#include<bits/stdc++.h>
using namespace std;
#define int int64_t
#define all(x) x.begin(),x.end()
#define all1(x) x.rbegin(),x.rend()
#define sz(x) (int)(x.size())
const int N=1e5+5,N1=1e18,mod=1e9+7;
template<class T> using min_heap=priority_queue<T,vector<T>,greater<T>>;
vector<int> adj1[N],adj2[N],adj3[N],disv(N,N1);
int memo[N];
int dp(int u){
if (memo[u]!=-1){return memo[u];}
int best=disv[u];
for (int it:adj1[u]){
best=min(best,dp(it));
}
return memo[u]=best;
}
int memo1[N];
int dpback(int u){
if (memo1[u]!=-1){return memo1[u];}
int best=disv[u];
for (int it:adj2[u]){
best=min(best,dpback(it));
}
return memo1[u]=best;
}
void solve(){
int n,m,s,t,u,v;
cin>>n>>m>>s>>t>>u>>v;
using gh=pair<int,int>;
vector<gh> adj[n+1];
for (int i=1,x,y,w;i<=m;i++){
cin>>x>>y>>w;
adj[x].emplace_back(y,w);
adj[y].emplace_back(x,w);
}
vector<int> disu(n+1,N1);
min_heap<pair<int,int>> q;
q.emplace(0,u);
disu[u]=0;
while(!q.empty()){
int nd,dis;
tie(dis,nd)=q.top();
q.pop();
for (const pair<int,int> &it:adj[nd]){
if (disu[it.first]>disu[nd]+it.second){
disu[it.first]=disu[nd]+it.second;
q.emplace(disu[it.first],it.first);
}
}
}
disv[v]=0;
q.emplace(0,v);
while(!q.empty()){
int nd,dis;
tie(dis,nd)=q.top();
q.pop();
for (const pair<int,int> &it:adj[nd]){
if (disv[it.first]>disv[nd]+it.second){
disv[it.first]=disv[nd]+it.second;
q.emplace(disv[it.first],it.first);
}
}
}
vector<int> curdis(n+1,N1);
curdis[s]=0;
q.emplace(0,s);
while(!q.empty()){
int nd,dis;
tie(dis,nd)=q.top();
q.pop();
for (const pair<int,int> &it:adj[nd]){
if (curdis[it.first]>curdis[nd]+it.second){
curdis[it.first]=curdis[nd]+it.second;
adj1[it.first].clear();
adj1[it.first].emplace_back(nd);
q.emplace(curdis[it.first],it.first);
}
else if (curdis[it.first]==curdis[nd]+it.second){
adj1[it.first].emplace_back(nd);
}
}
}
vector<bool> curvis(n+1);
queue<int> q1;
q1.emplace(t);
while(!q1.empty()){
int nd=q1.front();
q1.pop();
if (!curvis[nd]){
curvis[nd]=1;
for (int it:adj1[nd]){
adj2[it].emplace_back(nd);
q1.emplace(it);
}
}
}
memset(memo,-1,sizeof(memo));
memset(memo1,-1,sizeof(memo1));
int ans=disu[v];
for (int i=1;i<=n;i++){
if (!curvis[i]){continue;}
ans=min(ans,disu[i]+min(dp(i),dpback(i)));
}
cout<<ans;
}
int32_t main(){
ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
int tq=1;
//cin>>tq;
for (;tq;tq--){solve();}
}
