#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef tuple<ll,ll,ll> PP;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<bool> vb;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,k,n) for(ll i=(ll)(k);i<(ll)(n);i++)
#define all(a) a.begin(),a.end()
#define fi first
#define se second
#define pb emplace_back
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<'\n';}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<'\n';}
const ll inf=1001001001001001001;
struct UF{
ll n;
vi par,sz;
UF(ll n_):n(n_),par(n,-1),sz(n,1){}
void merge(ll a,ll b){
a=root(a);b=root(b);
if(a==b)return;
if(sz[a]>sz[b])swap(a,b);
par[a]=b;
sz[b]+=sz[a];
}
ll root(ll i){
if(par[i]==-1)return i;
par[i]=root(par[i]);
return par[i];
}
bool same(ll a,ll b){
return root(a)==root(b);
}
ll getsz(ll i){
return sz[root(i)];
}
};
int construct_roads(std::vector<int> x, std::vector<int> y) {
ll n=x.size();
UF uf(n);
vector<PP> v(n);
rep(i,n)v[i]=PP(x[i],y[i],i);
sort(all(v));
vi dx={2,0},dy={0,2};
set<P> S;
vector<int> U, V, A, B;
rep(k,4)rep(i,n)rep(j,2){
P a(x[i],y[i]),b(x[i]+dx[j],y[i]+dy[j]);
ll l=lb(v,PP(b.fi,b.se,-1));
if(l==n)continue;
l=get<2>(v[l]);
if(P(x[l],y[l])!=b)continue;
P c((a.fi+b.fi)/2,(a.se+b.se)/2);
if(a.fi==b.fi){
if((a.fi+a.se)%4!=k)continue;
if((a.fi+a.se)%4==0)c.fi--;
else c.fi++;
}
else{
if((a.fi+a.se)%4!=k)continue;
if((a.fi+a.se)%4==0)c.se++;
else c.se--;
}
uf.merge(i,l);
if(S.insert(c).se){
U.pb(i);
V.pb(l);
A.pb(c.fi);
B.pb(c.se);
}
}
if(uf.getsz(0)<n)return 0;
build(U,V,A,B);
return 1;
}
