#include <bits/stdc++.h>
#include "parks.h"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#define pb push_back
#define F first
#define pii pair<int,int>
#define all(a) a.begin(),a.end()
#define S second
#define sz(a) (int)a.size()
#define rep(i , a , b) for(int i = (a) ; i <= (b) ; i++)
#define per(i , a , b) for(int i = (a) ; i >= (b) ; i--)
#define ld double
#define ll long long
using namespace std ;
const int maxn = 1e6 + 10 , inf = 1e9+ 10 , mod = 998244353;
map <pii ,int> mp ;
map <int ,pii> mp2 ;
int cnt , dx[] = {2,-2, 0 , 0} , dy[] = {0 , 0 ,2 ,-2} ;
void add(int x, int y){
if(mp[{x,y}] == 0){
mp[{x,y}] = cnt ;
mp2[cnt] = {x,y} ;
cnt++;
}
}
int par[maxn] , d[maxn] , mark[maxn] , mc[maxn];
vector <int> G[maxn] ;
int find(int v){
if(par[v] == 0)return v;
return par[v] = find(par[v]) ;
}
void addedge(int v ,int u){
G[v].pb(u);
G[u].pb(v);
d[v]++;
d[u]++;
}
void dfs(int v , int d =0 ){
mark[v] =1 ;
for(int u : G[v]){
if(mark[u] == 1)continue ;
if(d==0)mc[v] = u ;
dfs(u , d^1) ;
}
}
int construct_roads(std::vector<int> x, std::vector<int> y){
cnt =sz(x) +1 ;
vector <pii> vec ;
rep(i , 1, sz(x)){
mp[{x[i-1],y[i-1]}] = i ;
}
vector <pii> ed ;
rep(i , 0 , sz(x)-1){
rep(j , 0 , 3){
int a = x[i] + dx[j] , b = y[i] + dy[j] ;
if(mp[{a,b}] ==0)continue ;
ed.pb({mp[{x[i],y[i]}] , mp[{a,b}]}) ;
if(j <= 1){
add((a+x[i])/2 , b-1);
add((a+x[i])/2 , b+1);
}else{
add(a-1 , (b+y[i])/2);
add(a+1 , (b+y[i])/2);
}
}
}
int ted= 0;
vector <int> V,U ;
rep(i ,0 , sz(ed)-1){
int v = ed[i].F, u = ed[i].S ;
if(find(v)==find(u))continue ;
if(x[v-1] == x[u-1]){
addedge(mp[{x[v-1]-1 , (y[v-1]+y[u-1])/2}] , ted) ;
addedge(mp[{x[v-1]+1 , (y[v-1]+y[u-1])/2}] , ted) ;
}else{
addedge(mp[{(x[v-1]+x[u-1])/2, y[v-1]-1}] , ted) ;
addedge(mp[{(x[v-1]+x[u-1])/2, y[v-1]+1}] , ted) ;
}
par[find(v)] = find(u) ;
V.pb(v-1);
U.pb(u-1);
ted++;
}
if(ted != sz(x)-1){
return 0 ;
}
queue <int> q ;
rep(i , ted ,cnt){
if(d[i] == 1){
q.push(i) ;
}
}
while(sz(q)){
int v =q.front() ;q.pop() ;
if(mark[v] == 1)continue ;
mark[v] =1 ;
int x= -1 ;
for(int u : G[v]){
if(mark[u] == 1)continue ;
x = u ;
}
if(x==-1)continue ;
mark[x] =1 ;
mc[x] = v ;
for(int w : G[x]){
if(d[w] ==2){
q.push(w);
}
d[w]-- ;
}
}
int o =0 ;
rep(i , 0 ,ted-1){
if(mark[i] == 0){
o++;
if(d[i] != 2)return 0 ;
}
}
rep(i , ted , cnt){
if(sz(G[i]) && mark[i] == 0){
o--;
}
}
if(o != 0){
return 0 ;
}
rep(i , 0 , ted-1){
if(mark[i] == 1)continue ;
dfs(i) ;
}
vector <int> A,B ;
rep(i ,0 ,ted-1){
A.pb(mp2[mc[i]].F);
B.pb(mp2[mc[i]].S);
}
build(V,U,A,B);
return 1;
}
