// clang-format off
#include <bits/stdc++.h>
using namespace std;
mt19937 rnd(time(0));
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("fast-math")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,tune=native")
#define int long long
#define ll long long
#define ld long double
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
const long long INF = 20000000000000000;
const int inf = 1000000010;
const int maxn = 262144;
const int mxlg = 20;
const double eps = 1e-13;
int mod = 1e9 + 9;
const int C = 340;
vector<vector<pair<int, int>>>
eds;
vector<vector<int>> g2;
int n;
vector<int> dij(int s) {
vector<int> d(n, INF);
d[s] = 0;
set<pair<int, int>> buf;
buf.insert({0, s});
while (!buf.empty()) {
int v = buf.begin()->second;
buf.erase(buf.begin());
for (auto [to, c]: eds[v]) {
if (d[v] + c < d[to]) {
buf.erase({d[to], to});
d[to] = d[v] + c;
buf.insert({d[to], to});
}
}
}
return d;
}
void solve() {
int m, s, t, v, u;
cin >> n >> m >> s >> t >> v >> u;
--s, --t, --v, --u;
eds.resize(n);
for (int i = 0; i < m; ++i) {
int x, y, c;
cin >> x >> y >> c;
--x, --y;
eds[x].push_back({y, c});
eds[y].push_back({x, c});
}
vector<int> st = dij(s);
vector<int> ts = dij(t);
vector<bool> dag(n);
g2.resize(n);
dag[s] = dag[t] = 1;
for (int i = 0; i < n; ++i) {
for (auto [to, w]: eds[i]) {
if (st[i] + w + ts[to] == st[t]) {
dag[i] = dag[to] = 1;
g2[i].push_back(to);
}
}
}
vector<int> dv = dij(v);
vector<int> du = dij(u);
int ans = dv[u];
set<pair<int, int>> buf;
vector<int> cost = dv;
for (int i = 0; i < n; ++i) {
if (dag[i]) {
buf.insert({dv[i], i});
}
}
while (!buf.empty()) {
int cur = buf.begin()->second;
buf.erase(buf.begin());
ans = min(ans, cost[cur] + du[cur]);
for (int to: g2[cur]) {
if (cost[cur] < cost[to]) {
buf.erase({cost[to], to});
cost[to] = cost[cur];
buf.insert({cost[to], to});
}
}
}
cost = du;
for (int i = 0; i < n; ++i) {
if (dag[i]) {
buf.insert({du[i], i});
}
}
while (!buf.empty()) {
int cur = buf.begin()->second;
buf.erase(buf.begin());
ans = min(ans, cost[cur] + dv[cur]);
for (int to: g2[cur]) {
if (cost[cur] < cost[to]) {
buf.erase({cost[to], to});
cost[to] = cost[cur];
buf.insert({cost[to], to});
}
}
}
cout << ans << "\n";
}
signed main() {
// freopen("kthzero.in", "r", stdin);
// freopen("kthzero.out", "w", stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
int __ = 1;
// cin >> __;
while (__--)
solve();
return 0;
}
