#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,dist1[MAXN],dist2[MAXN];
vector<ii> g[MAXN];
void prep(){
priority_queue<ii,vector<ii>,greater<ii>> pq;
pq.push({0,s});
memset(dist1,0x3f,sizeof(dist1));
dist1[s] = 0;
while(!pq.empty()){
int u = pq.top().se;
int du = pq.top().fi;
pq.pop();
if (du > dist1[u]) continue;
for(auto pt: g[u]){
int v = pt.fi;
int w = pt.se;
if (dist1[v] > dist1[u] + w){
dist1[v] = dist1[u] + w;
pq.push({dist1[v],v});
}
}
}
memset(dist2,0x3f,sizeof(dist2));
dist2[t] = 0;
pq.push({0,t});
while(!pq.empty()){
int u = pq.top().se;
int du = pq.top().fi;
pq.pop();
if (du > dist2[u]) continue;
for(auto pt: g[u]){
int v = pt.fi;
int w = pt.se;
if (dist2[v] > dist2[u] + w){
dist2[v] = dist2[u] + w;
pq.push({dist2[v],v});
}
}
}
}
int dist[MAXN];
ii best[MAXN];
void upd(ii &a,ii u){
if (dist[a.se] > dist[u.se]) a = u;
}
bool onpath(int u,int v,int w){
return (dist1[u] + dist2[v] + w == dist1[t] or dist1[v] + dist2[u] + w == dist1[t]);
}
void dijk(int s){
priority_queue<ii,vector<ii>,greater<ii>> pq;
pq.push({0,s});
memset(dist,0x3f,sizeof(dist));
dist[s] = 0;
best[s] = {0,s};
while(!pq.empty()){
int u = pq.top().se;
int du = pq.top().fi;
pq.pop();
if (du > dist[u]) continue;
// cout<<u<<' '<<du<<' '<<best[u].fi<<' '<<best[u].se<<endl;
for(auto pt: g[u]){
int v = pt.fi;
int w = pt.se;
int dx = best[u].fi; //khoang k den k1
int mx = best[u].se; //mx la dinh bat dau
// if (onpath(u,v,w)) cout<<u<<' '<<v<<' '<<w<<endl;
if (onpath(u,v,w) and onpath(best[u].se,v,best[u].fi + w)){
if (dist[v] > dist[best[u].se]){
dist[v] = dist[best[u].se];
pq.push({dist[v],v});
best[v] = {best[u].fi + w,best[u].se};
}
else upd(best[v],ii(best[u].fi + w, best[u].se));
}
if (dist[v] > dist[u] + w){
dist[v] = dist[u] + w;
best[v] = {0,v};
pq.push({dist[v],v});
}
}
}
cout<<dist[v]<<endl;
}
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});
}
prep();
dijk(u);
}
