#include "bits/stdc++.h"
using namespace std;
using ll = long long;
ll INF = 1000'000'000'000'000'000ll;
struct edge {
int fr, to;
ll we;
};
struct pqnode {
ll cDist;
int node;
};
void dijkstra(int n, const vector<vector<edge>>& E, int S, vector<ll>& dist) {
auto cmp = [](const pqnode& u, const pqnode& v) {
return u.cDist > v.cDist;
};
priority_queue<pqnode, vector<pqnode>, decltype(cmp)> Q(cmp);
dist = vector<ll>(n + 5, INF);
dist[S] = 0;
Q.push({.cDist = 0, .node = S});
while (!Q.empty()) {
auto [cDist, node] = Q.top();
Q.pop();
if (cDist > dist[node]) continue;
for (auto [fr, to, we] : E[node]) {
if (dist[fr] + we < dist[to]) {
dist[to] = dist[fr] + we;
Q.push({.cDist = dist[to], .node = to});
}
}
}
}
void dagDp(int cur, const vector<vector<edge>>& G, const vector<ll>& uDist, const vector<ll>& vDist, vector<ll>& dist1, vector<ll>& dist2) {
dist1[cur] = uDist[cur];
dist2[cur] = vDist[cur];
for (auto [fr, to, we]: G[cur]) {
if (dist1[to] == -1) {
dagDp(to, G, uDist, vDist, dist1, dist2);
}
dist1[cur] = min(dist1[cur], dist1[to]);
dist2[cur] = min(dist2[cur], dist2[to]);
}
// cout << cur << " : "<< dist1[cur] << " " << dist2[cur] << endl;
}
int main() {
int n, m;
int s, t, u, v;
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m >> s >> t >> u >> v;
vector<vector<edge>> E(n + 5, vector<edge>());
for (int i = 1; i <= m; i++) {
int a, b;
ll c;
cin >> a >> b >> c;
E[a].push_back({.fr = a, .to = b, .we = c});
E[b].push_back({.fr = b, .to = a, .we = c});
}
vector<ll> sDist;
dijkstra(n, E, s, sDist);
vector<ll> tDist;
dijkstra(n, E, t, tDist);
vector<ll> uDist;
dijkstra(n, E, u, uDist);
vector<ll> vDist;
dijkstra(n, E, v, vDist);
// for (int i = 1; i <= n; i++) {
// cout << "i: " << i << " s: " << sDist[i] << " t: " << tDist[i];
// cout << " u: " << uDist[i] << " v: " << vDist[i] << endl;
// }
vector<vector<edge>> G(n + 5, vector<edge>());
for (int i = 1; i <= n; i++) {
for (auto [fr, to, we]: E[i]) {
if (sDist[fr] + we + tDist[to] == sDist[t]) {
G[fr].push_back({.fr = fr, .to = to, .we = 0});
}
}
}
vector<ll> dist1(n + 5, -1);
vector<ll> dist2(n + 5, -1);
dagDp(s, G, uDist, vDist, dist1, dist2);
ll ans = uDist[v];
for (int i = 1; i <= n; i++) {
if (dist1[i] != -1) {
ans = min(ans, min(dist1[i] + vDist[i], dist2[i] + uDist[i]));
}
}
cout << ans << endl;
}
