#include <bits/stdc++.h>
using namespace std;
#define int long long
int n, m;
int s, t;
int u, v;
vector<vector<pair<int, int>>> g;
void dijkstra(int src, vector<int> &dist, vector<vector<int>> &par){
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
for(int i=1;i<=n;++i) dist[i]=1e9;
dist[src]=0;
pq.push({dist[src], src});
while(!pq.empty()){
int x, d;
tie(d, x)=pq.top();
pq.pop();
if(d!=dist[x]) continue;
for(auto it:g[x]){
int nx=it.first, nd=it.second+d;
if(nd<dist[nx]){
pq.push({nd, nx});
dist[nx]=nd;
par[nx].clear();
par[nx].push_back(x);
}
else if(nd==dist[nx]){
par[nx].push_back(x);
}
}
}
}
void dijkstra(int src, vector<int> &dist){
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
for(int i=1;i<=n;++i) dist[i]=1e18;
dist[src]=0;
pq.push({dist[src], src});
while(!pq.empty()){
int x, d;
tie(d, x)=pq.top();
pq.pop();
if(d!=dist[x]) continue;
for(auto it:g[x]){
int nx=it.first, nd=it.second+d;
if(nd<dist[nx]){
pq.push({nd, nx});
dist[nx]=nd;
}
}
}
}
void dfs(int x, vector<vector<int>> &out, vector<int> &dp, vector<int> &dist){
dp[x]=dist[x];
for(auto it:out[x]){
if(dp[it]==-1) dfs(it, out, dp, dist);
dp[x]=min(dp[x], dp[it]);
}
}
int32_t main(){
cin>>n>>m>>s>>t>>u>>v;
g.resize(n+1);
vector<vector<int>> par(n+1), rpar(n+1);;
vector<int> dists(n+1), distu(n+1), distv(n+1);
vector<int> dpf(n+1, -1), dpb(n+1, -1);
for(int i=1;i<=m;++i){
int a, b, c;
cin>>a>>b>>c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
dijkstra(u, distu);
dijkstra(v, distv);
dijkstra(s, dists, par);
queue<int> q;
vector<bool> used(n+1, 0);
q.push(t);
used[t]=1;
while(!q.empty()){
int x=q.front();
q.pop();
for(auto it:par[x]){
rpar[it].push_back(x);
if(used[it]) continue;
used[it]=1;
q.push(it);
}
}
dfs(s, rpar, dpf, distu);
dfs(t, par, dpb, distu);
int sol=distu[v];
for(int i=1;i<=n;++i){
if(!used[i]) continue;
sol=min(sol, distv[i]+min(dpf[i], dpb[i]));
}
cout<<sol<<"\n";
}
