#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll C=1e9;
const ll M=2e5;
vector<vector<pair<int,ll>>> adj;
void f(vector<ll> &v,int x){
v[x]=0;
auto comp=[&v](int i,int j){return v[i]>v[j];};
priority_queue<int,vector<int>,decltype(comp)>pq{comp};
pq.push(x);
while(!pq.empty()){
int i=pq.top();
pq.pop();
for(pair<int,ll> p:adj[i]){
ll j,c;
tie(j,c)=p;
if(v[j]>v[i]+c){
v[j]=v[i]+c;
pq.push(j);
}
}
}
}
void f1(vector<ll> &v,int x){
v[x]=0;
queue<int>q;
q.push(x);
while(!q.empty()){
int i=q.front();
q.pop();
for(pair<int,ll> p:adj[i]){
ll j,c;
tie(j,c)=p;
if(v[j]>v[i]+c){
v[j]=v[i]+c;
q.push(j);
}
}
}
}
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;
adj=vector<vector<pair<int,ll>>>(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> du(n+1,C*M);
vector<ll> dv(n+1,C*M);
vector<ll> dt(n+1,C*M);
vector<ll> ds(n+1,C*M);
f(du,u);
f(dv,v);
f(ds,s);
f(dt,t);
ll tot=C*M;
for(int i=1;i<=n;i++){
tot=min(tot,ds[i]+dt[i]);
}
vector<bool> b(n+1);
for(int i=1;i<=n;i++){
b[i]=ds[i]+dt[i]==tot;
}
vector<pair<ll,ll>> dp(n+1,{C*M,C*M});
dp[s]={du[s],dv[s]};
auto comp=[&ds](int i,int j){return ds[i]>ds[j];};
priority_queue<ll,vector<ll>,decltype(comp)>pq{comp};
pq.push(s);
ll res=M*C;
while(!pq.empty()){
int i=pq.top();
pq.pop();
for(pair<int,ll> p:adj[i]){
int j=p.first;
if(ds[j]>ds[i]&&b[j]){
pq.push(j);
dp[j].first=min({dp[i].first,dp[j].first,du[j]});
dp[j].second=min({dp[i].second,dp[j].second,dv[j]});
res=min({res,dp[j].first+dv[j],dp[j].second+du[j]});
}
}
}
cout<<min(res,du[v]);
}
