#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll inf = (ll)1e18;
const int N = (int)1e5 + 1;
int n, m;
ll dis[3][N], dp[2][N], ans = inf;
vector<pair<ll, int>> adj[N];
void sp(int st, int t) {
priority_queue<pair<ll, int>> q;
q.emplace(0, st);
dis[t][st] = 0;
while (!q.empty()) {
auto [w, u] = q.top();
q.pop();
if (-w > dis[t][u]) continue;
for (auto &[ww, v] : adj[u]) {
if (-w + ww >= dis[t][v]) continue;
dis[t][v] = -w + ww;
q.emplace(w - ww, v);
}
}
}
ll solve(int st, int en) {
for (int i = 1; i <= n; i++) dp[0][i] = dp[1][i] = inf, dis[2][i] = inf;
priority_queue<pair<ll, int>> q;
q.emplace(0, st);
dp[0][st] = dis[0][st], dp[1][st] = dis[1][st], dis[2][st] = 0;
while (!q.empty()) {
auto [w, u] = q.top();
q.pop();
if (-w > dis[2][u]) continue;
for (auto &[ww, v] : adj[u]) {
if (-w + ww > dis[2][v]) continue;
else if (-w + ww < dis[2][v]) q.emplace(w - ww, v);
dp[0][v] = min(dp[0][v], min(dp[0][u], dis[0][u]));
dp[1][v] = min(dp[1][v], min(dp[0][v] + dis[1][v], dp[1][u]));
dis[2][v] = -w + ww;
}
}
return dp[1][en];
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
int s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
while (m--) {
int u, v, w;
cin >> u >> v >> w;
adj[u].emplace_back(w, v);
adj[v].emplace_back(w, u);
}
for (int i = 1; i <= n; i++) dis[0][i] = dis[1][i] = inf;
sp(u, 0), sp(v, 1);
cout << min(dis[0][v], min(solve(s, t), solve(t, s)));
}
