#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define all(x) x.begin(), x.end()
#define pii pair<int, int>
#define fi first
#define se second
#define pb emplace_back
template <class T>
inline bool maximize(T &a, const T &b) {return (a < b ? (a = b, 1) : 0);}
template <class T>
inline bool minimize(T &a, const T &b) {return (a > b ? (a = b, 1) : 0);}
const int N = 1e5 + 5;
const ll INF = 1e18;
int n, m, s, t, u, v;
vector<pii> adj[N];
vector<int> par[N], child[N];
ll disU[N], disV[N], disS[N];
bool reach[N];
ll f[N], g[N], ans;
void dijkstra(int st, ll dis[N]){
fill(dis, dis+n+1, INF);
dis[st] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> q;
q.push({0, st});
while (q.size()){
int cur = q.top().se;
ll curW = q.top().fi;
q.pop();
if (dis[cur] != curW) continue;
for (auto[nxt, w] : adj[cur])
if (minimize(dis[nxt], curW + w))
q.push({dis[nxt], nxt});
}
}
void Dijkstra(int st, ll dis[N]){
fill(dis, dis+n+1, INF);
dis[st] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> q;
q.push({0, st});
while (q.size()){
int cur = q.top().se;
ll curW = q.top().fi;
q.pop();
if (dis[cur] != curW) continue;
for (auto[nxt, w] : adj[cur]){
if (minimize(dis[nxt], curW + w)){
q.push({dis[nxt], nxt});
par[nxt].clear();
par[nxt].push_back(cur);
}else if (dis[nxt] == curW + w){
par[nxt].push_back(cur);
}
}
}
}
ll dfs(int cur){
if (f[cur] != -1) return f[cur];
ll best = disV[cur];
for (int nxt : par[cur])
minimize(best, dfs(nxt));
return f[cur] = best;
}
ll Dfs(int cur){
if (g[cur] != -1) return g[cur];
ll best = disV[cur];
for (int nxt : child[cur])
minimize(best, Dfs(nxt));
return g[cur] = best;
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; ++i){
int a, b, w;
cin >> a >> b >> w;
adj[a].push_back({b, w});
adj[b].push_back({a, w});
}
dijkstra(u, disU);
dijkstra(v, disV);
Dijkstra(s, disS);
queue<int> q;
q.push(t);
while (q.size()){
int cur = q.front();
q.pop();
if (!reach[cur]){
reach[cur] = 1;
for (int nxt : par[cur]){
child[nxt].push_back(cur);
q.push(nxt);
}
}
}
memset(f, -1, sizeof f);
memset(g, -1, sizeof g);
ans = disU[v];
for (int i = 1; i <= n; ++i)
if (reach[i])
minimize(ans, disU[i] + min(dfs(i), Dfs(i)));
cout << ans;
}
