#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<tuple<int, int, int>> edges;
vector<pair<int, int>> adj[mxN];
vector<ll> dijkstra(int src) {
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 [v, c] : adj[u]) {
if (dist[v] > dist[u] + c) {
dist[v] = dist[u] + c;
pq.emplace(dist[v], v);
}
}
}
return dist;
}
void solve() {
cin >> N >> M;
cin >> S >> T;
cin >> U >> V;
FOR(i, 1, M) {
int a, b, c;
cin >> a >> b >> c;
edges.emplace_back(a, b, c);
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
vector<ll> distS = dijkstra(S);
vector<ll> distT = dijkstra(T);
vector<ll> distU = dijkstra(U);
ll best = INF;
// Xét mỗi cạnh trên đường ngắn nhất từ S -> T
for (auto &[a, b, c] : edges) {
bool onPath = false;
if (distS[a] + c + distT[b] == distS[T]) onPath = true;
if (distS[b] + c + distT[a] == distS[T]) onPath = true;
if (!onPath) continue;
// Tạm thời tạo graph mới với commuter pass miễn phí cho cạnh (a, b)
vector<vector<pair<int, int>>> newAdj(N + 1);
for (auto &[x, y, w] : edges) {
int cost = w;
if ((x == a && y == b) || (x == b && y == a)) cost = 0;
newAdj[x].emplace_back(y, cost);
newAdj[y].emplace_back(x, cost);
}
// Dijkstra lại từ U trong graph mới
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] : newAdj[u]) {
if (dist[v] > dist[u] + cost) {
dist[v] = dist[u] + cost;
pq.emplace(dist[v], v);
}
}
}
best = min(best, dist[V]);
}
// Ngoài ra, còn trường hợp không dùng commuter pass
vector<ll> distNormal = dijkstra(U);
best = min(best, distNormal[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;
}
