#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "debugger.cpp"
#else
#define debug(...)
#endif
template<class T>
int len(T &a){
return a.size();
}
using ll = long long;
using pii = pair<int,int>;
#define all(a) (a).begin(), (a).end()
#define ff first
#define ss second
string fileio = "";
mt19937 mt(time(nullptr));
const int mod = 1e9 + 7;
const int inf = 1e9;
const ll infl = 1e18;
const int maxn = 1e5 + 1;
void solve(){
int n, m; cin >> n >> m;
int s, t, lef, rig; cin >> s >> t >> lef >> rig;
s --, t --, lef --, rig --;
vector<vector<pair<int,int>>> g(n);
for(int i = 0; i < n; i ++){
int w;
int u, v; cin >> u >> v;
cin >> w;
u --; v --;
g[u].push_back({v, w});
g[v].emplace_back(u, w);
}
vector<ll> ds(n, infl), dt(n, infl);
{
priority_queue<pair<int, ll>> q;
vector<int> vis(n);
ds[s] = 0;
q.push({0, s});
while(!q.empty()){
int v = q.top().second;
q.pop();
if(vis[v]) continue;
vis[v] = 1;
for(auto [u, w] : g[v]){
if(ds[u] > ds[v] + w){
ds[u] = ds[v] + w;
q.push({-ds[u], u});
}
}
}
}
{
priority_queue<pair<int, ll>> q;
vector<int> vis(n);
q.push({0, t});
dt[t] = 0;
while(!q.empty()){
int v = q.top().second;
q.pop();
if(vis[v]) continue;
vis[v] = 1;
for(auto [u, w] : g[v]){
if(dt[u] > dt[v] + w){
dt[u] = dt[v] + w;
q.push({-dt[u], u});
}
}
}
}
vector<ll> ans(n, infl);
{
priority_queue<pair<int, ll>> q;
vector<int> vis(n);
q.push({0, lef});
ans[lef] = 0;
while(!q.empty()){
int v = q.top().second;
q.pop();
if(vis[v]) continue;
vis[v] = 1;
for(auto [u, w] : g[v]){
if(min(dt[u], dt[v]) + min(ds[u], ds[v]) + w == dt[s]) w = 0;
if(ans[u] > ans[v] + w){
ans[u] = ans[v] + w;
q.push({-ans[u], u});
}
}
}
}
debug(ans);
cout << ans[rig];
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
auto start = chrono::high_resolution_clock::now();
#ifndef LOCAL
if(fileio.size()){
freopen((fileio + ".in").c_str(), "r", stdin);
freopen((fileio + ".out").c_str(), "w", stdout);
}
#endif
int testcases = 1;
#ifdef Tests
cin >> testcases;
#endif
while(testcases --){
solve();
cout << '\n';
#ifdef LOCAL
cout << "_________________________" << endl;
#endif
}
#ifdef LOCAL
auto duration = chrono::duration_cast<chrono::microseconds>(chrono::high_resolution_clock::now() - start);
cout << "time: " << (double)duration.count()/1000.0 << " milliseconds" << endl;
#endif
return 0;
}
