#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
typedef long long ll;
typedef pair<ll, int> pli;
const ll INF = 1e18;
int main() {
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t;
cin >> u >> v;
// Store graph edges
vector<vector<pair<int, ll>>> graph(n + 1);
vector<tuple<int, int, ll>> railways(m);
for (int i = 0; i < m; i++) {
int a, b;
ll c;
cin >> a >> b >> c;
railways[i] = {a, b, c};
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
// Dijkstra function to compute shortest distances
auto dijkstra = [&](int start, vector<ll>& dist) {
dist.assign(n + 1, INF);
dist[start] = 0;
priority_queue<pli, vector<pli>, greater<pli>> pq;
pq.push({0, start});
while (!pq.empty()) {
auto [d, node] = pq.top();
pq.pop();
if (d > dist[node]) continue;
for (auto [next, weight] : graph[node]) {
if (dist[node] + weight < dist[next]) {
dist[next] = dist[node] + weight;
pq.push({dist[next], next});
}
}
}
};
// Compute distances from S to all nodes
vector<ll> dist_from_s(n + 1);
dijkstra(s, dist_from_s);
// Compute distances from all nodes to T
vector<ll> dist_to_t(n + 1);
dijkstra(t, dist_to_t);
// Find shortest path distance from S to T
ll min_st_dist = dist_from_s[t];
// Create a new graph where railways on min-cost S-T paths have cost 0
vector<vector<pair<int, ll>>> modified_graph(n + 1);
for (auto [a, b, c] : railways) {
// Check if this railway is on some minimum cost path from S to T
bool on_min_path = (dist_from_s[a] + c + dist_to_t[b] == min_st_dist) ||
(dist_from_s[b] + c + dist_to_t[a] == min_st_dist);
// If on minimum path, cost is 0; otherwise, original cost
ll new_cost = on_min_path ? 0 : c;
modified_graph[a].push_back({b, new_cost});
modified_graph[b].push_back({a, new_cost});
}
// Find shortest path from U to V in the modified graph
vector<ll> dist_from_u(n + 1, INF);
dist_from_u[u] = 0;
priority_queue<pli, vector<pli>, greater<pli>> pq;
pq.push({0, u});
while (!pq.empty()) {
auto [d, node] = pq.top();
pq.pop();
if (d > dist_from_u[node]) continue;
for (auto [next, weight] : modified_graph[node]) {
if (dist_from_u[node] + weight < dist_from_u[next]) {
dist_from_u[next] = dist_from_u[node] + weight;
pq.push({dist_from_u[next], next});
}
}
}
// Output the minimum cost from U to V
cout << dist_from_u[v] << endl;
return 0;
}
