#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5 + 5;
const ll inf = 1e18;
int n, m, uu, vv, s, t, deg[N], topo[N];
vector <pair<int, int>> g[N];
vector <int> adj[N], radj[N];
ll dist[3][N], dp[N];
bool vis[N];
void dijkstra(int u, int id) {
fill(dist[id], dist[id] + n + 1, inf);
dist[id][u] = 0;
priority_queue <pair<int, int>, vector <pair<int, int>>, greater<pair<int, int>>> pq;
pq.emplace(0, u);
while (!pq.empty()) {
int u = pq.top().second;
ll du = pq.top().first;
pq.pop();
if (du != dist[id][u]) continue;
for (pair <int, int> P : g[u]) {
int v = P.first, w = P.second;
if (du + w < dist[id][v]) {
dist[id][v] = du + w;
pq.emplace(dist[id][v], v);
}
}
}
}
vector <int> luu;
void dfs(int u) {
luu.push_back(u);
vis[u] = 1;
for (pair <int, int> P : g[u]) {
int v = P.first, w = P.second;
if (dist[0][u] == dist[0][v] + w) {
deg[u]++;
adj[v].push_back(u);
radj[u].push_back(v);
if (!vis[v]) dfs(v);
}
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
//freopen("test.inp", "r", stdin);
// freopen(".OUT", "w", stdout);
cin >> n >> m >> s >> t >> uu >> vv;
while (m--) {
int a, b, c;
cin >> a >> b >> c;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
dijkstra(s, 0);
dijkstra(uu, 1);
dijkstra(vv, 2);
dfs(t);
queue <int> q;
int idd = 0;
ll ans = dist[1][vv];
for (int u : luu) if (deg[u] == 0) q.push(u);
while (!q.empty()) {
int u = q.front();
q.pop();
topo[++idd] = u;
for (int v : adj[u]) if (--deg[v] == 0) q.push(v);
}
for (int i=idd;i>=1;--i) {
int u = topo[i];
dp[u] = dist[2][u];
for (int v : adj[u]) dp[u] = min(dp[u], dp[v]);
ans = min(ans, dist[1][u] + dp[u]);
}
fill(dp, dp + idd + 1, 0);
for (int i=1;i<=idd;++i) {
int u = topo[i];
dp[u] = dist[2][u];
for (int v : radj[u]) dp[u] = min(dp[u], dp[v]);
ans = min(ans, dist[1][u] + dp[u]);
}
cout << ans;
}
