#include <bits/stdc++.h>
#define F first
#define S second
#define SZ(x) ((int)(x).size())
#define ALL(x) x.begin(), x.end()
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vii = vector<pii>;
using vll = vector<pll>;
const ll inf = 0x3f3f3f3f3f3f3f3f;
void sol() {
int n, m, src, dest, U, V;
cin >> n >> m >> src >> dest >> U >> V;
--src, --dest, --U, --V;
vector<vii> adj(n);
for (int i = 0; i < m; i++) {
int u, v, w;
cin >> u >> v >> w;
adj[--u].push_back({--v, w});
adj[v].push_back({u, w});
}
auto dijkstra = [n, m, &adj](int src) -> pair<vl, vvi> {
vl dis(n, inf);
vvi from(n);
dis[src] = 0;
using T = pair<ll, int>;
priority_queue<T, vector<T>, greater<>> pq;
pq.push({0, src});
while (SZ(pq)) {
auto [w, u] = pq.top();
pq.pop();
if (w > dis[u]) continue;
for (auto [v, w2]: adj[u]) {
if (dis[v] > w + w2) {
dis[v] = w + w2;
from[v] = {u};
pq.push({dis[v], v});
} else if (dis[v] == w + w2) {
from[v].push_back(u);
}
}
}
return {dis, from};
};
auto [dis_src, from] = dijkstra(src);
vl dis_u = dijkstra(U).F;
vl dis_v = dijkstra(V).F;
vi deg(n, 0);
vi vec;
vector<bool>vis(n);
function<void(int)> dfs = [&](int u) -> void {
vis[u] = 1;
vec.push_back(u);
for (int v: from[u]) if (!vis[v]) dfs(v);
};
dfs(dest);
for (int u: vec) for (int v: from[u]) deg[v]++;
vl mn_u(n, inf), mn_v(n, inf);
queue<int> qq({dest});
ll ans = dis_u[V];
while (SZ(qq)) {
int u = qq.front();
qq.pop();
mn_u[u] = min(mn_u[u], dis_u[u]);
mn_v[u] = min(mn_v[u], dis_v[u]);
ans = min(ans, mn_u[u] + dis_v[u]);
ans = min(ans, mn_v[u] + dis_u[u]);
// cerr << u << '\n';
// cerr << mn_u[u] << ' ' << dis_v[u] << '\n';
// cerr << mn_v[u] << ' ' << dis_u[u] << '\n';
for (int v: from[u]) {
mn_u[v] = min(mn_u[v], mn_u[u]);
mn_v[v] = min(mn_v[v], mn_v[u]);
if (--deg[v] == 0) {
qq.push(v);
}
}
}
cout << ans << '\n';
}
signed main() {
cin.tie(nullptr)->sync_with_stdio(false);
sol();
}
