// #pragma optimize ("g",on)
// #pragma GCC optimize ("inline")
// #pragma GCC optimize ("Ofast")
// #pragma GCC optimize ("unroll-loops")
// #pragma GCC optimize ("03")
#include <bits/stdc++.h>
#define pb push_back
#define SS ios_base::sync_with_stdio(0);cin.tie(nullptr);cout.tie(nullptr);
#define int long long
#define all(v) v.begin(),v.end()
using namespace std;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
const int N = 2e5 + 1, inf = 1e18, mod = 998244353;
vector<array<int, 3>> g[N];
int ok[N], tin[N], tout[N], timer, used[N];
vector<vector<int>> p;
vector<array<int, 3>> e(N);
void f(int v, int r){
if(v == r){
ok[v] = 1;
return;
}
for(int to : p[v]){
tin[to] = ++timer;
int nxt = (e[to][0] != v ? e[to][0] : e[to][1]);
f(nxt, r);
tout[to] = timer;
if(ok[nxt]) used[to] = 1;
ok[v] = max(ok[v], ok[nxt]);
// break;
}
}
bool ch(int u, int v){
return (tin[u] <= tin[v] && tout[u] >= tout[v]);
}
void solve(){
int n, m;
cin >> n >> m;
p.resize(n + 1);
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
for(int i = 1; i <= m; i++){
int u, v, w;
cin >> u >> v >> w;
e[i] = {u, v, w};
g[u].push_back({v, w, i});
g[v].push_back({u, w, i});
}
vector<int> dist(n + 1, inf);
priority_queue<pair<int, int>> q;
q.push({0, s});
dist[s] = 0;
while(q.size()){
auto [musor, v] = q.top();
q.pop();
musor = -musor;
if(musor != dist[v]) continue;
for(auto [to, w, id] : g[v]){
if(dist[to] == dist[v] + w) p[to].push_back(id);
else if(dist[to] > dist[v] + w){
p[to].clear();
p[to].push_back(id);
dist[to] = dist[v] + w;
q.push({-dist[to], to});
}
}
}
f(t, s);
vector<int> tp(n + 1, 0ll);
dist.assign(n + 1, inf);
dist[u] = 0;
set<array<int, 3>> st;
st.insert({0, 0, u});
while(st.size()){
auto [c, t, v] = *st.begin();
st.erase(st.begin());
for(auto [to, w, id] : g[v]){
if(!used[id] && dist[to] > dist[v] + w){
st.erase({dist[to], tp[to], to});
dist[to] = dist[v] + w;
tp[to] = tp[v];
st.insert({dist[to], tp[to], to});
}
else{
if(tp[v] == 0 && dist[to] > dist[v]){
tp[v] = id;
st.erase({dist[to], tp[to], to});
dist[to] = dist[v];
tp[to] = tp[v];
st.insert({dist[to], tp[to], to});
}
else{
if(ch(id, tp[v]) || ch(tp[v], id)){
if(dist[to] > dist[v]){
tp[v] = id;
st.erase({dist[to], tp[to], to});
dist[to] = dist[v];
tp[to] = tp[v];
st.insert({dist[to], tp[to], to});
}
}
else if(dist[to] > dist[v] + w){
st.erase({dist[to], tp[to], to});
dist[to] = dist[v] + w;
tp[to] = tp[v];
st.insert({dist[to], tp[to], to});
}
}
}
}
}
cout << dist[v] << '\n';
/*
pref[i] = max(pref[i], pref[i - 1])
pref[i] - pref[i - 1]
*/
// for(int i = 1; i <= m; i++){
// if(used[i]) cout << tin[i] << ' ' << tout[i] << ' ' << i << '\n';
// }
}
signed main(){
SS
// freopen("trains.in", "r", stdin);
// freopen("trains.out", "w", stdout);
int t = 1;
// cin >> t;
while(t--){
solve();
}
}
