#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 100005;
int n, m, s, t, u, v;
vector<pair<ll,int>> adj[N];
bool minself(ll &a, ll b) {
if (a > b) {
a = b;
return 1;
}
return 0;
}
void dijkstra(int start, vector<ll> &dist) {
vector<int> vst(n + 1);
dist.assign(n + 1, 1e15);
dist[start] = 0;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
pq.push(make_pair(0, start));
while (pq.size()) {
auto i = pq.top(); pq.pop();
if (vst[i.second]) continue;
vst[i.second] = 1;
for (auto &j : adj[i.second]) {
ll comp = i.first + j.first;
if (comp < dist[j.second]) {
dist[j.second] = comp;
pq.push(make_pair(comp, j.second));
}
}
}
}
// S == U
namespace sub1 {
void Main() {
vector<ll> s_dist, v_dist, t_dist;
dijkstra(s, s_dist);
dijkstra(v, v_dist);
dijkstra(t, t_dist);
ll ans = s_dist[v];
for (int i = 1; i <= n; i++) {
if (s_dist[i] + t_dist[i] == s_dist[t]) {
minself(ans, v_dist[i]);
}
}
cout << ans << '\n';
}
}
// n <= 300
namespace sub3 {
void Main() {
vector<vector<ll>> mat_dist(n + 1, vector<ll>(n + 1, 1e15));
for (int i = 1; i <= n; i++) {
mat_dist[i][i] = 0;
for (auto &j : adj[i]) {
mat_dist[i][j.second] = mat_dist[j.second][i] = j.first;
}
}
for (int k = 1; k <= n; k++)
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) {
minself(mat_dist[i][j], mat_dist[i][k] + mat_dist[k][j]);
}
ll ans = mat_dist[u][v];
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) {
if (mat_dist[s][i] + mat_dist[i][j] + mat_dist[j][t] == mat_dist[s][t]) {
minself(ans, mat_dist[u][i] + mat_dist[j][v]);
minself(ans, mat_dist[u][j] + mat_dist[i][v]);
}
}
cout << ans << '\n';
}
}
// unique min path s -> t
namespace sub2 {
void Main() {
vector<ll> s_dist;
dijkstra(s, s_dist);
int tmp = t;
while (tmp != s) {
for (auto &j : adj[tmp]) {
if (s_dist[j.second] + j.first == s_dist[tmp]) {
j.first = 0;
for (auto &k : adj[j.second]) {
if (k.second == tmp) {
k.first = 0;
break;
}
}
tmp = j.second;
break;
}
}
}
vector<ll> u_dist;
dijkstra(u, u_dist);
cout << u_dist[v] << '\n';
}
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int u, v; ll c;
cin >> u >> v >> c;
adj[u].push_back(make_pair(c, v));
adj[v].push_back(make_pair(c, u));
}
if (s == u) sub1::Main();
else if (n <= 300) sub3::Main();
else sub2::Main();
}
