#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<vector<pair<int, int>>> adj;
vector<ll> d[3], dp[2];
const ll INF = 2e16;
int main() {
int N, M, S, T, U, V; cin >> N >> M >> S >> T >> U >> V;
adj.resize(N + 1);
d[0].assign(N + 1, INF);
d[1].assign(N + 1, INF);
d[2].assign(N + 1, INF);
dp[0].assign(N + 1, INF);
dp[1].assign(N + 1, INF);
for(int i = 0, u, v, w; i < M; ++i) {
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
function<void(int, int)> dj1 = [&](int start, int idx) {
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<>> q;
vector<bool> vis(N + 1, false);
q.push({0LL, start});
while(!q.empty()) {
auto[cur_weight, u] = q.top(); q.pop();
if(vis[u]) continue;
vis[u] = true;
d[idx][u] = cur_weight;
for(auto[v, w] : adj[u]) {
q.push({cur_weight + w, v});
}
}
};
dj1(U, 0);
dj1(V, 1);
ll ans = d[0][V];
function<void()> dj2 = [&] {
priority_queue<tuple<ll, int, int>, vector<tuple<ll, int, int>>, greater<>> q;
vector<bool> vis(N + 1, false);
q.push({0LL, S, 0});
while(!q.empty()) {
auto[cur_weight, u, p] = q.top(); q.pop();
if(!vis[u]) {
vis[u] = true;
d[2][u] = cur_weight;
dp[0][u] = min(d[0][u], dp[0][p]);
dp[1][u] = min(d[1][u], dp[1][p]);
for(auto[v, w] : adj[u]) {
q.push({cur_weight + w, v, u});
}
} else if(cur_weight == d[2][u]) {
if(
(min(d[0][u], dp[0][p]) +
min(d[1][u], dp[1][p])) <= dp[0][u] + dp[1][u]
) {
dp[0][u] = min(d[0][u], dp[0][p]);
dp[1][u] = min(d[1][u], dp[1][p]);
}
}
}
ans = min(ans, dp[0][T] + dp[1][T]);
};
dj2();
cout << ans << "\n";
}
