#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;
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);
}
// Precompute distances
auto distS = dijkstra(S, graph);
auto distT = dijkstra(T, graph);
auto distU = dijkstra(U, graph);
int totalST = distS[T];
int answer = INF;
for (auto &[a, b, c] : edges) {
bool onShortestPath = false;
if (distS[a] + c + distT[b] == totalST) onShortestPath = true;
if (distS[b] + c + distT[a] == totalST) onShortestPath = true;
if (!onShortestPath) continue;
// Build new graph with only (a,b) free
vector<vector<pair<int, int>>> newGraph(N + 1);
for (auto &[x, y, w] : edges) {
int cost = w;
if ((x == a && y == b) || (x == b && y == a)) {
cost = 0; // this edge is free
}
newGraph[x].emplace_back(y, cost);
newGraph[y].emplace_back(x, cost);
}
auto dist = dijkstra(U, newGraph);
answer = min(answer, dist[V]);
}
cout << answer << "\n";
}
