#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5+1;
const int MAXM = 2e5+1;
const long long inf = 1e18;
int N,M,S,T,U,V;
vector<pair<long long, long long>> G[MAXN];
vector<long long> distuv[2],distst[2],bestu[2],bestv[2];
vector<long long> dijkstra(int start){
vector<long long> dist(N+1,inf);
dist[start]=0;
priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<pair<long long, long long>>> pq;
pq.push({dist[start],start});
while(!pq.empty()){
auto p = pq.top(); pq.pop();
long long d = p.first, v = p.second;
if(d!=dist[v]) continue;
for(auto e: G[v]){
long long u=e.first,w=e.second;
if(d+w<dist[u]){
dist[u]=d+w;
pq.push({dist[u],u});
}
}
}
return dist;
}
vector<long long> dijkstra2(int start, int whichst, int whichuv){
vector<long long> best(N+1,inf);
priority_queue<array<long long, 3>, vector<array<long long, 3>>, greater<array<long long, 3>>> pq;
pq.push({0,start,distuv[whichuv][start]});
while(!pq.empty()){
auto p = pq.top(); pq.pop();
long long d = p[0], v = p[1], bestuv = p[2];
if(d+distst[whichst^1][v]!=distst[0][T]) continue;
if(bestuv>=best[v]) continue;
best[v]=bestuv;
for(auto e: G[v]){
long long u=e.first,w=e.second;
long long newdist = d+w;
if(newdist + distst[whichst^1][u]!=distst[0][T]) continue;
long long nb = min(bestuv,distuv[whichuv][u]);
pq.push({newdist,u,nb});
}
}
return best;
}
void solve(){
cin >> N >> M >> S >> T >> U >> V;
for(int i=0; i<M; i++){
long long a,b,w; cin >> a >> b >> w;
G[a].push_back({b,w});
G[b].push_back({a,w});
}
distst[0] = dijkstra(S);
distst[1] = dijkstra(T);
distuv[0] = dijkstra(U);
distuv[1] = dijkstra(V);
bestu[0]=dijkstra2(S,0,0);
bestu[1]=dijkstra2(T,1,0);
bestv[0]=dijkstra2(S,0,1);
bestv[1]=dijkstra2(T,1,1);
long long ans = distuv[0][V];
for(int i=1; i<=N; i++){
long long b1 = distuv[0][i]+min(bestv[0][i],bestv[1][i]);
long long b2 = distuv[1][i]+min(bestu[0][i],bestu[1][i]);
//cout << i << " " << b1 << " " << b2 << "xd\n";
ans=min(ans,min(b1,b2));
}
cout << ans << "\n";
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t=1;
//cin>>t;
while(t--)
solve();
}
