#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 3e2;
#define all(x) (x).begin(), (x).end()
int p[N];
int find(int x){
return (x == p[x] ? x : p[x] = find(p[x]));
}
bool unite(int x, int y){
x = find(x);
y = find(y);
if (x == y) return false;
if (rand() & 1) swap(x, y);
p[x] = y;
return true;
}
bool can(vector<int> &x, vector<int> &y, vector<int> &U, vector<int> &V, vector<int> &A, vector<int> &B, const vector<int> &dx, const vector<int> &dy){
int n = x.size();
bool ok = true;
set<pair<int, int>> points;
for (int it = 0; it < n - 1; it++){
A[it] = B[it] = 0;
int i = U[it], j = V[it];
int X = (x[i] + x[j]) / 2, Y = (y[i] + y[j]) / 2;
if (x[i] == x[j]){
for (int d : dx){
if (!points.count({x[i] + d, Y})){
A[it] = x[i] + d;
break;
}
}
B[it] = Y;
} else {
for (int d : dy){
if (!points.count({X, y[i] + d})){
B[it] = y[i] + d;
break;
}
}
A[it] = X;
}
if (A[it] == 0 || B[it] == 0) ok = false;
points.insert({A[it], B[it]});
}
return ok;
}
int construct_roads(vector<int> x, vector<int> y) {
int n = x.size();
if (n == 1) {
build({}, {}, {}, {});
return 1;
}
vector<int> perm(n);
iota(all(perm), 0);
sort(all(perm), [&](int i, int j){
return x[i] < x[j] || x[i] == x[j] && y[i] < y[j];
});
iota(p, p + n, 0);
map<pair<int, int>, int> id;
for (int i = 0; i < n; i++){
id[{x[i], y[i]}] = i;
}
vector<int> U, V, A(n - 1), B(n - 1);
vector<int> dx = {0, 2};
vector<int> dy = {2, 0};
for (int it = 0; it < dx.size(); it++){
for (int i : perm){
int X = x[i] + dx[it], Y = y[i] + dy[it];
if (id.find({X, Y}) != id.end()){
int j = id[{X, Y}];
if (!unite(i, j)) continue;
U.push_back(i);
V.push_back(j);
}
}
}
if (U.size() != n - 1) return 0;
if (can(x, y, U, V, A, B, {1, -1}, {1, -1})){
build(U, V, A, B);
return 1;
}
if (can(x, y, U, V, A, B, {1, -1}, {-1, 1})){
build(U, V, A, B);
return 1;
}
if (can(x, y, U, V, A, B, {-1, 1}, {1, -1})){
build(U, V, A, B);
return 1;
}
if (can(x, y, U, V, A, B, {-1, 1}, {-1, 1})){
build(U, V, A, B);
return 1;
}
return 0;
}
