#include <bits/stdc++.h>
using namespace std;
#define int long long
const int INF = 1e18;
int N, M;
vector<tuple<int, int, int>> edges;
vector<vector<pair<int, int>>> graph; // adjacency list
vector<int> dijkstra(int start, const vector<vector<pair<int, int>>>& g) {
vector<int> dist(N + 1, INF);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<>> pq;
dist[start] = 0;
pq.emplace(0, start);
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto &[v, cost] : g[u]) {
if (dist[v] > dist[u] + cost) {
dist[v] = dist[u] + cost;
pq.emplace(dist[v], v);
}
}
}
return dist;
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int S, T, U, V;
cin >> N >> M;
cin >> S >> T;
cin >> U >> V;
graph.resize(N + 1);
edges.reserve(M);
for (int i = 0; i < M; ++i) {
int a, b, c;
cin >> a >> b >> c;
edges.emplace_back(a, b, c);
graph[a].emplace_back(b, c);
graph[b].emplace_back(a, c);
}
// Step 1: Run Dijkstra from S, T, and U
auto distS = dijkstra(S, graph);
auto distT = dijkstra(T, graph);
auto distU = dijkstra(U, graph);
int totalDistST = distS[T];
// Step 2: Build new graph where commuter pass edges are free
vector<vector<pair<int, int>>> newGraph(N + 1);
for (auto &[a, b, c] : edges) {
if (distS[a] + c + distT[b] == totalDistST ||
distS[b] + c + distT[a] == totalDistST) {
// Edge is part of some S-T shortest path
newGraph[a].emplace_back(b, 0);
newGraph[b].emplace_back(a, 0);
} else {
newGraph[a].emplace_back(b, c);
newGraph[b].emplace_back(a, c);
}
}
// Step 3: Dijkstra from U to V on new graph
auto finalDist = dijkstra(U, newGraph);
cout << finalDist[V] << "\n";
}
