///breaker
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define ii pair<int,int>
#define iii pair<int,ii>
#define mp make_pair
const int inf=1e18+7;
const int maxn=1e5+7;
int du[maxn];
int dv[maxn];
vector<ii>adj[maxn];
int n,m,s,t,u,v;
int dp[maxn][2];
int vst[maxn];
int d[maxn];
void dijkstra1(int start,int arr[])
{
for(int i=1;i<=n;i++)arr[i]=inf;
arr[start]=0;
priority_queue<ii,vector<ii>,greater<ii>>q;
q.push(mp(0,start));
while(q.size()){
int u=q.top().se;
int du=q.top().fi;
q.pop();
if(du>arr[u])continue;
for(auto [v,w]:adj[u]){
if(arr[v]>du+w){
arr[v]=du+w;
q.push({arr[v],v});
}
}
}
}
int dijkstra2(int start,int endd)
{
for(int i=0;i<=n;i++){
d[i]=inf;
dp[i][0]=inf;
dp[i][1]=inf;
vst[i]=0;
}
priority_queue<iii,vector<iii>,greater<iii>>q;
q.push(mp(0,mp(start,0)));
d[start]=0;
while(q.size()){
int u=q.top().se.fi;
int duu=q.top().fi;
int par=q.top().se.se;
q.pop();
if(vst[u]==0){
vst[u]=1;
dp[u][0]=min(dp[par][0],du[u]);
dp[u][1]=min(dp[par][1],dv[u]);
d[u]=duu;
for(auto [v,w]:adj[u]){
q.push(mp(duu+w,mp(v,u)));
}
}
else if(duu==d[u]){
if(min(du[u],dp[par][0])+min(dv[u],dp[par][1])<=dp[u][0]+dp[u][1]){
dp[u][0]=min(du[u],dp[par][0]);
dp[u][1]=min(dv[u],dp[par][1]);
}
}
}
return dp[endd][0]+dp[endd][1];
}
void sol(){
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
for(int i=1;i<=m;i++){
int u,v,w;
cin>>u>>v>>w;
adj[u].push_back({v,w});
adj[v].push_back({u,w});
}
dijkstra1(u,du);
int ans=du[v];
dijkstra1(v,dv);
ans=min(ans,dijkstra2(s,t));
ans=min(ans,dijkstra2(t,s));
cout<<ans;
}
main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int t=1;
while(t--){
sol();
}
// you should actually read the stuff at the bottom
return 0;
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
*/
