#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define ii pair<ll,ll>
const ll maxn=1e5+7,inf=1e16;
int n,m,s,t,op,ed;
vector<ll> d1,d2,t1,t2;
vector<ii> adj[maxn];
vector<ll> g[maxn];
vector<int> ver;
bool ok[maxn];
bool pass[maxn];
ll ans=inf;
ll dp[maxn],pd[maxn];
int p[maxn];
void dij(int st, vector<ll> &dis){
dis.resize(n+9,inf);
priority_queue <ii,vector<ii>,greater<ii>> pq;
pq.push({0,st});
dis[st]=0;
while(!pq.empty()){
int u=pq.top().se;
int d=pq.top().fi;
pq.pop();
if (dis[u]<d) continue;
for (ii v:adj[u]){
if (dis[v.fi]>dis[u]+v.se){
if (st==s){
g[v.fi].clear();
}
dis[v.fi]=dis[u]+v.se;
pq.push({dis[v.fi],v.fi});
}
if (st==s&& dis[v.fi]>=d+v.se){
p[v.fi]=u;
g[v.fi].push_back(u);
}
}
}
}
void dfs(int u){
if (pass[u]) return;
pass[u]=1;
//cout<<u<<endl;
for (int v: g[u]){
dp[v]=min(dp[v],dp[u]);
pd[v]=min(pd[v],pd[u]);
dfs(v);
}
}
int main(){
cin>>n>>m>>s>>t>>op>>ed;
while (m--){
int a,b,c; cin>>a>>b>>c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
dij(s,d1);
dij(t,d2);
dij(op,t1);
dij(ed,t2);
for (int i=1;i<=n;++i){
dp[i]=t1[i];
pd[i]=t2[i];
if (d1[i]+d2[i] == d1[t]){
ver.push_back(i);
ok[i]=1;
}
}
dfs(t);
if (s==op){
for (int i:ver){
ans=min(ans,t2[i]);
}
cout<<ans;
return 0;
}
/*ll sna=inf;
for (int i:ver){
ans=min(ans,t1[i]);
sna=min(sna,t2[i]);
}
cout<<min(ans+sna,t1[ed]);
return 0;*/
/*for (int i: ver){
for (ii x: adj[i]) if (ok[x.fi]) g[i].push_back(x.fi);
}*/
/*
/*queue<ii> qu;
qu.push({s,s});
pass[s]=1;
while (!qu.empty()){
int u=qu.front().fi;
int p=qu.front().se;
//cout<<u<<endl;
qu.pop();
dp[u]=min(dp[p],t2[u]);
for (int v: g[u]){
dp[v]=min(dp[u],t2[v]);
if (pass[v]==0){
pass[v]=1;
qu.push({v,u});
}
}
}*/
/*pass[s]=1;
for (int i: ver){
while (pass[i]==0){
//cout<<i<<" ";
pass[i]=1;
dp[i]=min(dp[i],dp[p[i]]);
pd[i]=min(pd[i],pd[p[i]]);
i=p[i];
}
//cout<<i<<" i\n";
}*/
/*for (int i: ver){
for (int j: g[i]) cout<<j<<" "; cout<<i<<endl;
}*/
for (int u:ver) ans=min(ans,t2[u]+dp[u]);
for (int v:ver) ans=min(ans,t1[v]+pd[v]);
//for (int i:ver) cout<<i<<" "<<p[i]<<endl;
cout<<min(ans,t1[ed]);
}
