#include <bits/stdc++.h>
using namespace std;
const long long INF=1e18;
struct Edge
{
int to, weight;
};
int n,m,s,t,u,v;
vector<vector<Edge>> adj;
void dijkstra(int start, vector<long long>& dist)
{
fill(dist.begin(), dist.end(), INF);
dist[start]=0;
priority_queue<pair<long long,int>, vector<pair<long long,int>>, greater<pair<long long,int>>> pq;
pq.push({0,start});
while(!pq.empty())
{
long long d=pq.top().first;
int u=pq.top().second;
pq.pop();
if(d>dist[u])
{
continue;
}
for(const auto& e : adj[u])
{
if(dist[u]+e.weight<dist[e.to])
{
dist[e.to]=dist[u]+e.weight;
pq.push({dist[e.to], e.to});
}
}
}
}
long long dag(const vector<long long>& ds, const vector<long long>& dt, const vector<long long>& du, const vector<long long>& dv)
{
long long sp=ds[t];
vector<int> nodes;
for(int i=1; i<=n; i++)
{
if(ds[i]!=INF && dt[i]!=INF && ds[i]+dt[i]==sp)
{
nodes.push_back(i);
}
}
sort(nodes.begin(), nodes.end(), [&](int a, int b)
{
return ds[a]<ds[b];
});
vector<long long> ndu(n+1,INF);
long long current=INF;
for(int u : nodes)
{
if(du[u]<ndu[u])
{
ndu[u]=du[u];
}
if(ndu[u]!=INF && dv[u]!=INF)
{
long long cost=ndu[u]+dv[u];
if(cost<current)
{
current=cost;
}
}
for(const auto& e : adj[u])
{
if(ds[u]+e.weight+dt[e.to]==sp)
{
int v=e.to;
if(ndu[u]<ndu[v])
{
ndu[v]=ndu[u];
}
}
}
}
return current;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cin>>n>>m>>s>>t>>u>>v;
adj.resize(n+1);
for(int i=0; i<m; i++)
{
int q,w,e;
cin>>q>>w>>e;
adj[q].push_back({w,e});
adj[w].push_back({q,e});
}
vector<long long> ds(n+1);
vector<long long> dt(n+1);
vector<long long> du(n+1);
vector<long long> dv(n+1);
dijkstra(s,ds);
dijkstra(t,dt);
dijkstra(u,du);
dijkstra(v,dv);
long long ans=du[v];
ans=min(ans, dag(ds,dt,du,dv));
ans=min(ans,dag(ds,dt,dv,du));
cout<<ans<<endl;
return 0;
}
