#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll inf = 1e18;
const int MAXN = 2e5 + 25;
vector <pair <ll, ll>> adj[MAXN];
ll dist[MAXN][2], dist2[MAXN], dist3[MAXN];
int main () {
ios::sync_with_stdio(0); cin.tie(0);
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
for (int i = 1; i <= m; i++) {
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
priority_queue <pair <ll, int>, vector <pair <ll, int>>, greater <>> pq;
pq.push({0, s});
for (int i = 1; i <= n; i++) {
dist[i][0] = dist[i][1] = inf;
}
dist[s][0] = dist[t][1] = 0;
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist[k.second][0]) continue;
for (auto j : adj[k.second]) {
if (dist[j.first][0] > j.second + k.first) {
dist[j.first][0] = j.second + k.first;
pq.push({dist[j.first][0], j.first});
}
}
}
pq.push({0, t});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist[k.second][1]) continue;
for (auto j : adj[k.second]) {
if (dist[j.first][1] > j.second + k.first) {
dist[j.first][1] = j.second + k.first;
pq.push({dist[j.first][1], j.first});
}
}
}
for (int i = 1; i <= n; i++) dist2[i] = dist3[i] = inf;
dist2[u] = dist3[u] = 0;
pq.push({0, u});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist2[k.second]) continue;
for (auto j : adj[k.second]) {
ll cost = k.first;
if (dist[k.second][0] + j.second == dist[j.first][0] && dist[j.first][1] + j.second == dist[k.second][1]) {
} else {
cost += j.second;
}
if (dist2[j.first] > cost) {
dist2[j.first] = cost;
pq.push({dist2[j.first], j.first});
}
}
}
pq.push({0, u});
while (!pq.empty()) {
auto k = pq.top();
pq.pop();
if (k.first > dist3[k.second]) continue;
for (auto j : adj[k.second]) {
ll cost = k.first;
if (dist[k.second][1] + j.second == dist[j.first][1] && dist[j.first][0] + j.second == dist[k.second][0]) {
} else {
cost += j.second;
}
if (dist3[j.first] > cost) {
dist3[j.first] = cost;
pq.push({dist3[j.first], j.first});
}
}
}
cout << min(dist3[v], dist2[v]) << '\n';
}
