#include<bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int, int> pii;
const int inf=1e18;
int n, m, s, t, u, v;
vector<vector<pii>> adj;
void dijkstra(int s, vector<int>& d) {
priority_queue<pii> pq;
pq.push({0, s}); d[s]=0;
while (!pq.empty()) {
auto [c, u]=pq.top();
pq.pop(); c=-c;
if (d[u]<c) continue;
for (auto [v, w] : adj[u]) {
if (c+w>=d[v]) continue;
else d[v]=w+c;
pq.push({-d[v], v});
}
}
}
vector<int> spg(bool rev, vector<int>& d, vector<int>& ds, vector<int>& dt) {
vector<int> ind(n+1, 0);
vector<vector<int>> spg(n+1, vector<int>());
for (int u = 1; u <= n; ++u) {
for (auto [v, w] : adj[u]) {
if (ds[u]+w+dt[v]>ds[t]) continue;
if (rev) spg[v].push_back(u);
else spg[u].push_back(v);
ind[rev?u:v]++;
}
}
int r=d[v];
queue<int> q; q.push(rev?t:s);
vector<int> dp(n+1, inf); dp[rev?t:s]=d[rev?t:s];
while (!q.empty()) {
auto u=q.front(); q.pop();
if (--ind[u]!=-1) continue;
for (auto v : spg[u]) {
if (--ind[v]==0) q.push(v);
dp[v]=min(dp[v], min(dp[u], d[v]));
}
} return dp;
}
signed main() {
cin.tie(0)->sync_with_stdio(false);
cin >> n >> m >> s >> t >> u >> v;
adj.assign(n+1, vector<pii>());
for (int i = 0; i < m; ++i) {
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<int> ds(n+1, inf), dt(n+1, inf), du(n+1, inf), dv(n+1, inf);
dijkstra(s, ds); dijkstra(t, dt); dijkstra(u, du); dijkstra(v, dv);
int r=du[v];
auto dp=spg(false, du, ds, dt);
auto dq=spg(true, du, ds, dt);
for (int u = 1; u <= n; ++u) {
r=min(r, min(dp[u], dq[u])+dv[u]);
} cout << r << '\n';
return 0;
}
