void meow(int s){
priority_queue<pii> pq;
pq.push({dist[s],s});
valid[s] = true;
while (!pq.empty()){
int u = pq.top().se;
int d = pq.top().fi;
pq.pop();
dp[u].se.fi = min(dp[u].se.fi,du[u]);
dp[u].se.se = min(dp[u].se.se,dv[u]);
if (dp[u].fi > dp[u].se.fi + dv[u]){
dp[u].fi = dp[u].se.fi + dv[u];
}
if (dp[u].fi > dp[u].se.se + du[u]){
dp[u].fi = dp[u].se.se + du[u];
}
for (auto in:a[u]){
int v = in.fi;
int delta = in.se;
if (d - delta == dist[v]){
if (!valid[v]){
valid[v] = true;
pq.push({d-delta,v});
}
dp[v].fi = min(dp[v].fi,dp[u].fi);
dp[v].se.fi = min(dp[v].se.fi,dp[u].se.fi);
dp[v].se.se = min(dp[v].se.se,dp[u].se.se);
}
}
}
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
while (m--){
int x,y,z;
cin >> x >> y >> z;
a[x].push_back({y,z});
a[y].push_back({x,z});
}
dijkstra(s,dist);
dijkstra(u,du);
dijkstra(v,dv);
// for (int i=1; i<=n; i++){
// cout << dist[i] << " ";
// }
// cout << endl;
for (int i=1; i<=n; i++){
dp[i] = {INF,{INF,INF}};
}
meow(t);
cout << min(dp[s].fi,du[v]);
return 0;
}
