#include <bits/stdc++.h>
using namespace std;
using ld = long double;
using ll = long long;
const ll INF = 3e18, MOD = 1e9 + 7;
void solve();
signed main() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
ios::sync_with_stdio(false);
cin.tie(0);
int q = 1;
while (q--) {
solve();
}
}
vector<vector<pair<ll, ll>>> g;
ll n;
vector<ll> dist(ll s) {
vector<ll> ds(n, INF);
ds[s] = 0;
set<pair<ll, ll>> dj;
dj.insert({0, s});
while (!dj.empty()) {
ll v = dj.begin()->second;
dj.erase(dj.begin());
for (auto [u, c] : g[v]) {
if (ds[u] > ds[v] + c) {
dj.erase({ds[u], u});
ds[u] = ds[v] + c;
dj.insert({ds[u], u});
}
}
}
return ds;
}
vector<vector<ll>> g2;
vector<ll> dv, du;
ll ans;
vector<ll> dp1, dp2;
void dfs(ll v) {
dp1[v] = dv[v]; dp2[v] = du[v];
for (auto u : g2[v]) {
if (dp1[u] == -1) {
dfs(u);
}
dp1[v] = min(dp1[v], dp1[u]);
dp2[v] = min(dp2[v], dp2[u]);
}
ans = min({ans, dv[v] + dp2[v], du[v] + dp1[v]});
}
void solve() {
ll m; cin >> n >> m;
ll s, t; cin >> s >> t; s--, t--;
ll u, v; cin >> u >> v; u--, v--;
g.resize(n);
for (int i = 0; i < m; i++) {
ll a, b, c; cin >> a >> b >> c;
a--, b--;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
vector<ll> d1 = dist(s), d2 = dist(t);
g2.resize(n);
for (int a = 0; a < n; a++) {
for (auto [b, c] : g[a]) {
if (d1[a] + c == d1[b] && d2[b] + c == d2[a]) {
g2[a].push_back(b);
}
}
}
dv = dist(v);
du = dist(u);
ans = dv[u];
dp1.resize(n, -1), dp2.resize(n, -1);
dfs(s);
cout << ans;
}
