#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define bupol __builtin_popcount
#define int long long
#define ll long long
#define ld long double
#define fi first
#define se second
#define pb push_back
#define lf (id<<1)
#define rg ((id<<1)|1)
#define md ((l+r)>>1)
using namespace std;
const int MAXN = 2e5+5;
const int LOG = 20;
const int MOD = 1e9+7;
const int SQRT = 520;
const int INF = 1e18;
typedef pair<int,int> pii;
typedef pair<int,pii> ipii;
int n, m;
int s, t, x, y;
int u[MAXN], v[MAXN], c[MAXN];
vector <pii> adj[MAXN];
int dis[MAXN];
priority_queue<pii, vector<pii>, greater<pii>> pq;
map<pii,int> ma;
void dji(int sta){
for(int i=1; i<=n; i++) dis[i] = INF;
pq.push({0, sta});
dis[sta] = 0;
while(!pq.empty()){
int tp = pq.top().se; int dist = pq.top().fi; pq.pop();
if(dis[tp] < dist) continue;
for(auto ed : adj[tp]){
int nx = ed.fi; int wei = ed.se;
if(dis[nx] > dist+wei){
dis[nx] = dist+wei;
pq.push({dis[nx], nx});
}
}
}
}
signed main(){
//ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin >> n >> m;
cin >> s >> t; cin >> x >> y;
for(int i=1; i<=m; i++){
cin >> u[i] >> v[i] >> c[i];
if(u[i] > v[i]) swap(u[i], v[i]);
ma[pii(u[i], v[i])] = i;
adj[u[i]].pb({v[i], c[i]}); adj[v[i]].pb({u[i], c[i]});
}
dji(s);
//cout << dis[t] << " dis\n";
vector <int> path; path.pb(t);
int nw = t, dist = dis[t];
while(nw != s){
for(auto ed : adj[nw]){
if(dis[ed.fi] == dist-ed.se){
path.pb(ed.fi); nw = ed.fi;
dist -= ed.se; break;
}
}
}
for(int i=0; i+1<path.size(); i++){
int nw = path[i], nx = path[i+1];
if(nw > nx) swap(nw, nx);
int idx = ma[pii(nw, nx)];
c[idx] = 0;
}
for(int i=1; i<=n; i++) adj[i].clear();
for(int i=1; i<=m; i++){
adj[u[i]].pb({v[i], c[i]}); adj[v[i]].pb({u[i], c[i]});
}
dji(x);
cout << dis[y] << '\n';
}
