#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ari2 = array<int, 2>;
using ari3 = array<int, 3>;
using arl2 = array<ll, 2>;
using arl3 = array<ll, 3>;
template <class T> using vt = vector<T>;
#define all(x) begin(x), end(x)
#define size(x) (int((x).size()))
#define REP(a,b,c,d) for(int a=(b);(d)>0?a<=(c):a>=(c);a+=(d))
#define FOR(a,b,c) REP(a,b,c,1)
#define ROF(a,b,c) REP(a,b,c,-1)
struct DSU {
vt<int> uf;
DSU(const int n) : uf(n, -1) {}
int find(const int i) {
return uf[i] < 0 ? i : uf[i] = find(uf[i]);
}
bool unite(int a, int b) {
if ((a = find(a)) == (b = find(b)))
return false;
if (uf[a] > uf[b])
swap(a, b);
uf[a] += uf[b];
uf[b] = a;
return true;
}
};
constexpr int dir[5] = {2, 0, -2, 0, 2};
int construct_roads(vt<int> X, vt<int> Y) {
const int N = size(X);
map<ari2, int> points;
vt<ari2> edges;
FOR(i, 0, N-1) {
FOR(j, 0, 3) {
const int x = X[i] + dir[j];
const int y = Y[i] + dir[j+1];
if (points.find({x, y}) != points.end()) {
const int k = points[{x, y}];
edges.push_back({i, k});
}
}
points[{X[i], Y[i]}] = i;
}
if (*max_element(all(X)) <= 6) {
DSU uf(N);
vt<int> A, B, C, D;
vt<ari3> fours;
for (const auto &[i, j] : edges) {
if (X[i] == X[j]) {
uf.unite(i, j);
if (X[i] == 2) {
A.push_back(i);
B.push_back(j);
C.push_back(1);
D.push_back(Y[i] + Y[j] >> 1);
} else if (X[i] == 6) {
A.push_back(i);
B.push_back(j);
C.push_back(7);
D.push_back(Y[i] + Y[j] >> 1);
} else {
fours.push_back({Y[i] + Y[j] >> 1, i, j});
}
}
}
sort(all(fours));
int add = 1;
set<ari2> have;
for (const auto &[_, i, j] : fours) {
A.push_back(i);
B.push_back(j);
C.push_back(4 + add);
D.push_back(Y[i] + Y[j] >> 1);
have.insert({4 + add, Y[i] + Y[j] >> 1});
add *= -1;
}
for (const auto &[i, j] : edges) {
if (Y[i] == Y[j]) {
if (!uf.unite(i, j))
continue;
A.push_back(i);
B.push_back(j);
const int x = X[i] + X[j] >> 1;
C.push_back(x);
if (have.count({x, Y[i] + 1})) {
assert(!have.count({x, Y[i] - 1}));
have.insert({x, Y[i] - 1});
D.push_back(Y[i] - 1);
} else {
have.insert({x, Y[i] + 1});
D.push_back(Y[i] + 1);
}
}
}
assert(size(A) == size(B) && size(B) == size(C) && size(C) == size(D));
if (size(A) != N - 1)
return 0;
build(A, B, C, D);
return 1;
}
DSU uf(N);
vt<array<int, 4>> hori;
for (const auto &[i, j] : edges) {
if (Y[i] != Y[j] || !uf.unite(i, j))
continue;
hori.push_back({Y[i], X[i] + X[j] >> 1, i, j});
}
vt<int> A, B, C, D;
sort(all(hori));
int add = 1;
set<ari2> have;
for (const auto &[y, x, i, j] : hori) {
assert(!have.count({x, y + add}));
have.insert({x, y + add});
A.push_back(i);
B.push_back(j);
D.push_back(y + add);
C.push_back(x);
add *= -1;
}
for (const auto &[i, j] : edges) {
if (X[i] != X[j] || !uf.unite(i, j))
continue;
A.push_back(i);
B.push_back(j);
const int y = Y[i] + Y[j] >> 1;
D.push_back(y);
if (have.count({X[i] - 1, y})) {
assert(!have.count({X[i] + 1, y}));
have.insert({X[i] + 1, y});
C.push_back(X[i] + 1);
} else {
have.insert({X[i] - 1, y});
C.push_back(X[i] - 1);
}
}
assert(size(A) == size(B) && size(B) == size(C) && size(C) == size(D));
if (size(A) != N - 1)
return 0;
build(A, B, C, D);
return 1;
}
