/*************************************
* author: marvinthang *
* created: 02.07.2023 11:47:17 *
*************************************/
#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i--; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
// end of template
struct DisjointSet {
int n, *lab = nullptr;
DisjointSet(int _n = 0) {
resize(_n);
}
void reset(void) {
memset(lab, -1, (n + 1) * sizeof(int));
}
void resize(int _n) {
if (lab != nullptr) delete[] lab;
n = _n;
lab = new int[n + 1];
reset();
}
int find(int u) {
assert(u <= n);
return lab[u] < 0 ? u : lab[u] = find(lab[u]);
}
bool connected(int u, int v) { return find(u) == find(v); }
bool isRoot(int u) { return lab[u] < 0; }
int size(int u) { return -lab[find(u)]; }
bool join(int u, int v) {
if ((u = find(u)) == (v = find(v))) return false;
if (lab[u] > lab[v]) swap(u, v);
lab[u] += lab[v];
lab[v] = u;
return true;
}
};
using DSU = DisjointSet;
int construct_roads(vector <int> x, vector <int> y) {
int n = x.size();
map <pair <int, int>, int> id;
vector <pair <int, int>> p;
REP(i, n) {
p.emplace_back(x[i], y[i]);
id[p.back()] = i;
}
sort(ALL(p));
vector <int> U, V, A, B;
set <pair <int, int>> used;
DSU dsu(n);
auto addEdge = [&] (int u, int v, int a, int b) {
if (!~u || !~v || !dsu.join(u, v) || !used.insert(make_pair(a, b)).se) return false;
U.push_back(u);
V.push_back(v);
A.push_back(a);
B.push_back(b);
return true;
};
for (auto [x, y]: p) {
int a = id[make_pair(x, y)];
int b = id.count(make_pair(x - 2, y)) ? id[make_pair(x - 2, y)] : -1;
int c = id.count(make_pair(x, y - 2)) ? id[make_pair(x, y - 2)] : -1;
if (x + y & 3) {
addEdge(a, b, x - 1, y - 1);
addEdge(a, c, x + 1, y - 1);
} else {
addEdge(a, c, x - 1, y - 1);
addEdge(a, b, x - 1, y + 1);
}
}
if (U.size() != n - 1) return 0;
build(U, V, A, B);
return 1;
}
