#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = 1e18;
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
int n,m,S,T,U,V;
cin>>n>>m>>S>>T>>U>>V;
vector<int>a(m),b(m),c(m);
vector<vector<pair<int,int>>> adj(n+1);
for(int i=0;i<m;i++){
cin>>a[i]>>b[i]>>c[i];
adj[a[i]].emplace_back(b[i],c[i]);
adj[b[i]].emplace_back(a[i],c[i]);
}
vector<ll> dist_s(n+1,INF), dist_t(n+1,INF);
auto dijkstra=[&](int src, vector<ll>& dist){
dist.assign(n+1,INF);
dist[src]=0;
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
pq.push({0,src});
while(!pq.empty()){
auto [d,u]=pq.top(); pq.pop();
if(d>dist[u]) continue;
for(auto [v,w]:adj[u]) if(dist[v]>d+w){
dist[v]=d+w;
pq.push({dist[v],v});
}
}
};
dijkstra(S,dist_s);
dijkstra(T,dist_t);
map<pair<int,int>,ll> mp_cost;
map<pair<int,int>,int> mp_id;
int K=0;
for(int i=0;i<m;i++){
int u=a[i], v=b[i];
int x=min(u,v), y=max(u,v);
if((dist_s[u]+c[i]+dist_t[v]==dist_s[T])||(dist_s[v]+c[i]+dist_t[u]==dist_s[T])){
mp_cost[{x,y}]=0;
mp_id[{x,y}]=++K;
} else {
mp_cost[{x,y}]=c[i];
mp_id[{x,y}]=0;
}
}
vector<vector<ll>> dist_ans(n+1, vector<ll>(K+1,INF));
using State = tuple<ll,int,int>;
priority_queue<State,vector<State>,greater<State>> pq;
dist_ans[U][0]=0;
pq.push({0,U,0});
while(!pq.empty()){
auto [d,u,pid]=pq.top(); pq.pop();
if(d>dist_ans[u][pid]) continue;
for(auto [v,_w]:adj[u]){
int x=min(u,v), y=max(u,v);
ll w = mp_cost[{x,y}];
int eid = mp_id[{x,y}];
if(w>0){
if(d+w<dist_ans[v][pid]){
dist_ans[v][pid]=d+w;
pq.push({dist_ans[v][pid],v,pid});
}
} else {
int next_pid = pid;
if(pid==0) next_pid=eid;
else if(pid!=eid) continue;
if(d<dist_ans[v][next_pid]){
dist_ans[v][next_pid]=d;
pq.push({d,v,next_pid});
}
}
}
}
ll ans=INF;
for(int pid=0;pid<=K;pid++) ans=min(ans,dist_ans[V][pid]);
cout<<ans;
return 0;
}
