#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MX = 1e5 + 5;
int N, M, S, T, U, V;
vector<pair<int,int>> g[MX];
ll dist[5][MX];
void work(int src, int id) {
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> pq;
pq.push({0, src});
dist[id][src] = 0;
while(!pq.empty()) {
auto [cost, v] = pq.top();
pq.pop();
if(cost > dist[id][v]) continue;
for(auto [u, w] : g[v]) {
if(dist[id][u] > dist[id][v] + w) {
dist[id][u] = dist[id][v] + w;
pq.push({dist[id][u], u});
}
}
}
}
int main() {
cin.tie(0); ios_base::sync_with_stdio(0);
cin >> N >> M >> S >> T >> U >> V;
for(int i = 0; i < M; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
ll ans = 1e18;
for(int it = 0; it < 2; it++) {
for(int j = 0; j < 5; j++)
for(int i = 0; i < MX; i++)
dist[j][i] = 1e18;
work(S, 0);
work(T, 1);
work(U, 2);
work(V, 3);
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> pq;
for(int i = 1; i <= N; i++) {
if(dist[0][i] + dist[1][i] == dist[0][T]) {
dist[4][i] = dist[2][i];
pq.push({dist[2][i], i});
}
}
while(!pq.empty()) {
auto [cost, v] = pq.top(); pq.pop();
if(cost > dist[4][v]) continue;
for(auto [u, w] : g[v]) {
if(w + dist[0][v] + dist[1][u] == dist[0][T] && dist[4][u] > cost) {
dist[4][u] = cost;
pq.push({cost, u});
}
}
}
ans = min(ans, dist[2][V]);
for(int i = 1; i <= N; i++) {
if(dist[0][i] + dist[1][i] == dist[0][T]) {
ans = min(ans, dist[4][i] + dist[3][i]);
}
}
swap(U, V);
}
cout << ans << '\n';
}
