#include <bits/stdc++.h>
#define endl '\n'
#define int long long
using namespace std;
int32_t main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cout.precision(0);
cout<<fixed;
int n,m;
cin>>n>>m;
vector<pair<int,int>> x[n+1];
int s,t;
cin>>s>>t;
int u,v;
cin>>u>>v;
for (int i = 0; i < m; i++)
{
int uu,vv,w;
cin>>uu>>vv>>w;
x[uu].push_back({w,vv});
x[vv].push_back({w,uu});
}
queue<int> q;
q.push(s);
vector<int> p(n+1);
p[s]=-1;
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<>> pq;
pq.push({0,s});
vector<int> vis(n+1,1e18+1);
vis[s]=0;
while(!pq.empty())
{
auto [w,e]=pq.top();pq.pop();
//cout<<w<<" "<<e<<endl;
for(const auto &[ww,ee]:x[e])
{
//cout<<"adyacente a:"<<ee<<endl;
if(ww+w<vis[ee])
{
vis[ee]=ww+w;
p[ee]=e;
pq.push({ww+w,ee});
}
}
}
int vv=t;
int pv;
while(p[vv]!=-1)
{
//cout<<vv<<" "<<p[vv]<<endl;
for( auto &[w,e]:x[vv])
{
if(e==p[vv]){
w=0;
//cout<<"from "<<vv<<" to "<<e<<" now is free!"<<endl;
break;
}
}
if(vv!=t)
for(auto&[w,e]:x[vv])
if(e==pv){
w=0;
//cout<<"from "<<vv<<" to "<<e<<" now is free!"<<endl;
break;
}
pv=vv;
//if(pv==vv)break;
vv=p[vv];
if(p[vv]==-1)
for(auto&[w,e]:x[vv])
if(e==pv){
w=0;
//cout<<"from "<<vv<<" to "<<e<<" now is free!"<<endl;
break;
}
}
pq.push({0,u});
vector<int> vvis(n+1,1e18+1);
while(!pq.empty())
{
auto [w,e]=pq.top();pq.pop();
//cout<<"e:"<<e<<" with:"<<w<<endl;
if(vvis[e]<=w)continue;
vvis[e]=w;
for(const auto &[ww,ee]:x[e])
{
//cout<<"adyacente a:"<<ee<<endl;
pq.push({ww+w,ee});
}
}
cout<<vvis[v]<<endl;
return 0;
}
