#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ld long double
#define show(x,y) cout << y << " " << #x << endl;
#define show2(x,y,i,j) cout << y << " " << #x << " " << j << " " << #i << endl;
#define show3(x,y,i,j,p,q) cout << y << " " << #x << " " << j << " " << #i << " " << q << " " << #p << endl;
#define show4(x,y) for(auto it:y) cout << it << " "; cout << #x << endl;
typedef pair<long long,int>pii;
typedef pair<int,pii>pi2;
vector<pii>adj[100005];
void solve(){
int n,m;
cin >> n >> m;
int a,b;
cin >> a >> b;
int s,t;
cin >> s >> t;
int temp,temp2,temp3;
for(int x=0;x<m;x++){
cin >> temp >> temp2 >> temp3;
adj[temp].push_back({temp2,temp3});
adj[temp2].push_back({temp,temp3});
}
int dist[n+5]; //a
int dist2[n+5]; //b
memset(dist,-1,sizeof(dist));
memset(dist2,-1,sizeof(dist2));
priority_queue<pii,vector<pii>,greater<pii>>pq;
dist[a]=0;
pq.push({0,a});
while(!pq.empty()){
pii cur=pq.top();
pq.pop();
int index=cur.second;
int d=cur.first;
if(dist[index]!=d) continue;
for(auto it:adj[index]){
int nx=it.first;
int nd=d+it.second;
if(dist[nx]!=-1&&dist[nx]<=nd) continue;
dist[nx]=nd;
pq.push({nd,nx});
}
}
dist2[b]=0;
pq.push({0,b});
while(!pq.empty()){
pii cur=pq.top();
pq.pop();
int index=cur.second;
int d=cur.first;
if(dist2[index]!=d) continue;
for(auto it:adj[index]){
int nx=it.first;
int nd=d+it.second;
if(dist2[nx]!=-1&&dist2[nx]<=nd) continue;
dist2[nx]=nd;
pq.push({nd,nx});
}
}
priority_queue<pi2,vector<pi2>,greater<pi2>>pq2;
int dist3[n+5][5];
memset(dist3,-1,sizeof(dist3));
dist3[s][0]=0;
pq2.push({0,{s,0}});
int target=dist[b];
while(!pq2.empty()){
pi2 cur=pq2.top();
pq2.pop();
int index=cur.second.first;
int k=cur.second.second;
int d=cur.first;
//show3(index,index,k,k,d,d);
for(auto it:adj[index]){
int nx=it.first;
int path=0;
if(dist[index]+it.second+dist2[nx]==target) path=1;
if(dist[nx]+it.second+dist2[index]==target) path=2;
if(k==0){
if( !(dist3[nx][k]!=-1&&dist3[nx][k]<=d+it.second) ){
dist3[nx][k]=d+it.second;
pq2.push({d+it.second,{nx,k}});
}
if( !(dist3[nx][path]!=-1&&dist3[nx][path]<=d) && (path!=0) ){
dist3[nx][path]=d;
pq2.push({d,{nx,path}});
}
}
else if(k==1||k==2){
if(path==k){
if( !(dist3[nx][path]!=-1&&dist3[nx][path]<=d) ){
dist3[nx][path]=d;
pq2.push({d,{nx,path}});
}
}
else{
if( !(dist3[nx][3]!=-1&&dist3[nx][3]<=d+it.second) ){
dist3[nx][3]=d+it.second;
pq2.push({d+it.second,{nx,3}});
}
}
}
else if(k==3){
if( !(dist3[nx][k]!=-1&&dist3[nx][k]<=d+it.second) ){
dist3[nx][k]=d+it.second;
pq2.push({d+it.second,{nx,k}});
}
}
}
}
int best=1e18;
for(int x=0;x<4;x++){
if(dist3[t][x]==-1) continue;
best=min(best,dist3[t][x]);
}
cout << best;
}
int32_t main(){
ios::sync_with_stdio(0);
cin.tie(0);
int t=1;
//cin >> t;
while(t--){
solve();
}
}
