#include "bits/stdc++.h"
using namespace std;
#ifdef Nero
#include "Deb.h"
#else
#define deb(...)
#endif
using T = pair<long long, int>;
const int N = 1e5 + 5;
const long long INF = 1e16;
int n, m;
vector<pair<int, int>> g[N];
vector<long long> dij(int src) {
vector<long long> ret(n + 1, INF);
ret[src] = 0;
priority_queue<T, vector<T>, greater<T>> pq;
pq.emplace(0, src);
while (!pq.empty()) {
auto [c, v] = pq.top();
pq.pop();
if (c != ret[v]) {
continue;
}
for (auto [u, w] : g[v]) {
if (w + c < ret[u]) {
ret[u] = w + c;
pq.emplace(ret[u], u);
}
}
}
return ret;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m;
int s, t;
cin >> s >> t;
int qu, qv;
cin >> qu >> qv;
for (int i = 0; i < m; ++i) {
int u, v, w;
cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
vector<long long> ds = dij(s);
vector<long long> dt = dij(t);
vector<long long> dv = dij(qv);
vector<long long> du = dij(qu);
long long ans = du[qv];
for (int rep = 0; rep < 2; ++rep) {
vector<int> ord(n);
iota(ord.begin(), ord.end(), 1);
sort(ord.begin(), ord.end(), [&](int i, int j) {
return ds[i] < ds[j];
});
vector<long long> dp(n + 1, INF);
for (int v : ord) {
ans = min(ans, dp[v] + dv[v]);
for (auto [u, w] : g[v]) {
if (ds[v] + w + dt[u] == ds[t]) {
dp[u] = min({dp[u], dp[v], du[v]});
}
}
}
swap(qu, qv);
swap(du, dv);
}
cout << ans << '\n';
return 0;
}
