#include <bits/stdc++.h>
#define ll long long
#define ff first
#define ss second
#define pb push_back
#define all(x) x.begin(),x.end()
#define vodka void
#define ertunt return
using namespace std;
int main(){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
ll n, m;
cin >> n >> m;
ll s, t;
cin >> s >> t;
ll u, v;
cin >> u >> v;
vector<set<pair<ll,ll>>> adj(n+4);
for(ll i = 0; i < m; i++){
ll a, b, c;
cin >> a >> b >> c;
adj[a].insert({b, c});
adj[b].insert({a, c});
}
set<pair<ll,ll>> st;
vector<ll> dist(n+5, (ll)1e18);
vector<bool> vis(n+5, 0);
vector<ll> bef(n+5, -1);
st.insert({0, s});
dist[s] = 0;
while(!st.empty()){
pair<ll,ll> p = *st.begin();
st.erase(p);
if(vis[p.ss]) continue;
vis[p.ss] = 1;
for(auto [x, y] : adj[p.ss]){
if(dist[p.ss] + y < dist[x]){
dist[x] = dist[p.ss] + y;
st.insert({dist[x], x});
bef[x] = p.ss;
}
}
}
vector<ll> arr;
ll cur = t;
while(cur > 0){
arr.pb(cur);
cur = bef[cur];
}
reverse(all(arr));
for(ll i = 1; i < arr.size(); i++){
auto it = adj[arr[i]].lower_bound({arr[i-1], 0});
adj[arr[i]].erase(it);
it = adj[arr[i-1]].lower_bound({arr[i], 0});
adj[arr[i-1]].erase(it);
adj[arr[i-1]].insert({arr[i],0});
adj[arr[i]].insert({arr[i-1],0});
}
fill(all(dist), (ll)1e18);
st.clear();
st.insert({0, u});
fill(all(vis), 0);
dist[u] = 0;
while(!st.empty()){
pair<ll,ll> p = *st.begin();
st.erase(p);
if(vis[p.ss]) continue;
vis[p.ss] = 1;
for(auto [x, y] : adj[p.ss]){
if(dist[p.ss] + y < dist[x]){
dist[x] = dist[p.ss] + y;
st.insert({dist[x], x});
}
}
}
cout << dist[v];
}
