#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define fast ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
#define MOD 1000000007
#define INF 1e18
#define fi first
#define se second
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define FORD(i,a,b) for(int i=a;i>=b;i--)
#define sz(a) ((int)(a).size())
#define endl '\n'
#define pi 3.14159265359
#define TASKNAME "bus"
template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
using namespace std;
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
typedef vector<int> vi;
const int MAXN = 2e5 + 9;
int n,m,s,t,u,v,distfroms[MAXN],distfromu[MAXN],distfromv[MAXN];
vector<ii> g[MAXN];
set<int> traceback[MAXN];
vector<int> shortestpath[MAXN];
void dijkstra(int start,int dist[],bool kt){
for(int i=1;i<=n;i++){
dist[i] = INF;
}
priority_queue<ii,vector<ii>,greater<ii>> pq;
dist[start] = 0;
pq.push({0,start});
while(!pq.empty()){
int u = pq.top().se;
int du = pq.top().fi;
pq.pop();
if (du > dist[u]) continue;
for(auto pt: g[u]){
int v = pt.fi;
int w = pt.se;
if (dist[v] > dist[u] + w){
dist[v] = dist[u] + w;
pq.push({dist[v],v});
if (kt) traceback[v].clear();
if (kt) traceback[v].insert(u);
}
else if (dist[v] == dist[u] + w){
if (kt) traceback[v].insert(u);
}
}
}
}
int best1[MAXN],best2[MAXN];
bool visited[MAXN];
main()
{
fast;
// freopen(TASKNAME".inp","r",stdin);
// freopen(TASKNAME".out","w",stdout);
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
for(int i=1;i<=m;i++){
int u,v,w;
cin>>u>>v>>w;
g[u].pb({v,w});
g[v].pb({u,w});
}
dijkstra(s,distfroms,1);
dijkstra(u,distfromu,0);
dijkstra(v,distfromv,0);
queue<int> q;
q.push(t);
visited[t] = true;
// for(int i=1;i<=n;i++){
// for(auto x: traceback[i]){
// cout<<x<<' ';
// }
// cout<<endl;
// }
// cout<<endl;
while (!q.empty()){
int u = q.front();
q.pop();
// cout<<u<<endl;
for(auto v: traceback[u]){
shortestpath[v].pb(u);
if (!visited[v]){
visited[v] = true;
q.push(v);
}
}
}
// cout<<endl;
// for(int i=1;i<=n;i++){
// for(auto x: shortestpath[i]){
// cout<<i<<' '<<x<<endl;
// }
// cout<<endl;
// }
q.push(s);
int ans = distfromu[v];
memset(best1,0x3f,sizeof(best1));
memset(best2,0x3f,sizeof(best2));
memset(visited,false,sizeof(visited));
while(!q.empty()){
int u = q.front();
q.pop();
best1[u] = min(best1[u], distfromu[u]);
best2[u] = min(best2[u], distfromv[u]);
// cout<<u<<' '<<best1[u]<<' '<<best2[u]<<endl;
ans = min(ans, best1[u] + distfromv[u]);
ans = min(ans, best2[u] + distfromu[u]);
for(auto v: shortestpath[u]){
best1[v] = min(best1[v],best1[u]);
best2[v] = min(best2[v],best2[u]);
if (!visited[v]){
visited[v] = true;
q.push(v);
}
}
}
cout<<ans<<endl;
}
