#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef pair<ll,ll> pi;
typedef vector<pi> vpi;
typedef long double ld;
#define pb emplace_back
#define mp make_pair
#define lb lower_bound
#define ub upper_bound
#define ALL(x) x.begin(), x.end()
#define SZ(x) (ll)x.size()
#define f first
#define s second
const ll MAXN = 200100;
const ll INF = 1e18;
const ll MOD = 1e9+7;
typedef pair<ll,pi> pip;
vector<pip> E;
vpi V[MAXN];
ll d1[MAXN];
ll d2[MAXN];
ll N,M,a,b,w;
ll S,T,X,Y;
priority_queue<pi,vpi,greater<pi>>pq;
map<pi,ll> Z;
vpi useful;
ll ans=INF;
void dijkstra(int rt){
memset(d1,-1,sizeof(d1));
d1[rt]=0;
pq.push(mp(0,rt));
while (SZ(pq)){
ll n = pq.top().s;
ll d =pq.top().f;
pq.pop();
if (d1[n]!=d)continue;
for (auto v:V[n]){
ll w=d+v.s;
if (d1[v.f]!=-1&&d1[v.f]<=w)continue;
d1[v.f]=w;
pq.push(mp(w,v.f));
}
}
// cout<<"Distances from node "<<rt<<'\n';
// for (int i=1;i<=N;++i)cout<<d1[i]<<' ';cout<<'\n';
}
ll D[300100];
void dijkstra2(int rt){
memset(D,-1,sizeof(D));
D[rt]=0;
pq.push(mp(0,rt));
while (SZ(pq)){
ll n = pq.top().s;
ll d =pq.top().f;
pq.pop();
if (D[n]!=d)continue;
ll b=((n-1)/N);n-=b*N;
// cerr<<b<<' '<<n<<' '<<d<<'\n';
if (b==0){ // Hvae not gone anywhere
for (auto v:V[n]){
ll w=d+v.s;
ll c=v.f;
if(v.s==0)c=N+v.f;
if (D[c]!=-1&&D[c]<=w)continue;
D[c]=w;
pq.push(mp(w,c));
}
}else if (b==1){
for (auto v:V[n]){
ll w=d+v.s;
ll c=v.f+2*N;
if(v.s==0){c=N+v.f;}
if (D[c]!=-1&&D[c]<=w)continue;
D[c]=w;
pq.push(mp(w,c));
}
}else{
for (auto v:V[n]){
ll w=d+v.s;
ll c=v.f+2*N;
if (v.s==0)continue;
if (D[c]!=-1&&D[c]<=w)continue;
D[c]=w;
pq.push(mp(w,c));
}
}
}
for (int i=0;i<3;++i)if(D[i*N+Y]!=-1)ans=min(ans,D[i*N+Y]);
// cout<<'\n';
}
int main(){
cin>>N>>M>>S>>T>>X>>Y;
swap(X,Y);
for (int i=0;i<M;++i){
cin>>a>>b>>w;
E.pb(w, mp(a,b));
V[a].pb(b,w);
V[b].pb(a,w);
}
dijkstra(S);
for (int i=1;i<=N;++i)d2[i]=d1[i];
dijkstra(T);
// d2 is distance from S, d1 is distance from T
ll tar = d2[T];
for (auto x:E){
ll a=x.s.f;
ll b=x.s.s;
ll w=x.f;
if (d1[a]+w+d2[b]==tar){
useful.pb(b,a);
}else if(d1[b]+w+d2[a]==tar){
useful.pb(a,b);
}
}
for (auto i:useful)V[i.f].pb(i.s,0);
dijkstra2(X);
for (auto i:useful)V[i.f].pop_back();
for (auto i:useful)V[i.s].pb(i.f,0);
dijkstra2(X);
cout<<ans<<'\n';
}
