#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
const ll INF = LLONG_MAX, MOD = 1e9 + 7, P = 239;
const ld PI = 3.1415926535897938462643383279502, EPS = 1e-7;
template <typename T>
inline ll sz(const T &a) {
return a.size();
}
template <typename T, typename C>
istream &operator >> (istream &in, pair<T, C> &a) {
return in >> a.first >> a.second;
}
template <typename T, typename C>
ostream &operator << (ostream &out, pair<T, C> a) {
return out << a.first << ' ' << a.second;
}
template <typename T>
istream & operator >> (istream &in, vector<T> &a) {
for (auto &i : a) {
in >> i;
}
return in;
}
template <typename T>
ostream &operator << (ostream &out, vector<T> a) {
for (auto i : a) {
out << i << ' ';
}
return out;
}
template <typename T>
void prnt(vector<T> a, string c = "\n") {
for (T i : a) {
cout << i << c;
}
}
const ll MAXN = 1e5 + 1;
vector<pair<ll, ll>> g[MAXN];
ll dp[MAXN][2];
void dijkstra(vector<ll> &d, int start) {
fill(d.begin(), d.end(), INF);
set<pair<ll, ll>> q;
q.insert({0, start});
d[start] = 0;
while (!q.empty()) {
auto [dist, v] = *q.begin();
q.erase(q.begin());
if (dist > d[v]) {
continue;
}
for (auto [u, w] : g[v]) {
if (d[u] > d[v] + w) {
d[u] = d[v] + w;
q.insert({d[u], u});
}
}
}
}
void solve() {
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < n; ++i) {
int a, b, w;
cin >> a >> b >> w;
g[a].push_back({b, w});
g[b].push_back({a, w});
}
vector<ll> du(n + 1), dv(n + 1), ds(n + 1), dt(n + 1);
dijkstra(du, u);
dijkstra(dv, v);
dijkstra(ds, s);
dijkstra(dt, t);
vector<ll> flex(n);
iota(flex.begin(), flex.end(), 1ll);
sort(flex.begin(), flex.end(), [&](int a, int b) {
return ds[a] < ds[b];
});
fill(dp[0], dp[0] + MAXN * 2, INF);
dp[s][0] = ds[u];
dp[s][1] = ds[v];
for (int i = 0; i < n; ++i) {
int a = flex[i];
if (dp[a][0] == INF) {
continue;
}
for (auto [b, w] : g[a]) {
if (dt[b] + w + ds[a] == ds[t]) {
dp[b][0] = min(dp[a][0], du[b]);
dp[b][1] = min(dp[a][1], dv[b]);
}
}
}
ll ans = dv[u];
for (int i = 1; i <= n; ++i) {
if (dp[i][0] == INF) {
continue;
}
ans = min(ans, min(dp[i][0] + dv[i], dp[i][1] + du[i]));
}
cout << ans;
}
signed main() {
#ifdef LOCAL
freopen("inp.txt", "r", stdin);
freopen("out.txt", "w", stdout);
freopen("err.txt", "w", stderr);
auto start_time = clock();
#endif
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int times = 1;
// cin >> times;
while (times--)
solve(), cout << '\n';
#ifdef LOCAL
auto end_time = clock();
cerr << setprecision(3) << fixed << "Execution time: " << (end_time - start_time) * (int) 1e3 / CLOCKS_PER_SEC << " ms\n";
#endif
return 0;
}
