#include <bits/stdc++.h>
#define f first
#define s second
using namespace std;
typedef long long ll;
typedef pair<ll,int> pii;
const int MN=1e5+2;
int N,M,S,T,U,V;
ll du[MN],dv[MN],dis[MN],uU[MN],uV[MN],mU[MN],mV[MN],vU[MN],vV[MN];
bool vis[MN];
vector<pii> gr[MN];
int main() {
ios::sync_with_stdio(0);cin.tie(0);
cin>>N>>M>>S>>T>>U>>V;
for(int i=1;i<=M;++i) {
int u,v,w;
cin>>u>>v>>w;
gr[u].push_back(pii(w,v));
gr[v].push_back(pii(w,u));
}
fill(du+1,du+1+N,2e18);
memset(vis,0,sizeof(vis));
priority_queue<pii,vector<pii>,greater<pii>> pq;
pq.push(pii(0,U));
du[U]=0;
while(!pq.empty()) {
int u=pq.top().s;
ll d=pq.top().f;
pq.pop();
if(vis[u]) continue;
vis[u]=1;
for(pii p:gr[u]) {
int v=p.s;
ll ed=p.f;
if(!vis[v]&&d+ed<du[v]) {
du[v]=d+ed;
pq.push(pii(du[v],v));
}
}
}
fill(dv+1,dv+1+N,2e18);
memset(vis,0,sizeof(vis));
pq.push(pii(0,V));
dv[V]=0;
while(!pq.empty()) {
int u=pq.top().s;
ll d=pq.top().f;
pq.pop();
if(vis[u]) continue;
vis[u]=1;
for(pii p:gr[u]) {
int v=p.s;
ll ed=p.f;
if(!vis[v]&&d+ed<dv[v]) {
dv[v]=d+ed;
pq.push(pii(dv[v],v));
}
}
}
// S->T
fill(dis+1,dis+1+N,2e18);
memset(vis,0,sizeof(vis));
pq.push(pii(0,S));
dis[S]=0;
uU[S]=vU[S]=mU[S]=du[S];
uV[S]=vV[S]=mV[S]=dv[S];
while(!pq.empty()) {
int x=pq.top().s;
ll d=pq.top().f;
pq.pop();
if(vis[x]) continue;
vis[x]=1;
for(pii p:gr[x]) {
int y=p.s;
ll ed=p.f;
if(!vis[y]) {
if(d+ed<dis[y]) {
dis[y]=d+ed;
pq.push(pii(dis[y],y));
uU[y]=min(uU[x],du[y]);
uV[y]=min(uV[x],dv[y]);
mU[y]=min(mU[x],du[y]);
mV[y]=min(mV[x],dv[y]);
vU[y]=min(vU[x],du[y]);
vV[y]=min(vV[x],dv[y]);
if(uU[y]+uV[y]<=mU[y]+mV[y]) {
mU[y]=uU[y];
mV[y]=uV[y];
}
if(vU[y]+vV[y]<=mU[y]+mV[y]) {
mU[y]=vU[y];
mV[y]=vV[y];
}
}
if(d+ed==dis[y]) {
if(uU[x]<uU[y]) {
uU[y]=uU[x];
uV[y]=uV[x];
}
if(vV[x]<vV[y]) {
vU[y]=vU[x];
vV[y]=vV[x];
}
if(mU[x]+mV[x]<mU[y]+mV[y]) {
mU[y]=mU[x];
mV[y]=mV[x];
}
mU[y]=min(mU[y],du[y]);
mV[y]=min(mV[y],dv[y]);
if(uU[y]+uV[y]<=mU[y]+mV[y]) {
mU[y]=uU[y];
mV[y]=uV[y];
}
if(vU[y]+vV[y]<=mU[y]+mV[y]) {
mU[y]=vU[y];
mV[y]=vV[y];
}
}
}
}
}
cout<<min(mU[T]+mV[T],du[V])<<'\n';
return 0;
}
