#include <bits/stdc++.h>
using namespace std;
// ===== BITWISE ===== //
#define MASK(i) (1LL << (i))
#define BIT(x, i) (1LL & ((x) >> (i)))
#define ON(x, i) ((x) | MASK(i))
#define OFF(x, i) ((x) & ~MASK(i))
#define LASTBIT(mask) ((mask) & -(mask))
// ===== OTHER ===== //
#define Longgggg ios_base::sync_with_stdio(0); cin.tie(0);
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (a); i >= (b); i--)
#define mod(x, k) ((((x) % (k)) + (k)) % (k))
#define all(x) begin(x), end(x)
#define fi first
#define se second
#define ll long long
#define endl '\n'
// ===== FILE ===== //
#define IN "A.in"
#define OUT "A.out"
#define DEBUG "debug.out"
//==================//
const ll INF = 1e18;
const int mxN = 1e5 + 5;
int N, M, S, T, U, V;
vector<pair<int, int>> adj[mxN];
vector<tuple<int, int, int>> edges;
vector<ll> dijkstra(int start) {
vector<ll> dist(N + 1, INF);
priority_queue<pair<ll, int>, vector<pair<ll, 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] : adj[u]) {
if (dist[v] > dist[u] + cost) {
dist[v] = dist[u] + cost;
pq.emplace(dist[v], v);
}
}
}
return dist;
}
ll run_dijkstra_with_pass(set<pair<int, int>> &pass_edges) {
vector<ll> dist(N + 1, INF);
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<>> pq;
dist[U] = 0;
pq.emplace(0, U);
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto &[v, cost] : adj[u]) {
int realCost = pass_edges.count({u, v}) ? 0 : cost;
if (dist[v] > dist[u] + realCost) {
dist[v] = dist[u] + realCost;
pq.emplace(dist[v], v);
}
}
}
return dist[V];
}
void solve() {
cin >> N >> M;
cin >> S >> T;
cin >> U >> V;
FOR(i, 1, M) {
int a, b, c;
cin >> a >> b >> c;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
edges.emplace_back(a, b, c);
}
auto distS = dijkstra(S);
auto distT = dijkstra(T);
ll distST = distS[T];
// Build subgraph with only shortest-path edges
vector<vector<pair<int, int>>> spG(N + 1);
for (auto &[u, v, c] : edges) {
if (distS[u] + c + distT[v] == distST)
spG[u].emplace_back(v, c);
if (distS[v] + c + distT[u] == distST)
spG[v].emplace_back(u, c);
}
// Use DFS to trace multiple shortest paths from S → T
const int LIMIT_PATHS = 500;
vector<vector<int>> paths;
vector<int> path;
function<void(int)> dfs = [&](int u) {
if ((int)paths.size() >= LIMIT_PATHS) return;
path.push_back(u);
if (u == T) {
paths.push_back(path);
path.pop_back();
return;
}
for (auto &[v, _] : spG[u]) {
dfs(v);
}
path.pop_back();
};
dfs(S);
ll best = INF;
for (auto &p : paths) {
set<pair<int, int>> pass_edges;
for (int i = 0; i + 1 < (int)p.size(); i++) {
pass_edges.insert({p[i], p[i + 1]});
pass_edges.insert({p[i + 1], p[i]}); // bidirectional
}
best = min(best, run_dijkstra_with_pass(pass_edges));
}
// Also test no-pass case
auto distU = dijkstra(U);
best = min(best, distU[V]);
cout << best << endl;
}
signed main() {
if (fopen(IN, "r")) {
freopen(IN, "r", stdin);
freopen(OUT, "w", stdout);
freopen(DEBUG, "w", stderr);
}
Longgggg
solve();
return 0;
}
