#include<bits/stdc++.h>
using namespace std;
#define ll long long
struct edge{
int u, v;
ll w;
void wczyt(){
cin >> u >> v >> w;
}
void print(){
cerr << u << ' ' << v << ' ' << w << '\n';
}
};
const int MAXN = 1e5 + 7;
const ll inf = 1e18;
ll odl_s[MAXN], odl_t[MAXN], odl_u[MAXN];
void dijkstra(int start, ll odl[], vector<vector<pair<ll, int>>> &graf){
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push({0, start});
while(!pq.empty()){
auto [cost, v] = pq.top();
// cerr << "v: " << v << " cost: " << cost << '\n';
pq.pop();
if(odl[v] != inf) continue;
odl[v] = cost;
for(auto [u, w] : graf[v]){
// cerr << "u: " << u << " w: " << w << "\n";
if(odl[u] == inf) pq.push({cost + w, u});
}
}
// cerr << "###################\n";
}
void which_edges(int s, int t, vector<edge> &edges, vector<edge> &vec){
for(auto [u, v, w] : edges){
if((u == s || u == t) && (v == s || v == t)) continue;
if(odl_s[u] + w + odl_t[v] == odl_s[t]) vec.push_back({u, v, 0});
if(odl_s[v] + w + odl_t[u] == odl_s[t]) vec.push_back({v, u, 0});
}
}
void build_graf(vector<vector<pair<ll, int>>> &graf, vector<edge> &git, bool mod){
for(auto [u, v, w] : git){
if(mod) swap(u, v);
graf[u].push_back({v, w});
}
}
int main(){
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for(int i = 1; i <= n; i++){
odl_s[i] = inf;
odl_t[i] = inf;
odl_u[i] = inf;
}
vector<edge> edges(m);
vector<vector<pair<ll, int>>> graf(n + 1);
for(edge &e : edges){
e.wczyt();
graf[e.u].push_back({e.v, e.w});
graf[e.v].push_back({e.u, e.w});
}
dijkstra(s, odl_s, graf);
dijkstra(t, odl_t, graf);
vector<edge> git;
which_edges(s, t, edges, git);
// for(edge e : git){
// e.print();
// }
// cerr << "------------------\n";
vector<vector<pair<ll, int>>> graf1, graf2;
graf1 = graf2 = graf;
build_graf(graf1, git, 0);
build_graf(graf2, git, 1);
dijkstra(u, odl_u, graf1);
ll ans = odl_u[v];
for(int i = 1; i <= n; i++) odl_u[i] = inf;
dijkstra(u, odl_u, graf2);
ans = min({ans, odl_u[v], odl_u[s] + odl_t[v], odl_u[t] + odl_s[v]});
cout << ans << '\n';
}
