#include <bits/stdc++.h>
using namespace std;
#define N 300005
#define ll long long int
#define sz(x) (int)x.size()
#define ff first
#define ss second
ll T, n, m, s, t, u1, u2, dis[N], a[N], b[N], c[N]; vector <pair<int,int>> v[N]; map <pair<int,int>, bool> vis; void dfs(int x){ for(auto i : v[x]){ if(dis[x] == dis[i.ff] + i.ss){ vis[{x,i.ff}] = 1; vis[{i.ff,x}] = 1; dfs(i.ff); return; } }} int main(){ ios::sync_with_stdio(false); cin.tie(0); cin >> n >> m >> s >> t >> u1 >> u2; for(int i = 1; i <= m; i++){ cin >> a[i] >> b[i] >> c[i]; v[a[i]].push_back({b[i],c[i]}); v[b[i]].push_back({a[i],c[i]}); } for(int i = 1; i <= n; i++) dis[i] = 1e15; priority_queue <pair<ll,ll>> q; q.push({0,s}); dis[s] = 0; while(!q.empty()){ int x = q.top().ss; if(dis[x] != -q.top().ff){ q.pop(); continue; } q.pop(); for(auto i : v[x]){ if(dis[i.ff] > dis[x] + i.ss){ dis[i.ff] = dis[x] + i.ss; q.push({-dis[i.ff], i.ff}); } } } dfs(t); for(int i = 1; i <= n; i++) v[i].clear(); for(int i = 1; i <= m; i++){ if(vis[{a[i],b[i]}] == 0){ v[a[i]].push_back({b[i],c[i]}); v[b[i]].push_back({a[i],c[i]}); } else { v[a[i]].push_back({b[i],0}); v[b[i]].push_back({a[i],0}); } } for(int i = 1; i <= n; i++) dis[i] = 1e15; q.push({0,u1}); dis[u1] = 0; while(!q.empty()){ int x = q.top().ss; if(dis[x] != -q.top().ff){ q.pop(); continue; } q.pop(); for(auto i : v[x]){ if(dis[i.ff] > dis[x] + i.ss){ dis[i.ff] = dis[x] + i.ss; q.push({-dis[i.ff], i.ff}); } } } cout << dis[u2]; return 0;}
