#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define F first
#define S second
#define pb push_back
const ll INF=2e18;
vector<pll> ed[100005];
ll dist[100005][5],ds[100005],dt[100005],dv[100005];
ll s,t;
void dijk(ll n)
{
priority_queue<pair<ll,pll>,vector<pair<ll,pll> >,greater<pair<ll,pll> > > pq;
pq.push({0,{n,0}});
dist[n][0]=0;
while(!pq.empty())
{
auto p=pq.top();pq.pop();
ll d=p.F,u=p.S.F,x=p.S.S;
if(dist[u][x]<d) continue;
for(auto tmp:ed[u])
{
ll v=tmp.F,len=tmp.S;
if(x==0)
{
if(dist[v][0]>d+len)
{
dist[v][0]=d+len;
pq.push({d+len,{v,0}});
}
if(ds[u]+dt[v]+len==ds[t])
{
if(dist[v][1]>d)
{
dist[v][1]=d;
pq.push({d,{v,1}});
}
}
if(ds[v]+dt[u]+len==ds[t])
{
if(dist[v][3]>d)
{
dist[v][3]=d;
pq.push({d,{v,3}});
}
}
}
else if(x==1)
{
if(dist[v][2]>d+len)
{
dist[v][2]=d+len;
pq.push({d+len,{v,2}});
}
if(ds[u]+dt[v]+len==ds[t])
{
if(dist[v][1]>d)
{
dist[v][1]=d;
pq.push({d,{v,1}});
}
}
}
else if(x==3)
{
if(dist[v][2]>d+len)
{
dist[v][2]=d+len;
pq.push({d+len,{v,2}});
}
if(ds[v]+dt[u]+len==ds[t])
{
if(dist[v][3]>d)
{
dist[v][3]=d;
pq.push({d,{v,3}});
}
}
}
else
{
if(dist[v][2]>d+len)
{
dist[v][2]=d+len;
pq.push({d+len,{v,2}});
}
}
}
}
}
int main()
{
int n,m,a,b;
cin>>n>>m>>s>>t>>a>>b;
rep(i,m)
{
ll u,v,w;
cin>>u>>v>>w;
ed[u].pb({v,w});
ed[v].pb({u,w});
}
rep1(i,n) ds[i]=dt[i]=INF;
rep1(i,n) rep(j,5) dist[i][j]=INF;
priority_queue<pll,vector<pll>,greater<pll> > pq;
pq.push({0,s});
ds[s]=0;
while(!pq.empty())
{
ll d=pq.top().F,u=pq.top().S;pq.pop();
if(d>ds[u]) continue;
for(auto v:ed[u])
{
if(ds[v.F]<=v.S+d) continue;
ds[v.F]=v.S+d;
pq.push({ds[v.F],v.F});
}
}
pq.push({0,t});
dt[t]=0;
while(!pq.empty())
{
ll d=pq.top().F,u=pq.top().S;pq.pop();
if(d>dt[u]) continue;
for(auto v:ed[u])
{
if(dt[v.F]<=v.S+d) continue;
dt[v.F]=v.S+d;
pq.push({dt[v.F],v.F});
}
}
dijk(a);
cout<<min({dist[b][0],dist[b][1],dist[b][2],dist[b][3]});
}
