//___ ___ _ _ _____ _
//| \/ | | | | | / ___| | |
//| . . | __ _ __| | ___ | |__ _ _ \ `--. __ _ _ _| |
//| |\/| |/ _` |/ _` |/ _ \ | '_ \| | | | `--. \/ _` | | | | |
//| | | | (_| | (_| | __/ | |_) | |_| | /\__/ / (_| | |_| | |
//\_| |_/\__,_|\__,_|\___| |_.__/ \__, | \____/ \__,_|\__,_|_|
// __/ |
// |___/
#include <bits/stdc++.h>
#define endl '\n'
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
using namespace std;
#define int long long
void openFile(){
#define NAME "NAME"
if (fopen(NAME".INP","r")==NULL) return;
freopen(NAME".INP","r",stdin);
freopen(NAME".OUT","w",stdout);
}
const int N=1e5;
int n,m;
int s,t,u,v;
vector<pair<int,int> > edge[N+5];
int distU[N+5];
int distV[N+5];
int dist[N+5];
int ans;
int miU[N+5];
int miV[N+5];
void djk1(){
memset(distU,0x3f,sizeof(distU));
memset(distV,0x3f,sizeof(distV));
distU[u]=0;
distV[v]=0;
priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > > pq;
pq.push({0,u});
while(!pq.empty()){
int d=pq.top().fi;
int c=pq.top().se;
pq.pop();
if(distU[c]<d) continue;
for(pair<int,int> pii :edge[c]){
int x=pii.fi;
int w=pii.se;
int nd=d+w;
if(distU[x]>nd){
distU[x]=nd;
pq.push({nd,x});
}
}
}
pq.push({0,v});
while(!pq.empty()){
int d=pq.top().fi;
int c=pq.top().se;
pq.pop();
if(distV[c]<d) continue;
for(pair<int,int> pii :edge[c]){
int x=pii.fi;
int w=pii.se;
int nd=d+w;
if(distV[x]>nd){
distV[x]=nd;
pq.push({nd,x});
}
}
}
}
void djk2(int st,int ed){
memset(dist,0x3f,sizeof(dist));
memset(miU,0x3f,sizeof(miU));
memset(miV,0x3f,sizeof(miV));
priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > > pq;
pq.push({0,st});
miU[st]=distU[st];
miV[st]=distV[st];
while(!pq.empty()){
int d=pq.top().fi;
int c=pq.top().se;
pq.pop();
if(dist[c]<d) continue;
for(pair<int,int> pii:edge[c]){
int x=pii.fi;
int w=pii.se;
int nd=d+w;
if(dist[x]>nd){
dist[x]=nd;
miU[x]=min(distU[x],miU[c]);
miV[x]=min(distV[x],miV[c]);
pq.push({nd,x});
}
else if(dist[x]==nd){
if(min(distU[x],miU[c])+min(distV[x],miV[c])<miU[x]+miV[x]){
miU[x]=min(distU[x],miU[c]);
miV[x]=min(distV[x],miV[c]);
}
pq.push({nd,x});
}
}
}
ans=min(ans,miU[ed]+miV[ed]);
}
void solve(){
cin>>n>>m>>s>>t>>u>>v;
for(int i=1;i<=m;i++){
int u,v,w; cin>>u>>v>>w;
edge[u].push_back({v,w});
edge[v].push_back({u,w});
}
djk1();
ans=distU[v];
djk2(s,t);
djk2(t,s);
cout<<ans;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
openFile();
solve();
return 0;
}
