#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define ordered_set <int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>
#define ordered_multiset <int, null_type, less_equal <int>, rb_tree_tag, tree_order_statistics_node_update>
#define int long long
#define double long double
#define pii pair <int, int>
#define tiii tuple <int, int, int>
#define emb emplace_back
#define all(a) a.begin(), a.end()
#define iShowSpeed cin.tie(NULL)->sync_with_stdio(false)
const int mod = 1e9 + 7;
const int inf = 1e18;
const int N = 1e5 + 5;
int n, m, st, en, x, y, ans;
bool visited[N];
vector <pii> adj[N], check;
vector <vector <int>> dp(2, vector <int> (N, inf));
vector <int> disst, disen, disx, disy;
vector <int> dijkstra(int s){
priority_queue <pii, vector <pii>, greater <pii>> q; q.emplace(0, s);
vector <int> dis(n + 1, inf); dis[s] = 0;
while (!q.empty()) {
auto [w, u] = q.top(); q.pop();
if (w > dis[u]) continue;
for (auto [ww, v] : adj[u]) {
int www = w + ww;
if (www < dis[v]) {
dis[v] = www;
q.emplace(dis[v], v);
}
}
}
return dis;
}
void dfs(int u){
visited[u] = true;
dp[0][u] = disx[u];
dp[1][u] = disy[u];
for (auto [ww, v] : adj[u]) {
if (disst[v] + ww == disst[u]) {
if (!visited[v]) dfs(v);
dp[0][u] = min(dp[0][u], dp[0][v]);
dp[1][u] = min(dp[1][u], dp[1][v]);
}
}
ans = min({ans, dp[0][u] + disy[u], dp[1][u] + disx[u]});
// cout << u << ": " << "\n";
// cout << dp[0][u] << " " << disx[u] << "\n";
// cout << dp[1][u] << " " << disy[u] << "\n";
// cout << "-----------------------\n";
}
int32_t main(){
iShowSpeed;
cin >> n >> m >> st >> en >> x >> y;
for (int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w;
adj[u].emb(w, v);
adj[v].emb(w, u);
}
disst = dijkstra(st);
disen = dijkstra(en);
disx = dijkstra(x);
disy = dijkstra(y);
ans = disx[y];
dfs(en);
cout << ans;
}
