#include "bits/stdc++.h"
using namespace std;
#define int long long
const int INF = 1e18;
int n, m;
int s, t, u, v;
vector<pair<int, int>> graph[100005];
// Dijkstra's algorithm to compute shortest paths from a source
vector<int> dijkstra(int src) {
vector<int> dist(n + 1, INF);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
dist[src] = 0;
pq.push({0, src});
while (!pq.empty()) {
int d = pq.top().first;
int node = pq.top().second;
pq.pop();
if (d > dist[node]) continue;
for (auto edge : graph[node]) {
int next = edge.first;
int weight = edge.second;
if (dist[node] + weight < dist[next]) {
dist[next] = dist[node] + weight;
pq.push({dist[next], next});
}
}
}
return dist;
}
int solve() {
// Compute shortest paths from S and T
vector<int> dist_s = dijkstra(s);
vector<int> dist_t = dijkstra(t);
int shortest_s_to_t = dist_s[t]; // Shortest distance from S to T
// Build a new graph where edges on any shortest path from S to T have cost 0
vector<pair<int, int>> new_graph[100005];
for (int i = 1; i <= n; i++) {
for (auto [next, weight] : graph[i]) {
// Check if this edge (i -> next) is on any shortest path from S to T
bool on_shortest_path = (dist_s[i] + weight + dist_t[next] == shortest_s_to_t) ||
(dist_s[next] + weight + dist_t[i] == shortest_s_to_t);
// Add the edge to the new graph with appropriate cost
new_graph[i].push_back({next, on_shortest_path ? 0 : weight});
}
}
// Run Dijkstra from U to V on the new graph
vector<int> dist(n + 1, INF);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
dist[u] = 0;
pq.push({0, u});
while (!pq.empty()) {
int d = pq.top().first;
int node = pq.top().second;
pq.pop();
if (d > dist[node]) continue;
for (auto [next, weight] : new_graph[node]) {
if (dist[node] + weight < dist[next]) {
dist[next] = dist[node] + weight;
pq.push({dist[next], next});
}
}
}
return dist[v];
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> m;
cin >> s >> t >> u >> v;
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
cout << solve() << endl;
return 0;
}
