#include <bits/stdc++.h>
#define int long long
#define pb push_back
#define ff first
#define ss second
#define pii pair<int,int>
#define vi vector<int>
#define vii vector<pair<int,int>>
using namespace std;
const int inf = 1LL<<62;
void solve(){
int n,m;
cin >> n >> m;
int s,t;
cin >> s >> t;
--s; --t;
int u,v;
cin >> u >> v;
--u;--v;
vector<vii> adj(n);
for(int i=0;i<m;i++){
int a,b,c;
cin >> a >> b >> c;
adj[--a].pb({--b,c});
adj[b].pb({a,c});
}
vi distanceS(n,inf),distanceU(n,inf),distanceV(n,inf);
priority_queue<pii, vector<pii>, greater<>> pq;
vector<bool> visited(n,false);
distanceU[u] = 0;
pq.push({0,u});
while(pq.size()){
int a = pq.top().second;
pq.pop();
if(visited[a]) continue;
visited[a] = true;
for(auto x : adj[a]){
int b = x.first,w=x.second;
if(distanceU[a]+w<distanceU[b]){
distanceU[b] = distanceU[a]+w;
pq.push({distanceU[b],b});
}
}
}
visited.assign(n,false);
distanceV[v] = 0;
pq.push({0,v});
while(pq.size()){
int a = pq.top().second;
pq.pop();
if(visited[a]) continue;
visited[a] = true;
for(auto x : adj[a]){
int b = x.first,w=x.second;
if(distanceV[a]+w<distanceV[b]){
distanceV[b] = distanceV[a]+w;
pq.push({distanceV[b],b});
}
}
}
visited.assign(n,false);
vi ogmn(n),mn1(n);
for(int i=0;i<n;i++){
ogmn[i] = distanceV[i];
mn1[i] = distanceV[i];
}
distanceS[s] = 0;
pq.push({0,s});
while(pq.size()){
int a = pq.top().second;
pq.pop();
if(visited[a]) continue;
visited[a] = true;
for(auto x : adj[a]){
int b = x.first,w=x.second;
if(distanceS[a]+w<distanceS[b]){
distanceS[b] = distanceS[a]+w;
pq.push({distanceS[b],b});
mn1[b] = min(mn1[a],ogmn[b]);
} else if(distanceS[a]+w==distanceS[b]){
mn1[b] = min(mn1[b],mn1[a]);
}
}
}
vi distanceT(n,inf);
vi mn2(n);
for(int i=0;i<n;i++){
mn2[i] = distanceV[i];
}
distanceT[t] = 0;
pq.push({0,t});
visited.assign(n,false);
while(pq.size()){
int a = pq.top().second;
pq.pop();
if(visited[a]) continue;
visited[a] = true;
for(auto x : adj[a]){
int b = x.first,w=x.second;
if(distanceT[a]+w<distanceT[b]){
distanceT[b] = distanceT[a]+w;
pq.push({distanceT[b],b});
mn2[b] = min(mn2[a],ogmn[b]);
} else if(distanceT[a]+w==distanceT[b]){
mn2[b] = min(mn2[b],mn2[a]);
}
}
}
/*for(int i=0;i<n;i++){
cout << "for: " << i+1 << "distance to u is " << distanceU[i] << ". distance to v is " << distanceV[i];
cout << "distance to t is " << distanceT[i] << ". mn to v is " << mn[i] << "\n";
}*/
int len = distanceS[t];
int ans = inf;
for(int i=0;i<n;i++){
int res = distanceS[i]+distanceT[i];
if(res==len){
int cur = distanceU[i]+min(mn1[i],mn2[i]);
if(s==u){
cur-=distanceU[i];
}
ans = min(ans,cur);
}
}
ans = min(ans,distanceU[v]);
cout << ans << "\n";
}
signed main()
{
ios::sync_with_stdio(0);
cin.tie(0);
solve();
return 0;
}
