#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = numeric_limits<ll>::max() / 4;
// Standard Dijkstra to compute shortest paths
vector<ll> dijkstra(int src, const vector<vector<pair<int,ll>>> &adj) {
int n = adj.size();
vector<ll> dist(n, INF);
using pli = pair<ll,int>;
priority_queue<pli, vector<pli>, greater<pli>> 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 &[v, w] : adj[u]) {
if (dist[v] > d + w) {
dist[v] = d + w;
pq.emplace(dist[v], v);
}
}
}
return dist;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N, M;
cin >> N >> M;
int S, T;
cin >> S >> T;
int U, V;
cin >> U >> V;
vector<vector<pair<int,ll>>> adj(N + 1);
vector<tuple<int,int,ll>> edges;
edges.reserve(M);
for (int i = 0; i < M; ++i) {
int a, b;
ll c;
cin >> a >> b >> c;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
edges.emplace_back(a, b, c);
}
// Compute shortest distances from S, T, U, and V
auto dS = dijkstra(S, adj);
auto dT = dijkstra(T, adj);
auto dU = dijkstra(U, adj);
auto dV = dijkstra(V, adj);
ll bestST = dS[T];
// Build DAG of edges on some shortest path from S to T
vector<vector<int>> dag(N + 1), dag_rev(N + 1);
for (auto &[a, b, c] : edges) {
if (dS[a] + c + dT[b] == bestST) {
dag[a].push_back(b);
dag_rev[b].push_back(a);
}
if (dS[b] + c + dT[a] == bestST) {
dag[b].push_back(a);
dag_rev[a].push_back(b);
}
}
// Mark nodes reachable from S and reaching T in the DAG
vector<char> fromS(N + 1, false), toT(N + 1, false);
queue<int> q;
fromS[S] = true; q.push(S);
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v : dag[u]) {
if (!fromS[v]) {
fromS[v] = true;
q.push(v);
}
}
}
toT[T] = true; q.push(T);
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v : dag_rev[u]) {
if (!toT[v]) {
toT[v] = true;
q.push(v);
}
}
}
// Collect all nodes on some S-T shortest path
vector<int> sp_nodes;
for (int i = 1; i <= N; ++i) {
if (fromS[i] && toT[i]) sp_nodes.push_back(i);
}
// Sort by distance from S to impose topological order
sort(sp_nodes.begin(), sp_nodes.end(), [&](int a, int b) {
return dS[a] < dS[b];
});
// DP: Bmin[u] = minimal distance dV[x] over all x reachable from u in DAG
vector<ll> Bmin(N + 1, INF);
for (int u : sp_nodes) {
Bmin[u] = dV[u];
}
for (int i = (int)sp_nodes.size() - 1; i >= 0; --i) {
int u = sp_nodes[i];
for (int v : dag[u]) {
if (toT[v]) {
Bmin[u] = min(Bmin[u], Bmin[v]);
}
}
}
// Answer: either no pass (dU[V]) or boarding at some u and exiting at the best downstream node
ll answer = dU[V];
for (int u : sp_nodes) {
if (dU[u] < INF && Bmin[u] < INF) {
answer = min(answer, dU[u] + Bmin[u]);
}
}
cout << answer << '\n';
return 0;
}
