//Created by sangph2612
#include <bits/stdc++.h>
using namespace std;
// #define Sang 1
#define int long long
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define endl '\n'
#define FOR(i, a, b) for(__typeof(b) i = a, _b = b; i <= _b; ++i)
#define FORD(i, a, b) for(__typeof(a) i = a, _b = b; i >= _b; --i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define MASK(i) (1ll<<(i))
#define BIT(t, i) (((t)>>(i))&1)
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef pair<int, ii> pii;
const int MOD = 1e9+7;
const int N = 2e5+5;
const int INF = 0x3f3f3f3f;
template <class T> bool minimize(T &a, T b) { if (a > b) { a = b; return true; } return false;}
template <class T> bool maximize(T &a, T b) { if (a < b) { a = b; return true; } return false;}
// **** ****
// * * *
// * K.B *
// * *
// * *
int n, m, s, t, u, v, dist[3][N], best[N][2], ans;
// dist[i][0] : khoảng cách ngắn nhất từ s->i
// dist[i][1] : khoảng cách ngắn nhất từ u->i
// dist[i][2] : khoảng cách ngắn nhất từ v->i
vector<ii> G[N];
void dijkstra(int st, int type){
memset(dist[type], 0x3f, sizeof dist[type]);
priority_queue<ii, vector<ii>, greater<ii>> Q;
dist[type][st] = 0;
Q.push({dist[type][st], st});
while (!Q.empty()){
int u = Q.top().se, w = Q.top().fi; Q.pop();
if (w != dist[type][u]) continue;
for (auto v : G[u]){
if (minimize(dist[type][v.fi], dist[type][u] + v.se)){
Q.push({dist[type][v.fi], v.fi});
}
}
}
}
void dfs(int u){
best[u][0] = dist[1][u];
best[u][1] = dist[2][u];
// cerr << u << endl;
for (auto v : G[u]){
if (dist[0][v.fi] + v.se != dist[0][u]) continue;
dfs(v.fi);
minimize(best[u][0], best[v.fi][0]);
minimize(best[u][1], best[v.fi][1]);
}
minimize(ans, dist[1][u] + best[u][1]);
minimize(ans, dist[2][u] + best[u][0]);
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
FOR (i, 1, m){
int u, v, c; cin >> u >> v >> c;
G[u].pb({v,c});
G[v].pb({u,c});
}
dijkstra(s, 0);
dijkstra(u, 1);
dijkstra(v, 2);
ans = dist[1][v];
dfs(t);
// cout << dist[1][5] << ' ' << dist[2][2] << endl;
cout << ans;
return 0;
}
