#include <bits/stdc++.h>
using namespace std;
template <class T>
vector<T> dijkstra(const vector<vector<pair<int, T>>> &adj, vector<T> dist) {
int n = adj.size();
priority_queue<pair<T, int>, vector<pair<T, int>>, greater<>> pq;
for (int u = 0; u < n; u++) {
pq.push({dist[u], u});
}
while (!pq.empty()) {
auto [d, u] = pq.top();
pq.pop();
if (d != dist[u]) continue;
for (auto [v, w] : adj[u]) {
if (dist[u] + w < dist[v]) {
dist[v] = dist[u] + w;
pq.push({dist[v], v});
}
}
}
return dist;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
constexpr long long INF = 4e18;
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t; s--; t--;
int q, r;
cin >> q >> r; q--; r--;
vector<vector<pair<int, long long>>> adj(n);
for (int i = 0; i < m; i++) {
int u, v, w;
cin >> u >> v >> w;
u--; v--;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
auto edges_that_may_belong_to_a_shortest_path_from_s_to_t = [&]() -> vector<array<int, 2>> {
vector<array<int, 2>> ret;
vector<long long> dist(n, INF); dist[s] = 0;
dist = dijkstra<long long>(adj, dist);
vector<vector<int>> rev_dag(n);
for (int u = 0; u < n; u++) {
for (auto [v, w] : adj[u]) {
if (dist[u] + w == dist[v]) {
rev_dag[v].push_back(u);
}
}
}
vector<bool> vis(n, false);
queue<int> que;
vis[t] = true;
que.push(t);
while (!que.empty()) {
int u = que.front();
que.pop();
for (int v : rev_dag[u]) {
ret.push_back({v, u});
if (!vis[v]) {
vis[v] = true;
que.push(v);
}
}
}
return ret;
}();
auto dist_q_downstream = [&]() -> vector<long long> {
vector<long long> dist(n, INF); dist[q] = 0;
dist = dijkstra(adj, dist);
dist = dijkstra([&]() -> vector<vector<pair<int, long long>>> {
vector<vector<pair<int, long long>>> adj(n);
for (auto [u, v] : edges_that_may_belong_to_a_shortest_path_from_s_to_t) adj[u].push_back({v, 0});
return adj;
}(), dist);
dist = dijkstra(adj, dist);
return dist;
}();
auto dist_q_upstream = [&]() -> vector<long long> {
vector<long long> dist(n, INF); dist[q] = 0;
dist = dijkstra(adj, dist);
dist = dijkstra([&]() -> vector<vector<pair<int, long long>>> {
vector<vector<pair<int, long long>>> adj(n);
for (auto [u, v] : edges_that_may_belong_to_a_shortest_path_from_s_to_t) adj[v].push_back({u, 0});
return adj;
}(), dist);
dist = dijkstra(adj, dist);
return dist;
}();
cout << min(dist_q_downstream[r], dist_q_upstream[r]) << '\n';
}
