#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <map>
#include <unordered_map>
#include <set>
#include <queue>
#include <numeric>
#include <cmath>
#include <cstring>
#include <climits>
#include <stack>
#include <math.h>
#include <iomanip>
#include <bitset>
typedef long long ll;
using namespace std;
using vi = vector<int>;
using T = pair<ll,int>;
#define fst first
#define snd second
#define pll pair<ll,ll>
#define pi pair<int,int>
#define triple pair<pair<ll,ll>,ll>
#define pb push_back
#define all(x) (x).begin(), (x).end()
// JOI 2018
// https://oj.uz/problem/view/JOI18_commuter_pass
const ll MAXN = 1e5 +1;
const ll INF = LLONG_MAX;
vector<ll> dist_t(MAXN,INF);
vector<ll> dist_s(MAXN,INF);
vector<ll> dist_u(MAXN,INF);
vector<ll> dist_v(MAXN,INF);
vector<ll> dp_u(MAXN,INF);
vector<ll> dp_v(MAXN,INF);
vector<pair<int, ll>> adj[MAXN];
vector<ll> order_s; vector<ll> order_t;
ll s, t; vector<ll> opt;
void dijkstra(int source, vector<ll> &dist, bool record_order, vector<ll> &order = opt) {
priority_queue<T,vector<T>, greater<T>> pq;
pq.push({0,source}); dist[source] = 0;
while (!pq.empty()) {
auto temp = pq.top(); pq.pop();
int node = temp.snd; ll cdist = temp.fst;
if (cdist > dist[node]) continue;
if (record_order) order.pb(node);
for (auto &[next, w] : adj[node]) {
if (dist[node] + w < dist[next]) {
dist[next] = dist[node] + w;
pq.push({dist[next],next});
}
}
}
}
bool onpath(int v) { // on a shortest path from s to t?
return (dist_s[v] + dist_t[v] == dist_t[s]);
}
int main () {
ll n, m; cin >> n >> m;
cin >> s >> t;
ll u, v; cin >> u >> v;
for (int i = 0; i<m; i++) {
ll a, b, c; cin >> a >> b >> c;
adj[a].pb({b,c}); adj[b].pb({a,c});
}
dijkstra(s, dist_s, true, order_s);
dijkstra(t, dist_t, false);
dijkstra(u, dist_u, false);
dijkstra(v, dist_v, false);
dp_u[s] = dist_u[s];
dp_v[s] = dist_v[s];
for (auto vert : order_s) {
if (!onpath(vert)) continue;
dp_u[vert] = dist_u[vert];
dp_v[vert] = dist_v[vert];
for (auto &[nb, w] : adj[vert]) {
if (dist_s[nb] + w == dist_s[vert]) {
dp_u[vert] = min(dp_u[vert], dp_u[nb]);
dp_v[vert] = min(dp_v[vert], dp_v[nb]);
}
}
}
ll ans = dist_u[v];
for (int i =1; i<=n; i++) {
if (onpath(i)) {
ans = min(ans, dist_u[i] + dp_v[i]);
ans = min(ans, dist_v[i] + dp_u[i]);
}
}
cout << ans;
}
