#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MX = 1e5 + 5;
int N, M, S, T, U, V;
ll d[5][MX], dd[MX];
vector<pair<int,int>> g[MX];
void work(int s, int t) {
for(int i = 1; i <= N; i++) d[t][i] = 1e18;
priority_queue<pair<ll, ll>> pq;
pq.push({0, s});
d[t][s] = 0;
while(!pq.empty()) {
auto [c, v] = pq.top(); pq.pop();
c = -c;
if(d[t][v] < c) continue;
for(auto [u, w] : g[v]) {
if(d[t][u] > c + w) {
d[t][u] = c + w;
pq.push({-d[t][u], u});
}
}
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> N >> M >> S >> T >> U >> V;
for(int i = 0; i < M; i++) {
int u, v, w;
cin >> u >> v >> w;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
ll ans = 1e18;
for(int it = 0; it < 2; it++) {
work(S, 0);
work(T, 1);
work(U, 2);
work(V, 3);
// solve
priority_queue<pair<ll, ll>> pq;
for(int i = 1; i <= N; i++) {
if(d[0][i] + d[1][i] == d[0][T]) {
dd[i] = d[2][i];
pq.push({-dd[i], i});
} else {
dd[i] = 1e18;
}
}
while(!pq.empty()) {
auto [c, v] = pq.top(); pq.pop();
c = -c;
if(dd[v] < c) continue;
for(auto [u, w] : g[v]) {
if(d[0][v] + w + d[1][u] == d[0][T] && dd[u] > c) { // in shortest path
dd[u] = c;
pq.push({-dd[u], u});
}
}
}
for(int i = 1; i <= N; i++) {
ans = min(ans, dd[i] + d[3][i]);
}
ans = min(ans, d[2][V]);
swap(U, V);
}
cout << ans << '\n';
}
