#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define pii pair<int,int>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define int ll
const int N=1e5+10;
const ll inf=(ll)(1e18);
int n, m, s, t, u, v, dist[N][3];
vector<pii> g[N];
vector<int> adj[N];
int ans=inf;
bool was[N];
pii dp[N];
void Dijkstra(int root, int tp) {
vector<bool> vis(n+1, false);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.push(make_pair(0, root));
for (int i=1; i<=n; i++)
dist[i][tp]=inf;
dist[root][tp]=0;
while (pq.size()) {
int x=pq.top().second;
pq.pop();
if (vis[x])
continue;
vis[u]=true;
for (auto z:g[x]) {
int p, q;
tie(p, q)=z;
if (dist[p][tp]>dist[x][tp]+q) {
dist[p][tp]=dist[x][tp]+q;
pq.push(make_pair(dist[p][tp], p));
}
}
}
}
void dfs(int x) {
if (was[x])
return;
was[x]=true;
dp[x]={inf, inf};
if (x==t)
dp[x]={dist[x][1], dist[x][2]};
for (auto u:adj[x]) {
dfs(u);
dp[x].first=min(dp[x].first, dp[u].first);
dp[x].second=min(dp[x].second, dp[u].second);
}
if (dp[x].first!=inf) {
dp[x].first=min(dp[x].first, dist[x][1]);
dp[x].second=min(dp[x].second, dist[x][2]);
ans=min(ans, min(dist[x][1]+dp[x].second, dist[x][2]+dp[x].first));
}
}
int32_t main () {
ios::sync_with_stdio(false), cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i=1; i<=m; i++) {
int a, b, w;
cin >> a >> b >> w;
g[a].pb(make_pair(b, w));
g[b].pb(make_pair(a, w));
}
Dijkstra(s, 0);
Dijkstra(u, 1);
Dijkstra(v, 2);
for (int i=1; i<=n; i++) {
for (auto u:g[i]) {
if (dist[i][0]+u.second==dist[u.first][0]) {
adj[i].pb(u.first);
}
}
}
dfs(s);
cout << min(ans, dist[v][1]) << '\n';
return 0;
}
