#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define MAXN 200005
ll n, m, s, t, u, v;
vector<pair<ll, ll>> adj[MAXN];
void dijkstra(ll start, vector<ll> &dist)
{
dist[start] = 0;
vector<bool> visited(n + 1);
using T = pair<long long, int>;
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, start});
while(!pq.empty()){
const auto[cdist, node] = pq.top();
pq.pop();
if(visited[node]) continue;
visited[node] = true;
for(const pair<ll, ll> &i: adj[node]){
if(cdist + i.second < dist[i.first]){
pq.push({dist[i.first] = cdist + i.second, i.first});
}
}
}
}
vector<ll> dijkstra2(ll start, vector<ll> &dist, vector<ll> &cost)
{
dist[start] = 0;
vector<ll> min_cost(n + 1, LLONG_MAX);
vector<bool> visited(n + 1);
using T = pair<long long, int>;
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, start}); min_cost[start] = cost[start];
while(!pq.empty()){
const auto[cdist, node] = pq.top();
pq.pop();
if(visited[node]) continue;
visited[node] = true;
for(const pair<ll, ll> &i: adj[node]){
if(cdist + i.second < dist[i.first]){
min_cost[i.first] = min(cost[i.first], min_cost[node]);
pq.push({dist[i.first] = cdist + i.second, i.first});
}
else if(cdist + i.second == dist[i.first]){
min_cost[i.first] = min(cost[i.first], min(min_cost[i.first], min_cost[node]));
}
}
}
return min_cost;
}
int main()
{
cin >> n >> m >> u >> v >> s >> t;
for(int i = 0; i < m; i++){
ll a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<ll> tdist(n + 1, LLONG_MAX);
dijkstra(t, tdist);
// for(int i = 1; i <= n; i++){
// cout << tdist[i] << " ";
// }
// cout << "\n";
vector<ll> sdist(n + 1, LLONG_MAX);
dijkstra(s, sdist);
vector<ll> vdist(n + 1, LLONG_MAX);
vector<ll> udist(n + 1, LLONG_MAX);
vector<ll> cost1 = dijkstra2(v, vdist, tdist);
vector<ll> cost2 = dijkstra2(u, udist, tdist);
ll res = sdist[t];
for(int i = 1; i <= n; i++){
//cout << vdist[i] << " " << udist[i] << " " << vdist[u] << "\n";
if(vdist[i] + udist[i] == vdist[u]){
res = min(res, sdist[i] + min(cost1[i], cost2[i]));
}
}
cout << res << "\n";
}
