// Day Created: mar 16th 2026
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#define fname ""
#define ll long long
#define pii pair<int, int>
#define pli pair<ll, int>
#define fi first
#define se second
using namespace std;
int n, m, S, T, U, V;
struct road {
int v, w, id;
};
vector<road> edge[100005];
vector<int> dag[100005], rdag[100005];
ll distU[100005], distV[100005], dp[100005];
queue<int> q;
priority_queue<pli, vector<pli>, greater<pli>> pq;
bool f[400005];
void dijktra(ll dist[], const int &S) {
for(int i=1; i<=n; i++) dist[i]=1e16;
dist[S]=0;
pq.push({0, S});
while(!pq.empty()) {
auto [d, u]=pq.top();
pq.pop();
if(d!=dist[u]) continue;
for(const auto &[v, w, id]:edge[u]) {
int n_w=(f[id]?0:w);
if(d+n_w<dist[v])
dist[v]=d+n_w, pq.push({d+n_w, v});
}
}
}
bool vis[100005];
ll find_path(ll dU[], ll dV[]) {
for(int i=1; i<=n; i++) vis[i]=0;
ll res=1e16;
for(int i=1; i<=n; i++) dp[i]=dU[i];
vis[S]=1;
q.push(S);
while(!q.empty()) {
int u=q.front();
q.pop();
for(const auto &v:rdag[u])
dp[u]=min(dp[u], dp[v]);
for(const auto &v:dag[u]) {
if(!vis[v]) vis[v]=1, q.push(v);
dp[v]=min(dp[v], dp[u]);
}
}
for(int i=1; i<=n; i++) res=min(res, dp[i]+dV[i]);
return res;
}
void solve() {
cin>>n>>m>>S>>T>>U>>V;
for(int i=1; i<=m; i++) {
int u, v, w;
cin>>u>>v>>w;
edge[u].push_back({v, w, i});
edge[v].push_back({u, w, i+m});
}
// train process
dijktra(distU, S);
q.push(T);
while(!q.empty()) {
int v=q.front();
q.pop();
for(const auto &[u, w, id]:edge[v])
if(distU[u]+w==distU[v]) {
dag[u].emplace_back(v);
rdag[v].emplace_back(u);
f[id>m?id-m:id+m]=1;
if(!vis[u]) vis[u]=1, q.push(u);
}
}
// student process
dijktra(distU, U);
dijktra(distV, V);
// // cout<<distU[2];
// for(int i=1; i<=n; i++) cout<<distV[i]<<' ';
// cout<<'\n';
cout<<min(find_path(distU, distV), find_path(distV, distU));
}
main() {
if(fopen(fname".inp", "r")) {
freopen(fname".inp", "r", stdin);
freopen(fname".out", "w", stdout);
}
cin.tie(0)->sync_with_stdio(0);
int tc=1;
// cin>>tc;
while(tc--) {
solve();
cout<<'\n';
}
}
