#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct dsu {
int n;
vector<int> p, s;
dsu(int n) : n(n), p(n), s(n, 1) {
iota(p.begin(), p.end(), 0);
}
int find(int x) {
return x == p[x] ? x : p[x] = find(p[x]);
}
int size(int x) {
return s[find(x)];
}
bool same(int x, int y) {
return find(x) == find(y);
}
bool unite(int x, int y) {
x = find(x);
y = find(y);
if (x == y) {
return 0;
}
if (s[x] > s[y]) {
swap(x, y);
}
p[x] = y;
s[y] += s[x];
return 1;
}
};
constexpr int A = 200000;
struct road {
int a, b, c;
pair<int, int> t[2];
road() {
}
road(int A, int B, int C, pair<int, int> U, pair<int, int> V) {
a = A, b = B, c = C, t[0] = U, t[1] = V;
}
};
int construct_roads(vector<int> X, vector<int> Y) {
int N = X.size();
if (*max_element(X.begin(), X.end()) <= 6) {
vector f(7, vector(A + 3, -1));
for (int i = 0; i < N; i++) {
f[X[i]][Y[i]] = i;
}
dsu uf(N);
vector<int> u, v, a, b, m(A + 1, -1), l(A + 1, -1), r(A + 1, -1);
for (int y = 2; y <= A; y += 2) {
for (int x = 2; x <= 6; x += 2) {
if (f[x][y] != -1 && f[x][y + 2] != -1) {
if (x == 4) {
m[y + 1] = u.size();
}
u.push_back(f[x][y]);
v.push_back(f[x][y + 2]);
a.push_back(x == 2 ? 1 : 7);
b.push_back(y + 1);
uf.unite(f[x][y], f[x][y + 2]);
}
if (x != 6 && f[x][y] != -1 && f[x + 2][y] != -1) {
if (x == 2 && l[y - 2] == -1) {
l[y] = u.size();
u.push_back(f[x][y]);
v.push_back(f[x + 2][y]);
a.push_back(3);
b.push_back(-1);
uf.unite(f[x][y], f[x + 2][y]);
}
if (x == 4 && r[y - 2] == -1) {
r[y] = u.size();
u.push_back(f[x][y]);
v.push_back(f[x + 2][y]);
a.push_back(5);
b.push_back(-1);
uf.unite(f[x][y], f[x + 2][y]);
}
}
}
}
if (uf.size(0) != N) {
return 0;
}
vector<int> q(A, -1), s(A, -1), t(A, -1);
for (int i = 1; i <= A; i++) {
if (i % 2 == 1 && m[i] != -1) {
if (s[i - 1] != 1) {
a[m[i]] = 3;
q[i] = 0;
} else {
assert(t[i - 1] != 1);
a[m[i]] = 5;
q[i] = 1;
}
}
if (i % 2 == 0) {
if (l[i] != -1) {
if (q[i - 1] == 0) {
b[l[i]] = i + 1;
s[i] = 1;
} else {
b[l[i]] = i - 1;
s[i] = 0;
}
}
if (r[i] != -1) {
if (q[i - 1] == 1) {
b[r[i]] = i + 1;
t[i] = 1;
} else {
b[r[i]] = i - 1;
t[i] = 0;
}
}
}
}
build(u, v, a, b);
return 1;
}
map<int, int> mp[A + 1];
for (int i = 0; i < N; i++) {
mp[X[i]][Y[i]] = i;
}
dsu uf(N);
vector<road> roads;
for (int i = 0; i < N; i++) {
for (int dx = -2; dx <= 2; dx += 4) {
if (X[i] + dx < 0 || X[i] + dx > A) {
continue;
}
if (mp[X[i] + dx].count(Y[i])) {
int j = mp[X[i] + dx][Y[i]];
if (!uf.same(i, j)) {
uf.unite(i, j);
roads.push_back(road(i, j, -1, pair{X[i] + dx / 2, Y[i] + 1}, pair{X[i] + dx / 2, Y[i] - 1}));
}
}
}
for (int dy = -2; dy <= 2; dy += 4) {
if (Y[i] + dy < 0 || Y[i] + dy > A) {
continue;
}
if (mp[X[i]].count(Y[i] + dy)) {
int j = mp[X[i]][Y[i] + dy];
if (!uf.same(i, j)) {
uf.unite(i, j);
roads.push_back(road(i, j, -1, pair{X[i] - 1, Y[i] + dy / 2}, pair{X[i] + 1, Y[i] + dy / 2}));
}
}
}
}
if (uf.size(0) != N) {
return 0;
}
map<int, vector<pair<int, int>>> f[A + 3];
for (int z = 0; z < roads.size(); z++) {
auto r = roads[z];
for (int i = 0; i < 2; i++) {
auto [x, y] = r.t[i];
f[x][y].emplace_back(z, i);
}
}
for (int z = 0; z < roads.size(); z++) {
if (roads[z].c != -1) {
continue;
}
for (int d = 0; d < 2; d++) {
bool ok = 1;
vector<int> q;
roads[z].c = d;
q.push_back(z);
for (int i = 0; ok && i < q.size(); i++) {
int u = q[i];
int color = roads[u].c;
auto [x, y] = roads[u].t[color];
for (auto [v, w] : f[x][y]) {
if (roads[v].c == -1) {
roads[v].c = 1 - w;
q.push_back(v);
}
if (v != u && roads[v].c == w) {
ok = 0;
break;
}
}
}
if (ok) {
break;
}
if (!ok) {
if (d == 1) {
return 0;
}
for (int x : q) {
roads[x].c = -1;
}
}
}
}
vector<int> u, v, a, b;
for (auto r : roads) {
u.push_back(r.a);
v.push_back(r.b);
auto [x, y] = r.t[r.c];
a.push_back(x);
b.push_back(y);
}
build(u, v, a, b);
return 1;
}
