/*
Mayoeba Yabureru
*/
#include "parks.h"
#include<bits/stdc++.h>
using namespace std;
static vector<int> _u, _v, _a, _b;
int construct_roads(vector<int> x, vector<int> y) {
int n = x.size();
vector<vector<int>> gr(n + 1);
x.insert(x.begin(), 0);
y.insert(y.begin(), 0);
map<pair<int, int>, int> mp;
map<pair<int, int>, pair<int, int>> mpp;
for (int i = 1; i <= n; i ++) mp[{x[i], y[i]}] = i;
vector<int> u, v, a, b;
map<pair<int, int>, int> taken;
for (int i = 1; i <= n; i ++) {
if (mp[{x[i] + 2, y[i]}]) {
u.push_back(i), v.push_back(mp[{x[i] + 2, y[i]}]);
gr[i].push_back(mp[{x[i] + 2, y[i]}]);
gr[mp[{x[i] + 2, y[i]}]].push_back(i);
}
if (mp[{x[i], y[i] + 2}]) {
u.push_back(i), v.push_back(mp[{x[i], y[i] + 2}]);
gr[i].push_back(mp[{x[i], y[i] + 2}]);
gr[mp[{x[i], y[i] + 2}]].push_back(i);
}
}
int num = 0, st = 0;
vector<int> vis(n + 1);
for (int i = 1; i <= n; i ++) {
if (gr[i].size() == 1) {
st = i;
break;
}
}
function<void(int)> go = [&] (int v) {
num ++;
vis[v] = 1;
for (auto u : gr[v]) {
if (vis[u]) continue;
if (x[v] != x[u]) {
int xx = v, uu = u;
if (x[xx] > x[uu]) swap(xx, uu);
if (taken[{x[xx] + 1, y[xx] + 1}] == 0) {
mpp[{xx, uu}] = {x[xx] + 1, y[xx] + 1};
taken[{x[xx] + 1, y[xx] + 1}] = 1;
}
else if (taken[{x[xx] + 1, y[xx] - 1}] == 0) {
mpp[{xx, uu}] = {x[xx] + 1, y[xx] - 1};
taken[{x[xx] + 1, y[xx] - 1}] = 1;
}
else assert(0);
}
else {
int xx = v, uu = u;
if (y[xx] > y[uu]) swap(xx, uu);
if (taken[{x[xx] + 1, y[xx] + 1}] == 0) {
mpp[{xx, uu}] = {x[xx] + 1, y[xx] + 1};
taken[{x[xx] + 1, y[xx] + 1}] = 1;
}
else if (taken[{x[xx] - 1, y[xx] + 1}] == 0) {
mpp[{xx, uu}] = {x[xx] - 1, y[xx] + 1};
taken[{x[xx] - 1, y[xx] + 1}] = 1;
}
else assert(0);
}
go(u);
}
};
go(st);
for (int i = 0; i < u.size(); i ++) {
a.push_back(mpp[{u[i], v[i]}].first);
b.push_back(mpp[{u[i], v[i]}].second);
u[i] --;
v[i] --;
}
if (num == n) {
build(u, v, a, b);
return 1;
}
return 0;
}
