#include<bits/stdc++.h>
#define ll long long
#define int ll
#define pii pair<int,int>
#define tiii tuple<int,int,int>
using namespace std;
ll INF = numeric_limits<ll>::max()/4;
int32_t main(){
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
s--;t--;
int ug, vg;
cin >> ug >> vg;
ug--;vg--;
vector<vector<pii>> 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});
}
// Shortest paths from s to t
vector<int> dist(n,INF);
vector<set<int>> pre(n);
priority_queue<tiii, vector<tiii>, greater<tiii>> pq;
pq.push({0,s,s});
while(pq.size()){
int d, v, p;
tie(d,v,p) = pq.top();
pq.pop();
if(dist[v] < d) continue;
pre[v].insert(p);
if(dist[v] == d) continue;
dist[v] = d;
for(auto pa : adj[v]){
pq.push({pa.second+d, pa.first, v});
}
}
// run Dijkstra again
vector<int> dist2(n,INF);
pq.push({0,ug,ug});
while(pq.size()){
int d, v, p;
tie(d,v,p) = pq.top();
pq.pop();
if(dist2[v] <= d) continue;
dist2[v] = d;
for(auto pa : adj[v]){
pq.push({pa.second+d, pa.first, v});
}
}
// run Dijkstra again
vector<int> distVG(n,INF);
pq.push({0,vg,vg});
while(pq.size()){
int d, v, p;
tie(d,v,p) = pq.top();
pq.pop();
if(distVG[v] <= d) continue;
distVG[v] = d;
for(auto pa : adj[v]){
pq.push({pa.second+d, pa.first, v});
}
}
// remove add help vertices
queue<tiii> q; set<pii> used;
int mi = INF;
// cur | pre
q.push({t,t, INF});
while(q.size())
{
int v, u, d;
tie(v,u,d) = q.front();
q.pop();
//adj[v].push_back({u,0});
mi = min(mi, dist2[v] + d);
used.insert({v,u});
int newd = min(d, distVG[v]);
for(auto w : pre[v]){
if(!used.count({w,v}) && w != v)q.push({w,v,newd});
if(!used.count({w,v}) && w != v)q.push({v,w,newd});
}
}
cout << mi <<endl;
}
