#include <bits/stdc++.h>
#define task "BriantheCrab"
#define int long long
#define pii pair <int, int>
#define fi first
#define se second
#define szf sizeof
#define sz(s) (int)((s).size())
using namespace std;
template <class T> void mini (T &t, T f) {if (t > f) t = f;}
template <class T> void maxi (T &t, T f) {if (t < f) t = f;}
const int maxN = 1e5 + 5;
const int inf = 1e18 + 7;
const int mod = 1e9 + 7;
struct Edge {
int node, dis;
};
struct cmp {
bool operator () (Edge A, Edge B) {
return A.dis > B.dis;
}
};
int n, m, S, T, U, V;
int Ls[maxN], Lt[maxN], L[maxN * 4];
vector <Edge> adj[maxN], g[maxN * 4];
void dijkstraST () {
priority_queue <Edge, vector <Edge>, cmp> pq;
for (int i = 1; i <= n; i ++) {
Ls[i] = Lt[i] = inf;
}
Ls[S] = 0;
pq.push ({S, Ls[S]});
while (!pq.empty ()) {
auto [u, c] = pq.top ();
pq.pop ();
if (c > Ls[u]) {
continue;
}
for (auto [v, w] : adj[u]) {
if (Ls[v] > Ls[u] + w) {
Ls[v] = Ls[u] + w;
pq.push ({v, Ls[v]});
}
}
}
Lt[T] = 0;
pq.push ({T, Lt[T]});
while (!pq.empty ()) {
auto [u, c] = pq.top ();
pq.pop ();
if (c > Lt[u]) {
continue;
}
for (auto [v, w] : adj[u]) {
if (Lt[v] > Lt[u] + w) {
Lt[v] = Lt[u] + w;
pq.push ({v, Lt[v]});
}
}
}
}
void dijkstraUV () {
priority_queue <Edge, vector <Edge>, cmp> pq;
for (int i = 1; i <= n * 4; i ++) {
L[i] = inf;
}
L[U] = 0;
pq.push ({U, L[U]});
while (!pq.empty ()) {
auto [u, c] = pq.top ();
pq.pop ();
//cout << u << ' ' << c << '\n';
if (c > L[u]) {
continue;
}
for (auto [v, w] : g[u]) {
if (L[v] > L[u] + w) {
L[v] = L[u] + w;
pq.push ({v, L[v]});
}
}
}
}
int ts (int u, int t) {
return u + t * n;
}
void solve () {
cin >> n >> m >> S >> T >> U >> V;
for (int i = 1; i <= m; i ++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back ({v, w});
adj[v].push_back ({u, w});
}
dijkstraST ();
int best = Ls[T];
// dinh tien 4 chieu :
// 0 : chua di vao duong S -> T
// 1, 2 : dang di vao duong S -> T theo huong nguoc nhau
// 3 : best khi di xong
for (int u = 1; u <= n; u ++) {
g[ts (u, 0)].push_back ({ts (u, 1), 0});
g[ts (u, 0)].push_back ({ts (u, 2), 0});
g[ts (u, 1)].push_back ({ts (u, 3), 0});
g[ts (u, 2)].push_back ({ts (u, 3), 0});
for (auto [v, w] : adj[u]) {
if (Ls[u] + w + Lt[v] == best) {
g[ts (u, 1)].push_back ({ts (v, 1), 0});
g[ts (v, 2)].push_back ({ts (u, 2), 0});
}
g[ts (u, 0)].push_back ({ts (v, 0), w});
g[ts (u, 3)].push_back ({ts (v, 3), w});
}
}
dijkstraUV ();
cout << L[ts (V, 3)] << '\n';
// for (int i = 1; i <= n * 4; i ++) {
// cout << L[i] << ' ';
// if (i % n == 0) {
// cout << '\n';
// }
// }
return;
}
signed main () {
cin.tie (nullptr) -> sync_with_stdio (false);
if (fopen (task".inp", "r")) {
freopen (task".inp", "r", stdin);
freopen (task".out", "w", stdout);
}
int t = 1;
//cin >> t;
while (t --) {
solve ();
}
return 0;
}
// thfdgb
