#include <bits/stdc++.h>
using namespace std;
int main()
{
//freopen("i.txt","r",stdin);
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m;
cin >> n >> m;
int s, t, p, q;
cin >> s >> t >> p >> q;
s--;
t--;
p--;
q--;
typedef pair<long long, long long> ii;
vector<ii> adj[n];
for(int i = 0;i < m;i++){
int a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].push_back(ii(c,b));
adj[b].push_back(ii(c,a));
}
priority_queue<ii, vector<ii>, greater<ii> > dtr;
long long disp[n];
long long disq[n];
long long dis[n];
long long dist[n];
fill(disp,disp+n,102345678901234567ll);
fill(disq,disq+n,102345678901234567ll);
fill(dis,dis+n,102345678901234567ll);
fill(dist,dist+n,102345678901234567ll);
disp[p] = 0;
dtr.push(ii(0,p));
while(!dtr.empty()){
ii cur = dtr.top();
dtr.pop();
for(ii nei : adj[cur.second]){
if(disp[nei.second] > nei.first + cur.first){
disp[nei.second] = nei.first + cur.first;
dtr.push(ii(disp[nei.second],nei.second));
}
}
}
for(int i = 0;i < n;i++){
// cout << disp[i] << " ";
}
// cout << "\n";
disq[q] = 0;
dtr.push(ii(0,q));
while(!dtr.empty()){
ii cur = dtr.top();
dtr.pop();
for(ii nei : adj[cur.second]){
if(disq[nei.second] > nei.first + cur.first){
disq[nei.second] = nei.first + cur.first;
dtr.push(ii(disq[nei.second],nei.second));
}
}
}
for(int i = 0;i < n;i++){
// cout << disq[i] << " ";
}
//cout << "\n";
dis[s] = 0;
dtr.push(ii(0,s));
while(!dtr.empty()){
ii cur = dtr.top();
dtr.pop();
for(ii nei : adj[cur.second]){
if(dis[nei.second] > nei.first + cur.first){
dis[nei.second] = nei.first + cur.first;
dtr.push(ii(dis[nei.second],nei.second));
}
}
}
for(int i = 0;i < n;i++){
// cout << dis[i] << " ";
}
//cout << "\n";
dist[t] = 0;
dtr.push(ii(0,t));
while(!dtr.empty()){
ii cur = dtr.top();
dtr.pop();
for(ii nei : adj[cur.second]){
if(dist[nei.second] > nei.first + cur.first){
dist[nei.second] = nei.first + cur.first;
dtr.push(ii(dist[nei.second],nei.second));
}
}
}
for(int i = 0;i < n;i++){
//cout << dist[i] << " ";
}
// cout << "\n";
vector<int> dag[n];
int indegree[n];
fill(indegree,indegree+n,0);
for(int u = 0;u < n;u++){
if(dis[u]+dist[u] != dis[t]) continue;
for(ii v : adj[u]){
if(dis[v.second] + dist[v.second] != dis[t]) continue;
if(dis[u] + v.first == dis[v.second]){
// cout << v.second << " " << u << "\n";
dag[v.second].push_back(u);
indegree[u]++;
}
}
}
//cout << "\n\n";
ii dp[n];
for(int i = 0;i < n;i++){
dp[i] = ii(disp[i],disq[i]);
}
queue<int> bfs;
bfs.push(t);
while(!bfs.empty()){
int u = bfs.front();
bfs.pop();
//cout << u << " ";
for(int v : dag[u]){
indegree[v]--;
if(indegree[v] == 0) bfs.push(v);
dp[v].first = min(dp[v].first, dp[u].first);
dp[v].second = min(dp[v].second, dp[u].second);
}
}
long long ans = disp[q];
//cout << "\n";
for(int i = 0;i < n;i++){
//cout << dp[i].first << " " << dp[i].second << "\n";
if(dis[i]+dist[i] != dis[t]) continue;
ans = min(ans, disq[i] + dp[i].first);
ans = min(ans, disp[i] + dp[i].second);
}
cout << ans << "\n";
return 0;
}
