#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
#include <bits/stdc++.h>
using namespace std;
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
// template<typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define ll long long
#define ull unsigned long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pli pair<ll, int>
#define plpll pair<ll, pll>
#define pipii pair<int, pii>
#define plpii pair<ll, pii>
#define pipll pair<int, pll>
#define lll tuple<ll, ll, ll>
#define iii tuple<int, int, int>
#define lii tuple<ll, int, int>
#define lli tuple<ll, ll, int>
#define md 1000000007LL
#define linf 0x3f3f3f3f3f3f3f3f
#define inf 0x3f3f3f3f
#define lninf (ll)0xc0c0c0c0c0c0c0c0
#define ninf (int)0xc0c0c0c0
#define bruh ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ss << ' ' <<
#ifdef wizard
#define usaco(x)
#else
#define usaco(x) ifstream cin(#x ".in"); ofstream cout(#x ".out");
#endif
template<class T1, class T2>
istream& operator>>(istream& in, pair<T1, T2>& p) {
return in >> p.first >> p.second;
}
template<class T1, class T2>
ostream& operator<<(ostream& out, const pair<T1, T2>& p) {
return out << p.first << ' ' << p.second;
}
template<size_t I = 0, typename... Ts>
typename enable_if<I == sizeof...(Ts), istream&>::type
read_tuple(istream& in, tuple<Ts...>& t) { return in; }
template<size_t I = 0, typename... Ts>
typename enable_if<I < sizeof...(Ts), istream&>::type
read_tuple(istream& in, tuple<Ts...>& t) {
in >> get<I>(t);
return read_tuple<I + 1>(in, t);
}
template<typename... Ts>
istream& operator>>(istream& in, tuple<Ts...>& t) {
return read_tuple(in, t);
}
template<size_t I = 0, typename... Ts>
typename enable_if<I == sizeof...(Ts), void>::type
write_tuple(ostream& out, const tuple<Ts...>&) {}
template<size_t I = 0, typename... Ts>
typename enable_if<I < sizeof...(Ts), void>::type
write_tuple(ostream& out, const tuple<Ts...>& t) {
if (I) out << ' ';
out << get<I>(t);
write_tuple<I + 1>(out, t);
}
template<typename... Ts>
ostream& operator<<(ostream& out, const tuple<Ts...>& t) {
write_tuple(out, t);
return out;
}
template<typename T>
istream& operator>>(istream& in, vector<T>& v) {
for (auto& x : v) in >> x;
return in;
}
template<typename T>
ostream& operator<<(ostream& out, const vector<T>& v) {
for (size_t i = 0; i < v.size(); ++i)
out << (i ? " " : "") << v[i];
return out;
}
ll n, m, s, t, u, v, dist[100001], dist2[100001], dist3[100001];
bool flag[100001];
vector<pll> adj[100001];
vector<int> raw[100001], from[100001], to[100001];
priority_queue<pll, vector<pll>, greater<pll>> pq;
queue<int> q;
int main() {
bruh;
cin >> n >> m >> s >> t >> u >> v;
while (m--) {
static int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
memset(dist, 0x3f, sizeof dist);
pq.push({dist[s] = 0, s});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto [v, w]: adj[u]) {
if (dist[v] > dist[u] + w) {
pq.push({dist[v] = dist[u] + w, v});
raw[v].clear();
}
if (dist[v] == dist[u] + w) {
raw[v].push_back(u);
}
}
}
memset(dist, 0x3f, sizeof dist);
pq.push({dist[u] = 0, u});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto [v, w]: adj[u]) if (dist[v] > dist[u] + w) pq.push({dist[v] = dist[u] + w, v});
}
flag[t] = 1; q.push(t);
while (!q.empty()) {
auto u = q.front(); q.pop();
for (auto v: raw[u]) from[u].push_back(v), to[v].push_back(u);
for (auto v: raw[u]) if (!flag[v]) flag[v] = 1, q.push(v);
}
memset(dist2, 0x3f, sizeof dist2);
pq.push({dist2[t] = dist[t], t});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist2[u]) continue;
for (auto v: from[u]) {
ll dd = min(dist[v], dist2[u]);
if (dist2[v] > dd) pq.push({dist2[v] = dd, v});
}
}
memset(dist3, 0x3f, sizeof dist3);
pq.push({dist3[s] = dist[s], s});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist3[u]) continue;
for (auto v: to[u]) {
ll dd = min(dist[v], dist3[u]);
if (dist3[v] > dd) pq.push({dist3[v] = dd, v});
}
}
for (int i = 1; i <= n; i++) {
if (dist[i] > min(dist2[i], dist3[i])) pq.push({dist[i] = min(dist2[i], dist3[i]), i});
}
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto [v, w]: adj[u]) if (dist[v] > dist[u] + w) pq.push({dist[v] = dist[u] + w, v});
}
cout << dist[v];
}
