#include <bits/stdc++.h>
using namespace std;
vector<pair<int, int>>M[100001];
bool biju [100001]={};
long long U[100001]={};
long long V[100001]={};
long long bals[100001]={};
priority_queue<tuple<long long, long long, long long, long long, int>, vector<tuple<long long, long long, long long, long long, int>>, greater<tuple<long long, long long, long long, long long, int>>>pq={};
long long nxt(){
long long n;
cin>>n;
return n;
}
void DjikstrasimU(int sak){
U[sak]=0, pq.push(make_tuple(0, sak, 0, 0, 0));
while(pq.size()!=0){
int v=get<1>(pq.top());
long long att=get<0>(pq.top());
pq.pop();
if(biju[v]==0){
biju[v]=1;
for(auto c: M[v]){
if(att+c.second<U[c.first]){
U[c.first]=att+c.second, pq.push(make_tuple(U[c.first], c.first, 0, 0, 0));
}
}
}
}
}
void DjikstrasimV(int sak){
V[sak]=0, pq.push(make_tuple(0, sak, 0, 0, 0));
while(pq.size()!=0){
int v=get<1>(pq.top());
long long att=get<0>(pq.top());
pq.pop();
if(biju[v]==0){
biju[v]=1;
for(auto c: M[v]){
if(att+c.second<V[c.first]){
V[c.first]=att+c.second, pq.push(make_tuple(V[c.first], c.first, 0, 0, 0));
}
}
}
}
}
long long Djikstra(int sak, int ender, long long iss){
bals[sak]=0;
pq.push(make_tuple(0,min(V[sak]+U[sak], iss), V[sak], U[sak], sak));
while(get<4>(pq.top())!=ender){
int v=get<4>(pq.top());
long long att=get<0>(pq.top()), minv=get<2>(pq.top()), minu=get<3>(pq.top()), mini=get<1>(pq.top());
//cout<<v<<' '<<minv<<' '<<minu<<' '<<U[v]<<' '<<V[v]<<' '<<mini<<'\n';
pq.pop();
if(biju[v]==0){
biju[v]=1;
for(auto c: M[v]){
long long u=c.first, dist=c.second;
if(dist+att<=bals[u])
bals[u]=dist+att, pq.push(make_tuple(bals[u], min({minv+U[u], minu+V[u], V[u]+U[u], mini}), min(V[u], minv), min(U[u], minu), u));
}
}
}
return get<1>(pq.top());
}
int main()
{
long long n, m, s, t, u, v, sk1, sk2, sv;
cin>>n>>m>>s>>t>>u>>v;
for(int i=0; i<m; i++){
sk1=nxt(), sk2=nxt(), sv=nxt();
M[sk1].push_back({sk2, sv});
M[sk2].push_back({sk1, sv});
}
for(int i=1; i<=n; i++)U[i]=LONG_LONG_MAX, V[i]=LONG_LONG_MAX,
bals[i]=LONG_LONG_MAX;
DjikstrasimU(u);
fill(biju, biju+n+1, 0);
DjikstrasimV(v);
fill(biju, biju+n+1, 0);
cout<<Djikstra(s, t, U[v])<<endl;
return 0;
}
