#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define sz(a) (int)a.size()
#define all(a) begin(a),end(a)
using vi = vector<int>;
using ll = long long;
using ar2 = array<ll,2>;
const int N = (int)2e5+10;
const int INF = (int)1e9;
const ll LINF = (ll)2e18;
vi ts, radj[N];
int n, m, S, T, U, V;
ll dis[4][N], ans, D[N],vis[N];
vector<ar2> adj[N];
vector<array<ll,3>> edges;
void dijkstra(int s, int t){
priority_queue<ar2,vector<ar2>,greater<ar2>> pq;
while(sz(pq)) pq.pop();
for(int i = 1; i <= n; i++) dis[t][i]=LINF;
dis[t][s] = 0; pq.push({0,s});
while(sz(pq)){
auto [D,a] = pq.top(); pq.pop();
if(D!=dis[t][a]) continue;
for(auto [b,w] : adj[a]){
if(dis[t][a]+w<dis[t][b]){
dis[t][b] = dis[t][a]+w;
pq.push({dis[t][b],b});
}
}
}
}
void dfs(int s){
vis[s]=1;
for(auto [u,w] : adj[s])
if(!vis[u]) dfs(u);
ts.pb(s);
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(0);
cin >> n >> m >> S >> T >> U >> V;
for(int i = 0; i < m; i++){
int a, b, c; cin >> a >> b >> c;
adj[a].pb({b,c}), adj[b].pb({a,c});
edges.pb({a,b,c});
}
dijkstra(S,0); dijkstra(T,1); dijkstra(U,2); dijkstra(V,3);
for(int i = 1; i <= n; i++) adj[i].clear(),D[i]=LINF;
ans = dis[2][V];
for(auto [a,b,c] : edges){
if(dis[0][a]+c+dis[1][b]==dis[0][T])
adj[a].pb({b,0}),radj[b].pb(a);
swap(a,b);
if(dis[0][a]+c+dis[1][b]==dis[0][T])
adj[a].pb({b,0}),radj[b].pb(a);
}
dfs(S); //reverse(all(ts));
for(auto u : ts){
D[u] = dis[2][u];
for(auto v : radj[u])
D[u] = min(D[u],D[v]);
ans = min(ans, D[u]+dis[3][u]);
}
cout << ans << "\n";
}
