#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll INF = 1e18;
int N, M, S, T, U, V;
struct Edge {
int to;
ll cost;
int id;
};
vector<vector<Edge>> adj;
vector<tuple<int, int, ll>> edges;
// Dijkstra: returns shortest distance from src and previous node tracking
vector<ll> dijkstra(int src, vector<vector<Edge>>& graph) {
vector<ll> dist(N + 1, INF);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<>> pq;
dist[src] = 0;
pq.emplace(0, src);
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto& e : graph[u]) {
if (dist[e.to] > dist[u] + e.cost) {
dist[e.to] = dist[u] + e.cost;
pq.emplace(dist[e.to], e.to);
}
}
}
return dist;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> N >> M;
cin >> S >> T;
cin >> U >> V;
adj.resize(N + 1);
for (int i = 0; i < M; ++i) {
int a, b;
ll c;
cin >> a >> b >> c;
adj[a].push_back({b, c, i});
adj[b].push_back({a, c, i});
edges.push_back({a, b, c});
}
// First Dijkstra from S and from T
vector<ll> distS = dijkstra(S, adj);
vector<ll> distT = dijkstra(T, adj);
ll minPathST = distS[T];
// Build new graph with some edges 0-cost if they are on some shortest S→T path
vector<vector<Edge>> modified(N + 1);
for (int i = 0; i < M; ++i) {
auto [a, b, c] = edges[i];
bool inShortestPath = false;
if (distS[a] + c + distT[b] == minPathST ||
distS[b] + c + distT[a] == minPathST) {
inShortestPath = true;
}
if (inShortestPath) {
modified[a].push_back({b, 0, i});
modified[b].push_back({a, 0, i});
} else {
modified[a].push_back({b, c, i});
modified[b].push_back({a, c, i});
}
}
// Dijkstra on modified graph from U to V
vector<ll> distUV = dijkstra(U, modified);
cout << distUV[V] << "\n";
return 0;
}
