#include <stdio.h>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
#define mp make_pair
#define pb push_back
#define ll long long
const int N=100050;
vector<pair<int,int> > E[N];
vector<int> go[N];
ll dist[N],sol[N][3];
const ll inf=1e18;
bool ok[N];
bool mark[N];
void DFS(int u)
{
mark[u]=1;
for(int i=0;i<go[u].size();i++)
{
int v=go[u][i];
if(!mark[v]) DFS(v);
}
}
void Dijkstra1(int n, int s, int t)
{
int i;
for(i=1;i<=n;i++) dist[i]=inf,go[i].clear(),mark[i]=0;
priority_queue<pair<ll,int> > pq;
dist[s]=0;
pq.push(mp(0,s));
while(pq.size())
{
int u=pq.top().second;
ll w=-pq.top().first;
pq.pop();
if(w!=dist[u]) continue;
for(i=0;i<E[u].size();i++)
{
int v=E[u][i].first;
w=E[u][i].second;
if(dist[v]>dist[u]+w)
{
dist[v]=dist[u]+w;
go[v].clear();
pq.push(mp(-dist[v],v));
}
if(dist[v]==dist[u]+w) go[v].push_back(u);
}
}
DFS(t);
for(i=1;i<=n;i++) if(!mark[i]) go[i].clear();
}
ll Dijkstra2(int n, int s, int t)
{
int i;
for(i=1;i<=n;i++) sol[i][0]=sol[i][1]=sol[i][2]=inf;
priority_queue<pair<ll,pair<int,int> > > pq;
sol[s][0]=0;
pq.push(mp(0,mp(s,0)));
while(pq.size())
{
int u=pq.top().second.first;
int t=pq.top().second.second;
ll w=-pq.top().first;
pq.pop();
if(w!=sol[u][t]) continue;
if(t==0 || t==2)
{
if(t==0 && sol[u][0]<sol[u][1])
{
sol[u][1]=sol[u][0];
pq.push(mp(-sol[u][1],mp(u,1)));
}
for(i=0;i<E[u].size();i++)
{
int v=E[u][i].first;
w=E[u][i].second;
if(sol[v][t]>sol[u][t]+w)
{
sol[v][t]=sol[u][t]+w;
pq.push(mp(-sol[v][t],mp(v,t)));
}
}
}
else if(t==1)
{
if(sol[u][1]<sol[u][2])
{
sol[u][2]=sol[u][1];
pq.push(mp(-sol[u][2],mp(u,2)));
}
for(i=0;i<go[u].size();i++)
{
int v=go[u][i];
if(sol[v][t]>sol[u][t])
{
sol[v][t]=sol[u][t];
pq.push(mp(-sol[v][t],mp(v,t)));
}
}
}
}
return sol[t][2];
}
ll min(ll a, ll b){ return a>b?b:a;}
int main()
{
int n,m,u,v,w,i,a,b,s,t;
scanf("%i %i",&n,&m);
scanf("%i %i",&s,&t);
scanf("%i %i",&a,&b);
while(m--) scanf("%i %i %i",&u,&v,&w),E[u].pb(mp(v,w)),E[v].pb(mp(u,w));
Dijkstra1(n,t,s);
ll ans=Dijkstra2(n,a,b);
ans=min(ans,Dijkstra2(n,b,a));
Dijkstra1(n,t,s);
ans=min(ans,Dijkstra2(n,a,b));
ans=min(ans,Dijkstra2(n,b,a));
printf("%lld\n",ans);
return 0;
}
