#include <bits/stdc++.h>
#include <climits>
using namespace std;
#define f first
#define s second
#define all(a) a.begin(),a.end()
#define sz(a) (int)a.size()
#define int long long
const int N=1e5+5;
const int INF=1e16;
int n,m;
vector<pair<int,int>>E[N];
int D[N];
int par[N];
void Dij(int s){
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
for(int i=1;i<=n;++i){
D[i]=INF;
par[i]=i;
}
D[s]=0;
pq.push({0,s});
while(!pq.empty()){
auto [d,u] =pq.top();
pq.pop();
if(D[u]!=d) continue;
for(auto [v,w]:E[u]){
if(D[v]>D[u]+w){
D[v]=D[u]+w;
pq.push({D[v],v});
par[v]=u;
}
}
}
}
vector<pair<int,int>>can;
void Dij2(int s){
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
for(int i=1;i<=n;++i){
D[i]=INF;
par[i]=i;
}
D[s]=0;
pq.push({0,s});
while(!pq.empty()){
auto [d,u] =pq.top();
pq.pop();
if(D[u]!=d) continue;
for(auto [v,w]:E[u]){
int temp=D[u]+w;
int u1=min(u,v);
int v1=max(u,v);
int p=lower_bound(all(can),make_pair(u1,v1))-can.begin();
if(can[p]==make_pair(u1,v1)) temp=0;
if(D[v]>temp){
D[v]=temp;
pq.push({D[v],v});
par[v]=u;
}
}
}
}
void solve(){
cin>>n>>m;
int s,t;
cin>>s>>t;
int U,V;cin>>U>>V;
for(int i=1;i<=m;++i) {
int u,v,w;cin>>u>>v>>w;
E[u].push_back({v,w});
E[v].push_back({u,w});
}
Dij(s);
while(par[t]!=t){
can.push_back({min(t,par[t]),max(t,par[t])});
t=par[t];
}
sort(all(can));
Dij2(U);
cout<<D[V];
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);
int T=1;
while(T--) solve();
}
