// File commuterpass.cpp created on 02.10.2025 at 20:33:44
#include <bits/stdc++.h>
using i64 = long long;
#ifdef DEBUG
#include "/home/ahmetalp/Desktop/Workplace/debug.h"
#else
#define debug(...) void(23)
#endif
constexpr i64 inf = i64(1E18);
template<typename T>
bool chmin(T& a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<typename T>
using min_pq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int N, M;
std::cin >> N >> M;
int S, T;
std::cin >> S >> T;
--S, --T;
int U, V;
std::cin >> U >> V;
--U, --V;
std::vector<std::array<int, 3>> E(M);
std::vector<std::vector<int>> adj(N);
for (int i = 0; i < M; ++i) {
std::cin >> E[i][0] >> E[i][1] >> E[i][2];
--E[i][0], --E[i][1];
adj[E[i][0]].emplace_back(i);
adj[E[i][1]].emplace_back(i);
}
i64 ans = inf;
auto work = [&]() -> void {
std::vector<std::vector<int>> zdj(N);
{
std::vector<i64> dis(N, inf), dit(N, inf);
min_pq<std::pair<i64, int>> pq;
pq.emplace(dis[S] = 0, S);
while (!pq.empty()) {
auto[d, v] = pq.top();
pq.pop();
if (dis[v] != d) {
continue;
}
for (auto e : adj[v]) {
int u = E[e][0] ^ E[e][1] ^ v;
if (chmin(dis[u], dis[v] + E[e][2])) {
pq.emplace(dis[u], u);
}
}
}
pq.emplace(dit[T] = 0, T);
while (!pq.empty()) {
auto[d, v] = pq.top();
pq.pop();
if (dit[v] != d) {
continue;
}
for (auto e : adj[v]) {
int u = E[e][0] ^ E[e][1] ^ v;
if (chmin(dit[u], dit[v] + E[e][2])) {
pq.emplace(dit[u], u);
}
}
}
debug(dis[T]);
for (int i = 0; i < M; ++i) {
if (dis[E[i][0]] + dit[E[i][1]] + E[i][2] == dis[T]) {
zdj[E[i][0]].emplace_back(i);
}
if (dis[E[i][1]] + dit[E[i][0]] + E[i][2] == dis[T]) {
zdj[E[i][1]].emplace_back(i);
}
}
}
min_pq<std::tuple<int, int, int>> pq;
std::vector<std::array<i64, 3>> dis(N, {inf, inf, inf});
pq.emplace(dis[U][0] = 0, U, 0);
while (!pq.empty()) {
auto[d, v, t] = pq.top();
pq.pop();
if (dis[v][t] != d) {
continue;
}
if (t == 0) {
for (auto e : adj[v]) {
int u = E[e][0] ^ E[e][1] ^ v;
if (chmin(dis[u][0], dis[v][0] + E[e][2])) {
pq.emplace(dis[u][0], u, 0);
}
}
for (auto e : zdj[v]) {
int u = E[e][0] ^ E[e][1] ^ v;
if (chmin(dis[u][1], dis[v][0])) {
pq.emplace(dis[u][1], u, 1);
}
}
if (chmin(dis[v][2], dis[v][0])) {
pq.emplace(dis[v][2], v, 2);
}
} else if (t == 1) {
for (auto e : zdj[v]) {
int u = E[e][0] ^ E[e][1] ^ v;
if (chmin(dis[u][1], dis[v][1])) {
pq.emplace(dis[u][1], u, 1);
}
}
if (chmin(dis[v][2], dis[v][1])) {
pq.emplace(dis[v][2], v, 2);
}
} else {
for (auto e : adj[v]) {
int u = E[e][0] ^ E[e][1] ^ v;
if (chmin(dis[u][2], dis[v][2] + E[e][2])) {
pq.emplace(dis[u][2], u, 2);
}
}
}
}
ans = std::min(ans, dis[V][2]);
};
work();
std::swap(S, T);
work();
std::cout << ans << '\n';
return 0;
}
