#include <bits/stdc++.h>
#define pii pair <long long, long long>
#define fi first
#define se second
using namespace std;
using ll = long long;
const ll N = 100005, inf = 1e16;
int n, m, S, T, U, V;
vector <pii> adj[N];
ll dist_s[N], dist_t[N], dist_ans[N];
int a[N], b[N], c[N];
map <pair <int, int>, ll> mp;
void dijkstra(int x, ll *length) {
for (int i = 1; i <= n; i++) length[i] = inf;
length[x] = 0;
priority_queue <pii, vector <pii>, greater <pii> > q;
q.push({length[x], x});
while(q.size()) {
auto tmp = q.top();
q.pop();
int u = tmp.se, z = tmp.fi;
if (z > length[u]) continue;
for (auto v : adj[u]) {
if (length[v.fi] > length[u] + v.se) {
length[v.fi] = length[u] + v.se;
q.push({length[v.fi], v.fi});
}
}
}
}
void dijkstra1() {
for (int i = 1; i <= n; i++) dist_ans[i] = inf;
dist_ans[U] = 0;
priority_queue <pii, vector <pii>, greater <pii> > q;
q.push({dist_ans[U], U});
while(q.size()) {
auto tmp = q.top();
q.pop();
ll u = tmp.se, z = tmp.fi;
if (z > dist_ans[u]) continue;
for (auto v : adj[u]) {
int x = min(u, v.fi), y = max(u, v.fi);
if (dist_ans[v.fi] > dist_ans[u] + mp[{x, y}]) {
dist_ans[v.fi] = dist_ans[u] + mp[{x, y}];
q.push({dist_ans[v.fi], v.fi});
}
}
}
}
signed main() {
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= m; i++) {
cin >> a[i] >> b[i] >> c[i];
adj[a[i]].emplace_back(b[i], c[i]);
adj[b[i]].emplace_back(a[i], c[i]);
}
dijkstra(S, dist_s);
dijkstra(T, dist_t);
// for (int i = 1; i <= n; i++) cout << dist_s[i] << ' ' << dist_t[i] << '\n';
ll minn = dist_s[T]; // khoang cach ngan nhat tu s den t
for (int i = 1; i <= m; i++) {
int x = min(a[i], b[i]);
int y = max(a[i], b[i]);
if ((dist_s[a[i]] + c[i] + dist_t[b[i]] == minn) || (dist_s[b[i]] + c[i] + dist_t[a[i]] == minn)) {
int x = min(a[i], b[i]);
int y = max(a[i], b[i]);
mp[{x, y}] = 0;
}
else mp[{x, y}] = c[i];
// cout << a[i] << ' ' << b[i] << ' ' << mp[{x, y}] << '\n';
}
dijkstra1();
cout << dist_ans[V];
return 0;
}
