#pragma optimize("Bismillahirrahmanirrahim")
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//Allahuekber
//ahmet23 orz...
//Sani buyuk Osman Pasa Plevneden cikmam diyor.
//FatihSultanMehmedHan
//YavuzSultanSelimHan
//AbdulhamidHan
#define author tolbi
#include <bits/stdc++.h>
using namespace std;
template<typename X, typename Y> istream& operator>>(istream& in, pair<X,Y> &pr) {return in>>pr.first>>pr.second;}
template<typename X, typename Y> ostream& operator<<(ostream& os, pair<X,Y> pr) {return os<<pr.first<<" "<<pr.second;}
template<typename X> istream& operator>>(istream& in, vector<X> &arr) {for(auto &it : arr) in>>it; return in;}
template<typename X> ostream& operator<<(ostream& os, vector<X> arr) {for(auto &it : arr) os<<it<<" "; return os;}
template<typename X, size_t Y> istream& operator>>(istream& in, array<X,Y> &arr) {for(auto &it : arr) in>>it; return in;}
template<typename X, size_t Y> ostream& operator<<(ostream& os, array<X,Y> arr) {for(auto &it : arr) os<<it<<" "; return os;}
template<typename T> vector<int32_t> normalize(vector<T> &arr){vector<int> rv;rv.resize(arr.size());for (int i = 0; i < rv.size(); ++i){rv[i]=arr[i];}return rv;}
#define endl '\n'
#define vint(x) vector<int> x
#define deci(x) int x;cin>>x;
#define decstr(x) string x;cin>>x;
#define cinarr(x) for (auto &it : x) cin>>it;
#define coutarr(x) for (auto &it : x) cout<<it<<" ";cout<<endl;
#define sortarr(x) sort(x.begin(),x.end())
#define sortrarr(x) sort(x.rbegin(),x.rend())
#define det(x) cout<<"NO\0YES"+x*3<<endl;
#define INF LONG_MAX
#define rev(x) reverse(x.begin(),x.end());
#define ios ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define tol(bi) (1LL<<((int)(bi)))
const int MOD = 1e9+7;
mt19937 ayahya(chrono::high_resolution_clock().now().time_since_epoch().count());
#include "parks.h"
struct DSU{
vector<int> par;
DSU(int n){
par.resize(n);
iota(par.begin(), par.end(), 0ll);
}
int find(int node){
if (par[node]==node) return node;
return par[node]=find(par[node]);
}
void merge(int a, int b){
a=find(a);
b=find(b);
if (ayahya()%2) swap(a,b);
par[a]=b;
}
};
int construct_roads(vector<int> x, vector<int> y) {
map<pair<int,int>,int> mp;
int n = x.size();
for (int i = 0; i < n; ++i)
{
mp[{x[i],y[i]}]=i;
}
map<pair<int,int>,int> dikey;
map<pair<int,int>,int> yatay;
vector<bool> yat;
vector<int> u;
vector<int> v;
vector<int> a;
vector<int> b;
DSU dsu(n);
for (int i = 0; i < n; i++){
int xv = x[i];
int yv = y[i];
if (mp.count({xv+2,yv})){
if (dsu.find(i)!=dsu.find(mp[{xv+2,yv}])){
dsu.merge(i,mp[{xv+2,yv}]);
yatay[{xv,yv}]=u.size();
