#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <immintrin.h>
#ifndef DEBUG
//#pragma GCC optimize("O3")
//#pragma GCC target("avx2")
#endif
using namespace __gnu_pbds;
using namespace __gnu_cxx;
using namespace std;
//
using ld = long double;
using ll = long long;
using i128 = __int128;
using ull = unsigned long long;
using pll = std::pair<ll, ll>;
using cmpl = std::complex<ld>;
template<typename T>
using oset = tree<T, null_type, std::less<T>, rb_tree_tag, tree_order_statistics_node_update>;
constexpr ll MOD1 = 998244353;
constexpr ll MOD = 1000000007;
constexpr ll INV2 = 499122177;
constexpr ld PI = 3.141592653589793;
const ld eps = 1e-7;
const ll K = 500;
//const ll C = 200;
std::mt19937 rnd(std::chrono::steady_clock::now().time_since_epoch().count());
ld START_TIME = clock();
std::vector<ll> d, d1;
void Deikstr(ll str, std::vector<std::vector<pll>> &G) {
std::set<pll> q;
q.insert({0, str});
d[str] = 0;
while (!q.empty()) {
auto [dst, v] = *q.begin();
q.erase(q.begin());
for (auto [u, w]: G[v]) {
if (dst + w < d[u]) {
q.erase({d[u], u});
d[u] = dst + w;
q.insert({d[u], u});
}
}
}
}
void Deikstr1(ll str, std::vector<std::vector<pll>> &G) {
std::set<pll> q;
q.insert({0, str});
d1.assign(G.size(), 1e18);
d1[str] = 0;
while (!q.empty()) {
auto [dst, v] = *q.begin();
q.erase(q.begin());
for (auto [u, w]: G[v]) {
if (dst + w < d1[u]) {
q.erase({d1[u], u});
d1[u] = dst + w;
q.insert({d1[u], u});
}
}
}
}
void solve() {
ll n, m;
ll s, t, u, v;
std::cin >> n >> m;
std::cin >> s >> t;
--s, --t;
std::cin >> u >> v;
--u, --v;
std::vector<std::vector<pll>> G;
G.resize(n);
d.resize(n, 1e18);
d1.resize(n, 1e18);
for (int i = 0; i < m; ++i) {
ll v1, u1, w;
std::cin >> v1 >> u1 >> w;
--v1, --u1;
G[v1].push_back({u1, w});
G[u1].push_back({v1, w});
}
Deikstr(s, G);
Deikstr1(t, G);
std::vector<std::vector<pll>> G1(3 * n), G2(3 * n);
for (int i = 0; i < n; ++i) {
for (auto [uu, w]: G[i]) {
if (d[i] + w + d1[uu] == d[t]) {
G1[i].push_back({uu + n, 0});
G1[i].push_back({uu + 2 * n, 0});
G1[i + n].push_back({uu + 2 * n, 0});
G1[i + n].push_back({uu + n, 0});
G1[uu].push_back({i + n, 0});
G1[uu].push_back({i + 2 * n, 0});
G1[uu + n].push_back({i + 2 * n, 0});
G1[uu + n].push_back({i + n, 0});
}
}
}
for (ll i = 0; i < n; ++i) {
for (auto &[uu, w]: G[i]) {
G1[i].push_back({uu, w});
G1[i + 2 * n].push_back({uu + 2 * n, w});
G2[i].push_back({uu, w});
G2[i + 2 * n].push_back({uu + 2 * n, w});
}
}
Deikstr1(v, G1);
ll ans = std::min({d1[u], d1[u + n], d1[u + 2 * n]});
Deikstr1(v, G2);
ans = std::min({ans, d1[u], d1[u + n], d1[u + 2 * n]});
std::cout << ans;
}
signed main() {
#ifdef DEBUG
std::freopen("/home/anton/CLionProjects/untitled/input.txt", "r", stdin);
#else
// std::freopen("tri.in", "r", stdin); std::freopen("tri.out", "w", stdout);
#endif
std::cin.tie(nullptr)->std::ios_base::sync_with_stdio(false);
int tt = 1;
// ll g; std::cin >> g;
// std::cin >> tt;
while (tt--) {
solve();
}
#ifdef DEBUG
std::cerr << '\n';
ld TIME = (clock() - START_TIME) / CLOCKS_PER_SEC;
std::cerr << "Time: " << TIME << '\n';
#endif
}
