#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (a); i < (b); ++i)
#define per(i, a, b) for (int i = (b - 1); i >= (a); --i)
#define trav(a, x) for (auto &a : x)
#define all(x) x.begin(), x.end()
#define sz(x) x.size()
#define pb push_back
#define debug(x) cout << #x << " = " << x << endl
#define umap unordered_map
#define uset unordered_set
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<pll> vpll;
const int INF = 1'000'000'007;
vpll graph[100001];
int n, m, s, t, a, b;
int main() {
cin.tie(0)->sync_with_stdio(0);
cin.exceptions(cin.failbit);
cin >> n >> m >> s >> t >> a >> b;
--s;
--t;
--a;
--b;
rep(i, 0, m) {
ll u, v, w;
cin >> u >> v >> w;
graph[--u].emplace_back(--v, w);
graph[v].emplace_back(u, w);
}
ll dist[100001];
memset(dist, 63, sizeof(dist));
dist[s] = 0;
set<pll> pq;
pq.emplace(0, s);
while (!pq.empty()) {
ll u, d;
tie(d, u) = *pq.begin();
pq.erase(pq.begin());
trav(edge, graph[u]) {
ll v, w;
tie(v, w) = edge;
if (d + w >= dist[v]) continue;
pq.erase({dist[v], v});
dist[v] = d + w;
pq.emplace(d + w, v);
}
}
set<pll> marked;
bitset<100001> vis;
queue<ll> q;
q.push(t);
vis[t] = 1;
while (!q.empty()) {
ll u = q.front();
q.pop();
trav(edge, graph[u]) {
ll v, w;
tie(v, w) = edge;
if (dist[u] - w == dist[v]) {
marked.emplace(u, v);
marked.emplace(v, u);
if (!vis[v]) {
q.push(v);
vis[v] = 1;
}
}
}
}
ll cost[100001][4];
memset(cost, 63, sizeof(cost));
cost[a][0] = 0;
pq.emplace(0, a);
while (!pq.empty()) {
ll u, d, state;
tie(d, u) = *pq.begin();
pq.erase(pq.begin());
state = u >> 30;
u &= (1 << 30) - 1;
// cout<<"u = "<<u<<" d = "<<d<<" state = "<<state<<endl;
trav(edge, graph[u]) {
ll v, w;
tie(v, w) = edge;
if (state != 3 && marked.count(pll(u, v))) {
ll nstate = (dist[u] < dist[v]) + 1;
if ((!state || state == nstate) && d < cost[v][nstate]) {
pq.erase({cost[v][nstate], v | (nstate << 30)});
cost[v][nstate] = d;
pq.emplace(d, v | (nstate << 30));
}
}
ll nstate = state ? 3 : 0;
if (d + w < cost[v][nstate]) {
pq.erase({cost[v][nstate], v | (nstate << 30)});
cost[v][nstate] = d + w;
pq.emplace(d + w, v | (nstate << 30));
}
}
}
ll ans = 1e15;
rep(i, 0, 4) ans = min(ans, cost[b][i]);
cout << ans << endl;
return 0;
}
