#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#define pii pair<int, int>
#define t3 tuple<int, int, int>
#define pepperX ios_base::sync_with_stdio(false); cin.tie(0);
using ll = long long;
using namespace std;
#define int ll
struct A{
int a, w;
bool operator<(const A& o)const{
return w>o.w;
}
};
struct B{
int a, w, fu, fv;
bool operator<(const B& o)const{
if(w!=o.w)return w>o.w;
return fu+fv>o.fu+o.fv;
}
};
vector<A> g[100005];
int dis[100005], fare[100005];
int du[100005], dv[100005];
void solve(){
int n, m, s, t, U, V;
cin >> n >> m;
cin >> s >> t;
cin >> U >> V;
for(int i=1; i<=m; i++){
int a, b, w;
cin >> a >> b >> w;
g[a].push_back({b, w});
g[b].push_back({a, w});
}
//==================distance from U and V=======================
fill(du+1, du+n+1, 1e18);
fill(dv+1, dv+n+1, 1e18);
priority_queue<A> pq;
pq.push({U, 0});
du[U]=0;
while(!pq.empty()){
auto [u,w]=pq.top();
pq.pop();
if(w>du[u])continue;
for(auto [v,ww]:g[u]){
if(w+ww<du[v]){
du[v]=w+ww;
pq.push({v, w+ww});
}
}
}
pq.push({V, 0});
dv[V]=0;
while(!pq.empty()){
auto [u,w]=pq.top();
pq.pop();
if(w>dv[u])continue;
for(auto [v,ww]:g[u]){
if(w+ww<dv[v]){
dv[v]=w+ww;
pq.push({v, w+ww});
}
}
}
//========================================
fill(dis+1, dis+n+1, 1e18);
fill(fare+1, fare+n+1, 1e18);
priority_queue<B> pq2;
pq2.push({s, 0, du[s], dv[s]});
dis[s]=0;
fare[s]=du[s]+dv[s];
while(!pq2.empty()){
auto [u,w,fu,fv]=pq2.top();
pq2.pop();
if(w>dis[u] || fu+fv>fare[u])continue;
if(u==t){
cout << min(fu+fv, du[V]);
return;
}
for(auto [v,ww]:g[u]){
int nfu=min(fu, du[v]);
int nfv=min(fv, dv[v]);
if(w+ww<dis[v] || (w+ww==dis[v] && nfu+nfv<fare[v])){
dis[v]=w+ww;
pq2.push({v, w+ww, nfu, nfv});
}
}
}
}
int32_t main(){
pepperX;
int tcs=1;
//cin >> tcs;
while(tcs--) solve();
return 0;
}
