#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i, l, r) for (int i = (l); i <= (r); ++i)
#define FOD(i, r, l) for (int i = (r), _l = (l); i >= _l; i--)
#define pii pair<int,int>
#define endl '\n'
#define pb push_back
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define Konosuba tuple<int , int , int, int>
const int N = 3e5 + 5;
const int MOD = 1e9 + 7;
const int block = 320;
const int LOG = 30;
const int MAXN = 1e6 + 5;
const int INF = 1e18;
template<class A, class B>
bool umin(A& var, const B& val){ return (val < var) ? (var = val, true) : false; }
template<class A, class B>
bool umax(A& var, const B& val){ return (var < val) ? (var = val, true) : false; }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class X, class Y> int random(const int& l, const int& r) {
return uniform_int_distribution<int>(l,r)(rng);
}
int dist1[N];
int dist2[N];
int dp[2][N];
int dist3[N];
int res = INF;
int n , m , a , b , c , d;
vector<pii> adj[N];
void dijikstra(int Megumin , int dist[]){
FOR(i , 1 , n){
dist[i] = INF;
}
dist[Megumin] = 0;
priority_queue<pii , vector<pii> , greater<pii>> pq;
pq.push({dist[Megumin] , Megumin});
while(pq.size()){
int u = pq.top().second;
int val = pq.top().first;
pq.pop();
if(val > dist[u]) continue;
for(auto v : adj[u]){
if(dist[v.first] > dist[u] + v.second){
dist[v.first] = dist[u] + v.second;
pq.push({dist[v.first] , v.first});
}
}
}
}
void KonoDijikstra(int be , int ed){
FOR(i , 0 , 1){
FOR(j , 1 , n){
dp[i][j] = INF;
dist3[j] = INF;
}
}
priority_queue<Konosuba , vector<Konosuba> , greater<Konosuba>> pq;
dist3[be] = 0;
dp[0][be] = dist1[be];
dp[1][be] = dist2[be];
pq.push({0 , be , dist1[be] , dist2[be]});
while(pq.size()){
int val = get<0>(pq.top());
int u = get<1>(pq.top());
int c1 = get<2>(pq.top());
int c2 = get<3>(pq.top());
pq.pop();
if(val > dist3[u]) continue;
for(auto v : adj[u]){
int ndist = dist3[u] + v.second;
int ndp1 = (c1 < dist1[v.first] ? c1 : dist1[v.first]);
int ndp2 = (c2 < dist2[v.first] ? c2 : dist2[v.first]);
if(dist3[v.first] > dist3[u] + v.second){
dist3[v.first] = ndist;
dp[0][v.first] = ndp1;
dp[1][v.first] = ndp2;
pq.push({dist3[v.first] , v.first , dp[0][v.first] , dp[1][v.first]});
}
else if(dist3[v.first] == dist3[u] + v.second && ndp1 + ndp2 < dp[0][v.first] + dp[1][v.first]){
dist3[v.first] = ndist;
dp[0][v.first] = ndp1;
dp[1][v.first] = ndp2;
pq.push({dist3[v.first] , v.first , dp[0][v.first] , dp[1][v.first]});
}
}
}
res = min(res , dp[0][ed] + dp[1][ed]);
}
void solve(void){
cin >> n >> m >> a >> b >> c >> d;
FOR(i , 1 , m){
int u , v , w;
cin >> u >> v >> w;
adj[u].push_back({v , w});
adj[v].push_back({u , w});
}
dijikstra(c , dist1);
dijikstra(d , dist2);
res = dist1[d];
KonoDijikstra(a , b);
KonoDijikstra(b , a);
cout << res;
}
signed main(void) {
if (fopen("TASK.INP", "r")) {
freopen("TASK.INP", "r", stdin);
freopen("TASK.OUT", "w", stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int testCase = 1; //cin >> testCase;
FOR(i , 1 , testCase){
solve();
}
cerr << "Time elapsed: " << TIME << "s.\n";
return (0);
}
