/*ㅤ∧＿∧
( ･∀･)
( つ┳⊃
ε (_)へ⌒ヽﾌ
( ( ･ω･)
◎―◎ ⊃ ⊃
BePhuongSuperSiuwi
From TK4 - CHT
ㅤㅤ／ ⌒＼____
/・ ） \
/ノへ ノ /|
ノ ＼\ |/_/_/*/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define task "main"
#define endl '\n'
#define pb push_back
#define fi first
#define se second
#define ii pair<ll,ll>
const ll INF = LLONG_MAX;
const int MAXN = 100000 + 5;
int n, m;
int S, T, X, Y;
vector<ii> adj[MAXN];
vector<int> dag[MAXN];
ll ds[MAXN], dt[MAXN], dx_[MAXN], dy[MAXN];
vector<tuple<int,int,ll>> edges;
vector<char> inPath;
void dijkstra(int src, ll dist[]) {
fill(dist + 1, dist + n + 1, INF);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
dist[src] = 0;
pq.push({0, src});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d != dist[u]) continue;
for (auto &e : adj[u]) {
int v = e.fi;
ll w = e.se;
if (dist[v] > d + w) {
dist[v] = d + w;
pq.push({dist[v], v});
}
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
if (fopen(task ".inp", "r")) {
freopen(task ".inp", "r", stdin);
freopen(task ".out", "w", stdout);
}
cin >> n >> m;
cin >> S >> T >> X >> Y;
for (int i = 1; i <= n; i++) {
adj[i].clear();
dag[i].clear();
}
edges.clear();
for (int i = 0; i < m; i++) {
int u, v;
ll w;
cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
edges.emplace_back(u, v, w);
}
// Compute shortest distances
dijkstra(S, ds);
dijkstra(T, dt);
dijkstra(X, dx_);
dijkstra(Y, dy);
ll D = ds[T];
// Mark nodes on any shortest S->T path
inPath.assign(n+1, 0);
for (int u = 1; u <= n; u++) {
if (ds[u] + dt[u] == D) inPath[u] = 1;
}
// Build DAG of those edges
for (auto &e : edges) {
int u, v;
ll w;
tie(u, v, w) = e;
if (inPath[u] && inPath[v]) {
if (ds[u] + w + dt[v] == D) dag[u].pb(v);
if (ds[v] + w + dt[u] == D) dag[v].pb(u);
}
}
// Topo sort via Kahn
vector<int> indegree(n+1, 0);
for (int u = 1; u <= n; u++) if (inPath[u]) {
for (int v : dag[u]) indegree[v]++;
}
queue<int> q;
for (int u = 1; u <= n; u++) if (inPath[u] && indegree[u] == 0) q.push(u);
vector<int> topo;
while (!q.empty()) {
int u = q.front(); q.pop();
topo.pb(u);
for (int v : dag[u]) {
if (--indegree[v] == 0) q.push(v);
}
}
// DP
vector<ll> dp(n+1, INF);
ll ans = dx_[Y]; // not use ticket
for (int u : topo) {
dp[u] = dx_[u];
}
for (int u : topo) {
ans = min(ans, dp[u] + dy[u]);
for (int v : dag[u]) {
dp[v] = min(dp[v], dp[u]);
}
}
cout << ans << endl;
return 0;
}
