#include<bits/stdc++.h>
#define ll long long
using namespace std;
int n, m, s, t, u, v, a, b, c, now;
vector<pair<int,int>> edges[100002];
map<pair<int,int>, ll> rem;
bool kwek=false;
const ll INF=1e18;
void dijkstra(){
vector<ll> dist(n+2, INF);
vector<bool> vis(n+2, false);
vector<int> pred(n+2, -1);
priority_queue<pair<ll,pair<int,int>>, vector<pair<ll,pair<int,int>>>, greater<pair<ll,pair<int,int>>>> pq;
dist[s]=0;
pq.push({0, {0, s}});
while(!pq.empty()){
now=pq.top().second.second;
pq.pop();
if(!vis[now]){
vis[now]=true;
for(auto i: edges[now]){
if(dist[i.first] >= dist[now] + i.second){
dist[i.first]=dist[now]+i.second;
pred[i.first]=now;
pq.push({dist[i.first], {rem[{now, i.first}], i.first}});
}
}
}
}
vector<pair<int,int>> ubah;
vector<int> temp;
now=t;
while(pred[now] != -1){
// cout<<now<<"->"<<pred[now]<<"\n";
ubah.push_back({now, pred[now]});
ubah.push_back({pred[now], now});
now=pred[now];
}
sort(ubah.begin(), ubah.end());
int k;
for(int i=0; i<ubah.size(); i++){
k=0;
now=ubah[i].first;
temp.push_back(ubah[i].second);
while((i+1)<n && ubah[i+1].first == now){
temp.push_back(ubah[i+1].second);
i++;
}
sort(edges[now].begin(), edges[now].end());
for(int j=0; j<edges[now].size(); j++){
if(temp[k] == edges[now][j].first){
edges[now][j].second=0;
k++;
}
}
temp.clear();
}
}
void dijkstra2(){
vector<ll> dist(n+2, INF);
vector<bool> vis(n+2, false);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
vector<int> pred(n+2, -1);
dist[u]=0;
pq.push({0, u});
while(!pq.empty()){
now=pq.top().second;
pq.pop();
if(!vis[now]){
vis[now]=true;
for(auto i: edges[now]){
if(dist[i.first] > dist[now] + i.second){
dist[i.first]=dist[now]+i.second;
pred[i.first]=now;
pq.push({dist[i.first], i.first});
}
}
}
}
now=v;
if(kwek) cout<<dist[v]<<"\n";
else{
while(pred[now] != -1){
// cout<<now<<"->"<<pred[now]<<" "<<dist[now]-dist[pred[now]]<<"\n";
rem[{now, pred[now]}]=(ll)1e9-(dist[now]-dist[pred[now]]);
rem[{pred[now], now}]=(ll)1e9-(dist[now]-dist[pred[now]]);
now=pred[now];
}
}
kwek=true;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin>>n>>m>>s>>t>>u>>v;
for(int i=0; i<m; i++){
cin>>a>>b>>c;
edges[a].push_back({b, c});
edges[b].push_back({a, c});
}
dijkstra2();
dijkstra();
dijkstra2();
}
