#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int INF = 1e9 + 5;
const ll oo = 1e18 + 5;
const int MAXN = 1e5 + 5;
#define int ll
int n, m, s, t, u, v, dist[MAXN][3], best[MAXN][2];
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int> > > pq;
vector<pair<int, int>> adj[MAXN];
bool vis[MAXN];
int ans;
void DJ(int source, int type) {
for (int i = 1; i <= n; ++i) dist[i][type] = oo;
pq.push({0, source});
dist[source][type] = 0;
while (!pq.empty()) {
pair<int, int> t = pq.top(); pq.pop();
int u = t.second, kcu = t.first;
if (kcu > dist[u][type]) continue;
for (int i = 0; i < int(adj[u].size()); ++i) {
int v = adj[u][i].first, kcv = adj[u][i].second;
if (dist[v][type] > dist[u
][type] + kcv) {
dist[v][type] = dist[u][type] + kcv;
pq.push({dist[v][type], v});
}
}
}
}
void DFS(int u) {
best[u][0] = dist[u][1];
best[u][1] = dist[u][2];
// cout << u << ' ';
vis[u] = true;
for (int i = 0; i < int(adj[u].size()); ++i){
int v = adj[u][i].first, kcv = adj[u][i].second;
if (dist[v][0] == dist[u][0] - kcv) {
if (!vis[v]) DFS(v);
best[u][0] = min(best[u][0], best[v][0]);
best[u][1] = min(best[u][1], best[v][1]);
}
}
ans = min(ans, dist[u][1] + best[u][1]);
ans = min(ans, dist[u][2] + best[u][0]);
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; ++i) {
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
DJ(s, 0);
DJ(u, 1);
DJ(v, 2);
ans = dist[v][1];
DFS(t);
//
// cout << dist[3][0] << ' ';
//
cout << ans;
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(NULL); cout.tie(NULL);
// int T = 1; cin >> T; while(T--)
solve();
return 0;
}
