#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ull unsigned long long
#define pb(e) push_back(e)
#define sv(a) sort(a.begin(),a.end())
#define sa(a,n) sort(a,a+n)
#define mp(a,b) make_pair(a,b)
#define vf first
#define vs second
#define ar array
#define all(x) x.begin(),x.end()
const int inf = 0x3f3f3f3f;
const int mod = 1000000007;
const double PI=3.14159265358979323846264338327950288419716939937510582097494459230;
bool remender(ll a , ll b){return a%b;}
const int N = 100002;
vector<pair<int,ll>> adj[N];
ll dis[N];
void mem(){
for(int i = 0; i < N; i++)dis[i] = 1e18;
}
void Dijkstra(ll e){
priority_queue< pair<ll,ll>, vector <pair<ll,ll>> , greater<pair<ll,ll>> > pq;
dis[e]=0;
pq.push({0,e});
while(!pq.empty()){
ll node = pq.top().second,ww=pq.top().first;
pq.pop();
if(dis[node] < ww)continue;
for(auto i : adj[node]){
ll w = i.second;
if(dis[i.first] > dis[node] + w){
dis[i.first] = dis[node] + w;
pq.push({dis[i.first],i.first});
}
}
}
}
void solve(){
int n , m;
cin >> n >> m;
int s , t;
cin >> s >> t;
int a , b;
cin >> a >> b;
for(int i = 0; i < m; i++){
ll x , y , z;
cin >> x >> y >> z;
adj[x].pb(mp(y,z));
adj[y].pb(mp(x,z));
}
ll dis1[N] , dis2[N];
mem();
Dijkstra(a);
for(int i = 0; i <= n; i++)dis1[i] = dis[i];
mem();
Dijkstra(b);
for(int i = 0; i <= n; i++)dis2[i] = dis[i];
mem();
Dijkstra(s);
ll mn[N] , mx[N];
for(int i = 0; i <= n; i++)mn[i] = dis1[i];
for(int i = 0; i <= n; i++)mx[i] = dis2[i];
queue<int> q;
bool vis[N];
memset(vis,0,sizeof vis);
vis[t] = 1;
q.push(t);
int cnt[N];
memset(cnt,0,sizeof cnt);
while(q.size()){
int node = q.front();
q.pop();
for(auto i : adj[node]){
if(dis[i.vf] + i.vs == dis[node]){
cnt[i.vf]++;
if(!vis[i.vf]){
vis[i.vf] = 1;
q.push(i.vf);
}
}
}
}
ll ans = dis1[b];
q.push(t);
while(q.size()){
int node = q.front();
q.pop();
ans = min(ans , min(dis1[node] + mx[node] , dis2[node] + mn[node]));
for(auto i : adj[node]){
if(dis[i.vf] == dis[node] - i.vs){
mn[i.vf] = min(mn[i.vf] , mn[node]);
mx[i.vf] = min(mx[i.vf] , mx[node]);
cnt[i.vf]--;
if(cnt[i.vf] == 0){
q.push(i.vf);
}
}
}
}
cout << ans << '\n';
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
//int t;cin >> t;while(t--)
solve();
return 0;
}
