#include "bits/stdc++.h"
using namespace std;
#define int long long
const int N = 1e5 + 5;
const int INF = 1e18;
int n, m;
int s, t, u, v;
vector<pair<int, int>> graph[N];
map<pair<int, int>, bool> is_on_shortest_path;
// Find shortest path from src to all nodes
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() {
// Get shortest paths
vector<int> dist_from_s = dijkstra(s);
vector<int> dist_from_t = dijkstra(t);
int shortest_s_to_t = dist_from_s[t];
// Mark edges on any shortest path from s to t
for (int i = 1; i <= n; i++) {
for (auto edge : graph[i]) {
int j = edge.first;
int weight = edge.second;
// Check if this edge is part of any shortest path from s to t
if (dist_from_s[i] + weight + dist_from_t[j] == shortest_s_to_t ||
dist_from_s[j] + weight + dist_from_t[i] == shortest_s_to_t) {
// Store both edge directions
if (i < j) {
is_on_shortest_path[{i, j}] = true;
} else {
is_on_shortest_path[{j, i}] = true;
}
}
}
}
// Find shortest path from u to v with free edges
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 edge : graph[node]) {
int next = edge.first;
int weight = edge.second;
// Create a canonical edge representation (smaller node first)
pair<int, int> edge_key = (node < next) ? make_pair(node, next) : make_pair(next, node);
// If edge is on shortest path, cost is 0, otherwise it's the original weight
int cost = is_on_shortest_path.count(edge_key) ? 0 : weight;
if (dist[node] + cost < dist[next]) {
dist[next] = dist[node] + cost;
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;
}
