#include <bits/stdc++.h>
using namespace std;
vector<pair<int, int>>M[100001];
long long U[100001]={};
long long V[100001]={};
long long bals[100001]={};
long long kopy[100001]={};
priority_queue<tuple<long long, int, long long, long long>, vector<tuple<long long, int, long long, long long>>, greater<tuple<long long, int, long long, long long>>>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));
while(pq.size()!=0){
int v=get<1>(pq.top());
long long att=get<0>(pq.top());
pq.pop();
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));
}
}
}
}
void DjikstrasimV(int sak){
V[sak]=0, pq.push(make_tuple(0, sak, 0, 0));
while(pq.size()!=0){
int v=get<1>(pq.top());
long long att=get<0>(pq.top());
pq.pop();
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));
}
}
}
}
long long Djikstra(int sak, int ender, long long iss){
bals[sak]=0;
pq.push(make_tuple(0, sak, V[sak], U[sak]));
while(!pq.empty()){
//cout<<get<1>(pq.top())<<' '<<get<4>(pq.top())<<' '<<get<2>(pq.top())<<' '<<get<3>(pq.top())<<'\n';
int v=get<1>(pq.top());
long long att=get<0>(pq.top()), vak=get<2>(pq.top()), uak=get<3>(pq.top());
pq.pop();
for(auto c: M[v]){
if(c.second+att<=bals[c.first]&&kopy[c.first]>=min(vak, V[c.first])+min(uak, U[c.first]))bals[c.first]=c.second+att, kopy[c.first]=min(vak, V[c.first])+min(uak, U[c.first]), pq.push(make_tuple(bals[c.first], c.first, min(vak, V[c.first]), min(uak, U[c.first]))); }
}
return min(iss, kopy[ender]);
}
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});
}
fill(U, U+n+1, LONG_LONG_MAX);
fill(V, V+n+1, LONG_LONG_MAX);
fill(bals, bals+n+1, LONG_LONG_MAX);
fill(kopy, kopy+n+1, LONG_LONG_MAX);
DjikstrasimU(u);
DjikstrasimV(v);
cout<<Djikstra(s, t, U[v])<<endl;
return 0;
}
