#include<bits/stdc++.h>
using namespace std ;
#define ll long long
#define ii pair<int,int>
#define lll pair<ll,ll>
#define vi vector<int>
#define vvi vector<vector<int>>
int n,m,s,t,u,v;
ll du[100001],dv[100001],ds[100001],dp[2][100001],ans;
bool vs[100001];
vector<lll>a[100001];
void djk1(int st, ll ar[]){
memset(vs,false,sizeof vs);
for(int i=1;i<=n;i++)ar[i]=1e14;
priority_queue<lll>q;
q.push({0,st});
ar[st]=0;
//cout<<st<<'\n';
while(q.size()){
ll w=-q.top().first,u=q.top().second;
q.pop();
if(vs[u])continue;
vs[u]=true;
for(lll it:a[u]){
int v=it.first,w1=it.second;
if(ar[v]>w1+w){
ar[v]=w1+w;
q.push({-ar[v],v});
}
}
}
}
void djk2(int st,int ed){
memset(dp,31,sizeof dp);
memset(vs,false,sizeof vs);
priority_queue<pair<ll,lll>>q;
q.push({0,{st,0}});
while(q.size()){
ll c=q.top().first,node=q.top().second.first,par=q.top().second.second;
q.pop();
if(!vs[node]){
vs[node]=true;
ds[node]=-c;
dp[0][node]=min(du[node],dp[0][par]);
dp[1][node]=min(dv[node],dp[1][par]);
for(lll it:a[node])q.push({c-it.second,{it.first,node}});
}else if(-c==ds[node]){
if (min(du[node], dp[0][par]) + min(dv[node], dp[1][par]) <=
dp[0][node] + dp[1][node]) {
dp[0][node] = min(du[node], dp[0][par]);
dp[1][node] = min(dv[node], dp[1][par]);
}
}
}
ans=min(dp[0][ed]+dp[1][ed],ans);
}
void sc()
{
cin>>n>>m>>s>>t>>u>>v;
for(int i=1;i<=m;i++){
ll U,V,W;cin>>U>>V>>W;
a[U].push_back({V,W});
a[V].push_back({U,W});
}
djk1(u,du);
djk1(v,dv);
ans=du[v];
// cout<<ans<<'\n';
djk2(s,t);
djk2(t,s);
cout<<ans<<'\n';
}
int main()
{
ios_base :: sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0) ;
sc() ;
return 0 ; ///sc
}
