#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);
map<ari2, int> used;
FOR(x, 0, size(edges) - 1) {
auto &[i, j] = edges[x];
if (!uf.unite(i, j))
continue;
used[{i, j}] = used[{j, i}] = x;
}
if (size(used) != 2*(N-1))
return 0;
vt<ari2> pairs;
FOR(x, 0, size(edges) - 1) {
auto &[i, j] = edges[x];
if (used.find({i, j}) == used.end())
continue;
const auto calc = [&](const ari2 aa, const ari2 bb, const int p) {
if (points.find(aa) == points.end() || points.find(bb) == points.end())
return;
const int a = points[aa], b = points[bb];
if (used.find({a, p}) == used.end() || used.find({b, p}) == used.end())
return;
pairs.push_back({used[{a, p}], used[{b, p}]});
};
if (X[i] == X[j]) {
calc({X[i] + 2, Y[i]}, {X[i] - 2, Y[i]}, i);
calc({X[j] + 2, Y[j]}, {X[j] - 2, Y[j]}, j);
} else {
calc({X[i], Y[i] - 2}, {X[i], Y[i] + 2}, i);
calc({X[j], Y[j] - 2}, {X[j], Y[j] + 2}, j);
}
}
vt<int> seen(size(edges));
vt<int> A, B, C, D;
set<ari2> have;
for (const auto &[ea, eb] : pairs) {
if (seen[ea]) {
assert(seen[eb]);
continue;
}
seen[ea] = seen[eb] = 1;
const auto &[a, b] = edges[ea];
const auto &[c, d] = edges[eb];
A.push_back(edges[ea][0]);
B.push_back(edges[ea][1]);
A.push_back(edges[eb][0]);
B.push_back(edges[eb][1]);
if (X[a] == X[b]) {
assert(X[c] == X[d] && X[c] == X[a]);
if (have.count({X[a] + 1, Y[a] + Y[b] >> 1}) || have.count({X[a] - 1, Y[c] + Y[d] >> 1})) {
assert(!have.count({X[a] - 1, Y[a] + Y[b] >> 1}) && !have.count({X[a] + 1, Y[c] + Y[d] >> 1}));
have.insert({X[a] - 1, Y[a] + Y[b] >> 1});
have.insert({X[a] + 1, Y[c] + Y[d] >> 1});
C.push_back(X[a] - 1);
D.push_back(Y[a] + Y[b] >> 1);
C.push_back(X[a] + 1);
D.push_back(Y[c] + Y[d] >> 1);
} else {
have.insert({X[a] + 1, Y[a] + Y[b] >> 1});
have.insert({X[a] - 1, Y[c] + Y[d] >> 1});
C.push_back(X[a] + 1);
D.push_back(Y[a] + Y[b] >> 1);
C.push_back(X[a] - 1);
D.push_back(Y[c] + Y[d] >> 1);
}
} else {
assert(Y[a] == Y[b] && Y[a] == Y[c] && Y[a] == Y[d]);
if (have.count({X[a] + X[b] >> 1, Y[a] - 1}) || have.count({X[c] + X[d] >> 1, Y[a] + 1})) {
assert(!have.count({X[a] + X[b] >> 1, Y[a] + 1}) && !have.count({X[c] + X[d] >> 1, Y[a] - 1}));
have.insert({X[a] + X[b] >> 1, Y[a] + 1});
have.insert({X[c] + X[d] >> 1, Y[a] - 1});
C.push_back(X[a] + X[b] >> 1);
D.push_back(Y[a] + 1);
C.push_back(X[c] + X[d] >> 1);
D.push_back(Y[a] - 1);
} else {
have.insert({X[a] + X[b] >> 1, Y[a] - 1});
have.insert({X[c] + X[d] >> 1, Y[a] + 1});
C.push_back(X[a] + X[b] >> 1);
D.push_back(Y[a] - 1);
C.push_back(X[c] + X[d] >> 1);
D.push_back(Y[a] + 1);
}
}
}
FOR(x, 0, size(edges) - 1) {
if (seen[x])
continue;
const auto &[i, j] = edges[x];
A.push_back(i);
B.push_back(j);
if (X[i] == X[j]) {
if (have.count({X[i] + 1, Y[i] + Y[j] >> 1})) {
assert(!have.count({X[i] - 1, Y[i] + Y[j] >> 1}));
have.insert({X[i] - 1, Y[i] + Y[j] >> 1});
C.push_back(X[i] - 1);
D.push_back(Y[i] + Y[j] >> 1);
} else {
have.insert({X[i] + 1, Y[i] + Y[j] >> 1});
C.push_back(X[i] + 1);
D.push_back(Y[i] + Y[j] >> 1);
}
} else {
if (have.count({X[i] + X[j] >> 1, Y[i] + 1})) {
assert(!have.count({X[i] + X[j] >> 1, Y[i] - 1}));
have.insert({X[i] + X[j] >> 1, Y[i] - 1});
C.push_back(X[i] + X[j] >> 1);
D.push_back(Y[i] - 1);
} else {
have.insert({X[i] + X[j] >> 1, Y[i] + 1});
C.push_back(X[i] + X[j] >> 1);
D.push_back(Y[i] + 1);
}
}
}
build(A, B, C, D);
return 1;
}
