#include<bits/stdc++.h>
#define int long long
using namespace std;
const int maxn = 1e5;
int n, m, st, en, shop1, shop2;
struct line{
int u, v, w, id;
};
line l[2 * maxn + 1];
vector<line> adj[maxn + 1];
bool on_road[2 * maxn + 1];
vector<long long> dis_st, dis_en, dis_shop1, dis_shop2;
struct str{
bool operator ()(const pair<int, long long>& x, const pair<int, long long>& y) const {
return x.second > y.second;
}
};
inline vector<long long> dijkstra(int st){
vector<long long> ans(n + 1 , 1e18);
ans[st] = 0;
priority_queue<pair<int, long long>, vector<pair<int, long long>>, str> pq;
pq.push({st, 0});
while(!pq.empty()){
int u = pq.top().first, dis = pq.top().second;
pq.pop();
if (dis > ans[u]) continue;
for (line l : adj[u]){
int nxt = (u == l.u) ? l.v : l.u;
int w = l.w;
if (dis + w < ans[nxt]){
ans[nxt] = dis + w;
pq.push({nxt, ans[nxt]});
}
}
}
return ans;
}
inline long long solve(){
long long res = dis_shop1[shop2];
priority_queue<pair<int, long long>, vector<pair<int, long long>>, str> pq;
pq.push({st, dis_shop1[st]});
while(!pq.empty()){
int u = pq.top().first;
long long dis = pq.top().second;
pq.pop();
dis = min(dis, dis_shop1[u]);
res = min(res, dis + dis_shop2[u]);
for (line ln : adj[u]) if (on_road[ln.id]){
int nxt = (u == ln.u) ? ln.v : ln.u;
if (dis_st[u] + ln.w != dis_st[nxt]) continue;
pq.push({nxt, dis});
}
}
return res;
}
inline long long solve1(){
long long res = dis_shop1[shop2];
priority_queue<pair<int, long long>, vector<pair<int, long long>>, str> pq;
pq.push({st, dis_shop2[st]});
while(!pq.empty()){
int u = pq.top().first;
long long dis = pq.top().second;
pq.pop();
dis = min(dis, dis_shop2[u]);
res = min(res, dis + dis_shop1[u]);
for (line ln : adj[u]) if (on_road[ln.id]){
int nxt = (u == ln.u) ? ln.v : ln.u;
if (dis_st[u] + ln.w != dis_st[nxt]) continue;
pq.push({nxt, dis});
}
}
return res;
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m >> st >> en >> shop1 >> shop2;
for (int i = 1; i <= m; ++i){
cin >> l[i].u >> l[i].v >> l[i].w;
l[i].id = i;
adj[l[i].u].push_back(l[i]);
adj[l[i].v].push_back(l[i]);
}
dis_st = dijkstra(st);
dis_en = dijkstra(en);
dis_shop1 = dijkstra(shop1);
dis_shop2 = dijkstra(shop2);
for (int i = 1; i <= m; ++i){
int u = l[i].u, v = l[i].v, w = l[i].w;
if (dis_st[u] + dis_en[v] + w == dis_st[en] || dis_st[v] + dis_en[u] + w == dis_st[en])
on_road[l[i].id] = true;
}
cout << min(solve(), solve1());
}
