#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MOD = 1e9+7;
const int N =1e5+5;
const ll INF = 1e18;
int n,m,T;
bool vis[N];
ll du[N],dv[N],ds[N],dt[N],ans;
vector<pair<int,ll> >v[2*N];
priority_queue<pair<ll,int> >pq;
multiset<ll>su,sv;
void Dijkstra(ll *d,int s){
for(int i=1;i<=N;i++)d[i]=INF;
d[s]=0;
pq.push({-d[s],s});
while(!pq.empty()){
auto cur=pq.top();
pq.pop();
for(auto e:v[cur.second]){
if(d[cur.second]+e.second<d[e.first]){
d[e.first]=d[cur.second]+e.second;
pq.push({-d[e.first],e.first});
}
}
}
}
void dfs(int cur){
vis[cur]=true;
su.insert(du[cur]);
sv.insert(dv[cur]);
ans=min(ans,*(su.begin())+dv[cur]);
ans=min(ans,*(sv.begin())+du[cur]);
for(auto e:v[cur]){
if(ds[cur]+e.second+dt[e.first]==ds[T]&&!vis[e.first]){//if e is part of shortest path
dfs(e.first);
}
}
su.erase(su.find(du[cur]));
sv.erase(sv.find(dv[cur]));
}
int main()
{
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
int s,t,a,b,x,y,z;
cin>>n>>m;
cin>>s>>t;
cin>>a>>b;
T=t;
for(int i=1;i<=m;i++){
cin>>x>>y>>z;
v[x].push_back({y,z});
v[y].push_back({x,z});
}
Dijkstra(du,a);
Dijkstra(dv,b);
Dijkstra(ds,s);
Dijkstra(dt,t);
ans=INF;
dfs(s);
for(int i=1;i<=n;i++){
ans=min(ans,du[i]+du[b]);
ans=min(ans,dv[i]+dv[a]);
}
cout<<ans;
return 0;
}
