//ashoori is my love
//ashoori is my love//ashoori is my love//ashoori is my love//ashoori is my love//ashoori is my love
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef int it;
typedef pair<ll, ll> pii;
typedef pair<ll, pii> piii;
#pragma GCC optimize ("O3")
#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops,Ofast")
#define sep "\n"
#define pes " "
#define int long long
#define print(x,n) for(int i=1; i<=n ; i++)cout<<x[i]<<" "
#define scan(x,n) for(int i=1 ; i<=n ; i++)cin>>x[i]
#define all(x) x.begin(), x.end()
#define pb push_back
#define F first
#define Se second
#define sz size
#define cin2(r,j) cin>>r>>j
#define cin1(r) cin>>r
#define cin3(r,j,k) cin>>r>>j>>k
# define InTheNameOfGod ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
const int maxx=1e5+1000;
const ll MOD=1000000007;
const ll inf=1e18;
int S,T,U,V,n,m;
vector<pii> g[maxx];
vector<ll> distances[maxx];
void dij(int v , int T)
{
vector<ll> ashoori(maxx-10);
for(int i = 1 ; i <= n+10 ; i++)ashoori[i] = inf;
priority_queue<pair<ll,ll>,vector<pair<ll,ll>>,greater<pair<ll,ll>>> pq;
ashoori[v]=0;
pq.push({0,v});
while(!pq.empty()){
int node = pq.top().Se;
int ce = pq.top().F;
pq.pop();
//if(ce!=ashoori[node])continue;
for(auto U : g[node]){
if(ashoori[node] + U.Se < ashoori[U.F]){
ashoori[U.F] = ashoori[node] + U.Se;
pq.push({ashoori[U.F],U.F});
}
}
}
for(int i = 0 ; i <= n ; i++){
distances[T].pb(ashoori[i]);
}
}
bool comp(int a,int b){
return distances[S][a]<distances[S][b];
}
void solve(){
cin>>n>>m>>S>>T>>U>>V;
for(int i = 1 ; i <= m ; i++){
int u , v , c;
cin>>u>>v>>c;
g[u].pb({v,c});
g[v].pb({u,c});
}
dij(T , T);
dij(S , S);
dij(U , U );
dij(V , V);
/*for(auto J : distances[V])cout<<J<<" ";
cout<<"\n";*/
int answer = distances[U][V];
int mn[maxx];
for(int i = 0 ; i < maxx ; i++)mn[i] = inf;
vector<int> nodes;
for(int i = 1 ; i <= n ; i++){
if(distances[S][i] + distances[T][i] == distances[S][T])nodes.pb(i);
}
sort(all(nodes),comp);
for(int i = 0 ; i < nodes.sz() ; i ++){
mn[nodes[i]] = distances[U][nodes[i]];
for(auto K : g[nodes[i]]){
mn[nodes[i]] = min(mn[nodes[i]] , mn[K.F]);
}
answer = min(mn[nodes[i]] + distances[V][nodes[i]],answer);
}
for(int i = 0 ; i < maxx ; i++)mn[i] = inf;
for(int i = 0 ; i < nodes.sz() ; i ++){
mn[nodes[i]] = distances[V][nodes[i]];
for(auto K : g[nodes[i]]){
mn[nodes[i]] = min(mn[nodes[i]] , mn[K.F]);
}
answer = min(mn[nodes[i]] + distances[U][nodes[i]],answer);
}
cout<<answer;
}
/*===========================================================================================================================*/
signed main(){
//InTheNameOfGod;
//int tt = clock();
//cout << fixed << setprecision(6);
int tc = 1;
//cin>>tc;
//for(int i = 1 ; i <= 3 ; i++)cout<<dp[i]<<" ";
while(tc--){solve();
//cerr << "TIME = " << clock() - tt << endl;
//tt = clock();
}
}
