#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll C=1e9;
const ll M=2e5;
int main(){
ios_base::sync_with_stdio(0);cin.tie(0);
ll n,m,s,t,u,v;
cin>>n>>m>>s>>t>>u>>v;
vector<vector<pair<int,ll>>> adj(n+1);
for(int i=0;i<m;i++){
ll a,b,c;
cin>>a>>b>>c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
vector<ll> cu(n+1,C*M);
cu[u]=0;
queue<int> q;
q.push(u);
while(!q.empty()){
int i=q.front();
q.pop();
for(pair<int,ll> p:adj[i]){
ll j,c;
tie(j,c)=p;
if(cu[j]>cu[i]+c){
cu[j]=cu[i]+c;
q.push(j);
}
}
}
vector<ll> cv(n+1,C*M);
cv[v]=0;
q.push(v);
while(!q.empty()){
int i=q.front();
q.pop();
for(pair<int,ll> p:adj[i]){
ll j,c;
tie(j,c)=p;
if(cv[j]>cv[i]+c){
cv[j]=cv[i]+c;
q.push(j);
}
}
}
vector<vector<ll>> cs(n+1,vector<ll>(3,C*M));
cs[s][0]=0;
cs[s][1]=cu[s];
cs[s][2]=cv[s];
q.push(s);
while(!q.empty()){
int i=q.front();
q.pop();
for(pair<int,ll> p:adj[i]){
ll j,c;
tie(j,c)=p;
if(cs[j][0]>=cs[i][0]+c){
cs[j][0]=cs[i][0]+c;
ll mn1=min(cs[i][1],cu[j]);
ll mn2=min(cs[i][2],cv[j]);
if(cs[j][1]+cs[j][1]>mn1+mn2){
cs[j][1]=mn1;
cs[j][2]=mn2;
}
q.push(j);
}
}
}
cout<<min(cs[t][1]+cs[t][2],cu[v]);
}
