#include <bits/stdc++.h>
#define startt ios_base::sync_with_stdio(false);cin.tie(0);
typedef long long ll;
using namespace std;
#define vint vector<int>
#define all(v) v.begin(), v.end()
#define MOD 1000000007
#define MOD2 998244353
#define MX 1000000000
#define MXL 1000000000000000000
#define PI (ld)2*acos(0.0)
#define nax 200005
#define pb push_back
#define sc second
#define fr first
#define int long long
#define endl '\n'
#define ld long double
#define NO cout << "NO" << endl
#define YES cout << "YES" << endl
int ceildiv(int one, int two) {if (one % two == 0) {return one / two;}else {return one / two + 1;}} int power(int n, int pow, int m) {if (pow == 0) return 1;if (pow % 2 == 0) {ll x = power(n, pow / 2, m);return (x * x) % m;}else return (power(n, pow - 1, m) * n) % m;} int gcd(int a, int b) { if (!b)return a; return gcd(b, a % b);} int factorial(int n, int mod) {if (n > 1)return (n * factorial(n - 1, mod)) % mod; else return 1;} int lcm(int a, int b) {return (a * b) / gcd(a, b);} vector<int> read(int n) {vector<int> a; for (int i = 0; i < n; i++) { int x; cin >> x; a.pb(x);} return a;}struct prefix_sum{vint pref;void build(vint a){pref.pb(0);for(int i = 0; i < a.size(); i++){pref.pb(pref.back()+a[i]);}}int get(int l, int r){return pref[r]-pref[l-1];}};//ssense
template<typename T>
pair<vector<T>, vector<int>> Dijkstra(int start, vector<vector<pair<int,T>>> adj, T mx) {
int n = adj.size();
priority_queue<pair<T, int>> q;
vector<T> dist(n, mx);
vector<int> parent(n, -1);
dist[start] = 0;
q.push({0, start});
while(!q.empty()) {
int u = q.top().second;
T dist_u = -q.top().first;
q.pop();
if(dist_u != dist[u]) continue;
for(auto x: adj[u]) {
int v = x.first;
T w = x.second;
if(dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
parent[v] = u;
q.push({-dist[v], v});
}
}
}
return {dist, parent};
//start, adjlist, fill_max
}
void solve()
{
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
vector<vector<pair<int, int>>> adj;
vector<pair<int, int>> x;
adj.assign(n, x);
s--, t--, u--, v--;
for(int i = 0; i < n; i++)
{
int j, k, w;
cin >> j >> k >> w;
j--;
k--;
adj[j].pb({k, w});
adj[k].pb({j, w});
}
vector<int> distu = Dijkstra(u, adj, (int)MXL).fr;
vector<int> distv = Dijkstra(v, adj, (int)MXL).fr;
priority_queue<array<int, 4>> q;
vector<array<int, 3>> dist(n, {MXL, MXL, MXL});
dist[s] = {0, distu[s], distv[s]};
q.push({0, -distu[s], -distv[s], s});
while(!q.empty())
{
int now = q.top()[3];
int dist_now = -q.top()[0];
int distu_now = -q.top()[1];
int distv_now = -q.top()[2];
q.pop();
if(dist_now != dist[now][0] || distu_now != dist[now][1] || distv_now != dist[now][2]) continue;
for(auto x: adj[now])
{
int ve = x.first;
int w = x.second;
if(dist[ve][0] > dist_now+w || (dist[ve][0] == dist_now+w && dist[ve][1]+dist[ve][2] > min(distu[ve],dist[now][1])+min(distv[ve], dist[now][2]))) {
dist[ve][0] = dist_now + w;
dist[ve][1] = min(distu[ve], distu_now);
dist[ve][2] = min(distv[ve], distv_now);
q.push({-dist[ve][0], -dist[ve][1], -dist[ve][2], ve});
}
}
}
cout << dist[t][1]+dist[t][2] << endl;
}
int32_t main(){
startt
int t = 1;
//cin >> t;
while (t--) {
solve();
}
}
/*
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
*/
