#include <bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) x.begin(), x.end()
#define pb push_back
#define ar array
#define nl '\n'
template <typename A, typename B>
bool chmin(A &a, const B &b) {
if(a > b) {
return a = b, true;
}
return false;
}
template <typename A, typename B>
bool chmax(A &a, const B &b) {
if(a < b) {
return a = b, true;
}
return false;
}
const int inf = 1e18;
void solve() {
int n, m; cin >> n >> m;
int S, T, U, V; cin >> S >> T >> U >> V;
S--, T--, U--, V--;
vector<vector<ar<int, 2>>> adj(n);
for(int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w;
u--, v--;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
vector<ar<int, 4>> d(n, {inf, inf, inf, inf});
vector<int> p(n);
auto D = [&](int s, int j) -> void {
d[s][j] = 0;
p[s] = -1;
priority_queue<ar<int, 2>, vector<ar<int, 2>>, greater<>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto [d_v, v] = pq.top();
pq.pop();
if(d_v != d[v][j]) continue;
for(auto [to, w] : adj[v]) {
if( chmin(d[to][j], d_v + w) ) {
pq.push({d[to][j], to});
p[to] = v;
}
}
}
};
D(U, 0), D(V, 1), D(S, 2);
vector<int> path;
for(auto v = T; v != -1; v = p[v]) {
path.pb(v);
}
int ans1 = inf, ans2 = inf;
for(auto &x : path) {
chmin(ans1, d[x][0]);
chmin(ans2, d[x][1]);
}
int ans = d[V][0];
chmin(ans, ans1 + ans2);
cout << ans << nl;
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
}
