#include <bits/stdc++.h>
#define int long long
#define pii pair <long long, long long>
#define fi first
#define se second
using namespace std;
using ll = long long;
const ll N = 100005, inf = 1e16;
int n, m, S, T, U, V;
vector <pii> adj[N];
ll dist_s[N], dist_t[N], dist_ans[N][3];
int a[N], b[N], c[N];
void dijkstra(int x, ll *length) {
for (int i = 1; i <= n; i++) length[i] = inf;
length[x] = 0;
priority_queue <pii, vector <pii>, greater <pii> > q;
q.push({length[x], x});
while(q.size()) {
auto tmp = q.top();
q.pop();
ll u = tmp.se, z = tmp.fi;
if (z > length[u]) continue;
for (auto v : adj[u]) {
if (length[v.fi] > length[u] + v.se) {
length[v.fi] = length[u] + v.se;
q.push({length[v.fi], v.fi});
}
}
}
}
struct item {
ll val, x, pre;
bool operator <(const item &other) const {
return val > other.val;
}
};
struct node {
ll u, w, type;
};
vector <node> adj1[N], adj2[N];
void dijkstra1(int root, vector <node> adj_x[]) {
for (int i = 1; i <= n; i++) for (int j = 0; j < 3; j++) dist_ans[i][j] = inf;
dist_ans[root][0] = 0;
priority_queue <item> q;
q.push({dist_ans[root][0], root, 0});
while(q.size()) {
auto tmp = q.top();
q.pop();
ll val = tmp.val, u = tmp.x, pre = tmp.pre;
if (val > dist_ans[u][pre]) continue;
for (auto v : adj_x[u]) {
int x = min(u, v.u), y = max(u, v.u);
if (pre == 0) {
if (dist_ans[v.u][0] > dist_ans[u][pre] + v.w) { // tiep tuc ko dung ve va di tiep
dist_ans[v.u][0] = dist_ans[u][pre] + v.w;
q.push({dist_ans[v.u][0], v.u, 0});
}
if (v.type == 0 && dist_ans[v.u][1] > dist_ans[u][pre]) { // bat dau dung ve
dist_ans[v.u][1] = dist_ans[u][pre];
q.push({dist_ans[v.u][1], v.u, 1});
}
}
else if (pre == 1) {
if (v.type == 0 && dist_ans[v.u][1] > dist_ans[u][pre]) {
dist_ans[v.u][1] = dist_ans[u][pre];
q.push({dist_ans[v.u][1], v.u, 1});
}
if (dist_ans[v.u][2] > dist_ans[u][pre] + v.w) { // ko dung ve nua
dist_ans[v.u][2] = dist_ans[u][pre] + v.w;
q.push({dist_ans[v.u][2], v.u, 2});
}
}
else if (pre == 2) {
if (dist_ans[v.u][2] > dist_ans[u][pre] + v.w) {
dist_ans[v.u][2] = dist_ans[u][pre] + v.w;
q.push({dist_ans[v.u][2], v.u, 2});
}
}
}
}
}
signed main() {
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= m; i++) {
cin >> a[i] >> b[i] >> c[i];
adj[a[i]].emplace_back(b[i], c[i]);
adj[b[i]].emplace_back(a[i], c[i]);
}
dijkstra(S, dist_s);
dijkstra(T, dist_t);
// for (int i = 1; i <= n; i++) cout << dist_s[i] << ' ' << dist_t[i] << '\n';
ll minn = dist_s[T]; // khoang cach ngan nhat tu s den t
for (int i = 1; i <= m; i++) {
int u = a[i], v = b[i];
bool free_uv = (dist_s[u] + c[i] + dist_t[v] == minn);
bool free_vu = (dist_s[v] + c[i] + dist_t[u] == minn);
adj1[u].push_back({v, c[i], free_uv ? 0 : -1});
adj1[v].push_back({u, c[i], free_vu ? 0 : -1});
adj2[u].push_back({v, c[i], free_vu ? 0 : -1});
adj2[v].push_back({u, c[i], free_uv ? 0 : -1});
}
dijkstra1(U, adj1);
ll x = min({dist_ans[V][0], dist_ans[V][1], dist_ans[V][2]});
// cout << dist_ans[V][0] << ' ' << dist_ans[V][1] << ' ' << dist_ans[V][2] << '\n';
dijkstra1(U, adj2);
ll y = min({dist_ans[V][0], dist_ans[V][1], dist_ans[V][2]});
// cout << dist_ans[V][0] << ' ' << dist_ans[V][1] << ' ' << dist_ans[V][2] << '\n';
cout << min(x, y);
return 0;
}
