#include<bits/stdc++.h>
typedef long long ll;
#define pb push_back
#define mp make_pair
#define fi first
#define se second
using namespace std;
ll n,m,S,T,U,V,ta,tb,tc,i,j,has;
ll jar[4][101010];
vector<ll> v[101010];
vector<ll> w[101010];
vector<ll> vi[101010];
ll d[101010][2];
ll depe(ll aa,ll bb)
{
if(d[aa][bb]==-1)
{
if(bb==0)
d[aa][bb]=jar[2][aa];
else
d[aa][bb]=jar[3][aa];
ll ii;
for(ii=0;ii<vi[aa].size();ii++)
d[aa][bb]=min(d[aa][bb],depe(vi[aa][ii],bb));
}
return d[aa][bb];
}
void buat(ll aa,ll bb)
{
priority_queue<pair<ll,ll> > pq;
jar[bb][aa]=0;
pq.push(mp(0,aa));
while(!pq.empty())
{
ll dis=-pq.top().fi;
ll u=pq.top().se;
pq.pop();
if(dis>jar[bb][u])continue;
ll ii;
for(ii=0;ii<v[u].size();ii++)
if((jar[bb][v[u][ii]]==-1)||(jar[bb][v[u][ii]]>(dis+w[u][ii])))
{
jar[bb][v[u][ii]]=dis+w[u][ii];
pq.push(mp(-jar[bb][v[u][ii]],v[u][ii]));
}
}
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin>>n>>m;
cin>>S>>T;
cin>>U>>V;
for(i=1;i<=m;i++)
{
cin>>ta>>tb>>tc;
v[ta].pb(tb);
w[ta].pb(tc);
v[tb].pb(ta);
w[tb].pb(tc);
}
memset(jar,-1,sizeof(jar));
buat(S,0);
buat(T,1);
buat(U,2);
buat(V,3);
for(i=1;i<=n;i++)
for(j=0;j<v[i].size();j++)
{
//cout<<i<<" "<<v[i][j]<<" "<<jar[0][i]<<" "<<w[i][j]<<" "<<jar[1][v[i][j]]<<" "<<jar[0][T]<<"\n";
if(jar[0][i]+w[i][j]+jar[1][v[i][j]]==jar[0][T])
{
//cout<<v[i][j]<<" "<<i<<"\n";
vi[v[i][j]].pb(i);
}
}
has=jar[2][V];
memset(d,-1,sizeof(d));
for(i=1;i<=n;i++)
{
has=min(has,depe(i,0)+jar[3][i]);
has=min(has,depe(i,1)+jar[2][i]);
}
cout<<has<<"\n";
}
