#include "bits/stdc++.h"
#define int long long
using namespace std;
#ifdef Nero
#include "Deb.h"
#else
#define deb(...)
#endif
using T = pair<int, int>;
const int N = 100005;
int n, m;
int s, t;
int uu, vv;
int cnt;
vector<int> pr[N];
set<pair<int, int>> se;
vector<pair<int, int>> g[N];
vector<int> dijk (int src) {
cnt++;
vector<bool> vis(n + 1, false);
vector<int> cost(n + 1, 1e16);
cost[src] = 0;
priority_queue<T, vector<T>, greater<T>> pq;
pq.emplace(0, src);
while (!pq.empty()) {
auto [c, v] = pq.top();
pq.pop();
if (vis[v] == true) {
continue;
}
vis[v] = true;
for (auto [u, w] : g[v]) {
if (vis[u]) {
continue;
}
if (cnt > 3 && se.count({v, u})) {
w = 0;
}
if (c + w < cost[u]) {
cost[u] = c + w;
pq.emplace(cost[u], u);
}
if (cnt == 3 && c + w == cost[u]) {
pr[u].push_back(v);
}
}
}
return cost;
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m;
cin >> s >> t;
cin >> uu >> vv;
for(int i = 0; i < m; ++i) {
int u, v, w;
cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
auto cuu1 = dijk(uu);
auto cvv1 = dijk(vv);
auto cs = dijk(s);
vector<bool> vis(n + 1);
function<void(int)> Dfs = [&](int v) {
vis[v] = true;
for (int u : pr[v]) {
se.emplace(u, v);
if (!vis[u]) {
Dfs(u);
}
}
};
Dfs(t);
auto cuu2 = dijk(uu);
auto cvv2 = dijk(vv);
int ans = cuu2[vv];
for (int i = 1; i <= n; ++i) {
ans = min(ans, cuu1[i] + cvv2[i]);
ans = min(ans, cuu2[i] + cvv1[i]);
}
cout << ans << '\n';
return 0;
}