u.push_back(i);
v.push_back(mp[{xv+2,yv}]);
yat.push_back(true);
a.push_back(-23);
b.push_back(-23);
}
}
if (mp.count({xv,yv+2})){
if (dsu.find(i)!=dsu.find(mp[{xv,yv+2}])){
dsu.merge(i,mp[{xv,yv+2}]);
dikey[{xv,yv}]=u.size();
u.push_back(i);
v.push_back(mp[{xv,yv+2}]);
yat.push_back(false);
a.push_back(-23);
b.push_back(-23);
}
}
}
if (u.size()!=n-1) return 0;
map<pair<int,int>,bool> kap;
int mini = *min_element(x.begin(), x.end());
int minj = *min_element(y.begin(), y.end());
int mani = *max_element(x.begin(), x.end());
int manj = *max_element(y.begin(), y.end());
vector<int> sir;
vector<int> viss(u.size(),false);
for (int i = 0; i < u.size(); i++){
if (x[u[i]]==mini && !yat[i]){
a[i]=x[u[i]]-1;
b[i]=y[u[i]]+1;
viss[i]=true;
continue;
}
if (x[u[i]]==mani && !yat[i]){
a[i]=x[u[i]]+1;
b[i]=y[u[i]]+1;
viss[i]=true;
continue;
}
if (y[u[i]]==minj & yat[i]){
a[i]=x[u[i]]+1;
b[i]=y[u[i]]-1;
viss[i]=true;
continue;
}
if (y[u[i]]==manj && yat[i]){
a[i]=x[u[i]]+1;
b[i]=y[u[i]]+1;
viss[i]=true;
continue;
}
}
for (int i = 0; i < u.size(); ++i)
{
if (viss[i]) continue;
int xv = x[u[i]];
int yv = y[u[i]];
if (yatay.count({xv,yv}) && dikey.count({xv,yv}) && yatay.count({xv-2,yv}) && dikey.count({xv,yv-2})){
sir.push_back(i);
viss[i]=true;
}
}
for (int i = 0; i < u.size(); ++i){
if (!yat[i]) continue;
if (viss[i]) continue;
sir.push_back(i);
viss[i]=true;
}
for (int i = 0; i < u.size(); ++i)
{
if (viss[i]) continue;
sir.push_back(i);
}
for (int i = 0; i < sir.size(); i++){
int ed = sir[i];
queue<int> q;
q.push(i);
while (q.size()){
int ed = q.front();
q.pop();
if (a[ed]!=-23) continue;
if (yat[ed]){
if (!kap[{x[u[ed]]+1,y[u[ed]]+1}]){
kap[{x[u[ed]]+1,y[u[ed]]+1}]=true;
a[ed]=x[u[ed]]+1;
b[ed]=y[u[ed]]+1;
}
else {
if (kap[{x[u[ed]]+1,y[u[ed]]-1}]) return 0;
kap[{x[u[ed]]+1,y[u[ed]]-1}]=true;
a[ed]=x[u[ed]]+1;
b[ed]=y[u[ed]]-1;
}
}
else {
if (!kap[{x[u[ed]]+1,y[u[ed]]+1}]){
kap[{x[u[ed]]+1,y[u[ed]]+1}]=true;
a[ed]=x[u[ed]]+1;
b[ed]=y[u[ed]]+1;
}
else {
if (kap[{x[u[ed]]-1,y[u[ed]]+1}]) return 0;
kap[{x[u[ed]]-1,y[u[ed]]+1}]=true;
a[ed]=x[u[ed]]-1;
b[ed]=y[u[ed]]+1;
}
}
pair<int,int> pr;
pr={a[ed]-1,b[ed]-1};
if (yatay.count(pr) && yatay[pr]!=ed && a[yatay[pr]]==-23){
q.push(yatay[pr]);
}
pr={a[ed]-1,b[ed]+1};
if (yatay.count(pr) && yatay[pr]!=ed && a[yatay[pr]]==-23){
q.push(yatay[pr]);
}
pr={a[ed]-1,b[ed]-1};
if (dikey.count(pr) && dikey[pr]!=ed && a[dikey[pr]]==-23){
q.push(dikey[pr]);
}
pr={a[ed]+1,b[ed]-1};
if (dikey.count(pr) && dikey[pr]!=ed && a[dikey[pr]]==-23){
q.push(dikey[pr]);
}
}
}
build(u,v,a,b);
return 1;
}
