#include "parks.h"
//
#include <bits/stdc++.h>
#define ll long long
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define o cout<<"BUG"<<endl;
#define FOR(i, j, n) for(int j = i; j < n; ++j)
#define forn(i, j, n) for(int j = i; j <= n; ++j)
#define nfor(i, j, n) for(int j = n; j >= i; --j)
#define all(v) v.begin(), v.end()
#define ld long double
#define ull unsigned long long
using namespace std;
const int maxn=2e5+100,LOG=17,mod=1e9+7;
int block = 226, timer = 0;
const ld EPS = 1e-18;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define IOS ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define bt(i) (1 << (i))
//#define int ll
const int inf=2e9;
#define y1 yy
#define prev pre
#define pii pair <int, int>
int used[maxn], mt[maxn], to[maxn][3];
vector <int> edge[maxn];
map <int, int> mapp[maxn];
vector <pii> vec, edges;
void dfs(int v)
{
used[v] = 1;
shuffle(all(edge[v]), rng);
for(auto to : edge[v])
{
if(!used[to])
{
edges.pb({v, to});
dfs(to);
}
}
}
int try_kuhn(int v)
{
if(used[v] == timer) return 0;
used[v] = timer;
if(mt[to[v][0]] == -1)
{
mt[to[v][0]] = v;
return 1;
}
if(mt[to[v][1]] == -1)
{
mt[to[v][1]] = v;
return 1;
}
if(try_kuhn(mt[to[v][0]]))
{
mt[to[v][0]] = v;
return 1;
}
if(try_kuhn(mt[to[v][1]]))
{
mt[to[v][1]] = v;
return 1;
}
return 0;
}
int construct_roads(vector <int> x, vector <int> y)
{
int n = x.size();
forn(0, i, n-1)
{
mapp[x[i]][y[i]] = i;
}
forn(0, i, n-1)
{
if(mapp[x[i]].count(y[i] - 2))
{
edge[i].pb(mapp[x[i]][y[i]-2]);
}
if(mapp[x[i]].count(y[i] + 2))
{
edge[i].pb(mapp[x[i]][y[i]+2]);
}
if(mapp[x[i]+2].count(y[i]))
{
edge[i].pb(mapp[x[i]+2][y[i]]);
}
if(mapp[x[i]-2].count(y[i]))
{
edge[i].pb(mapp[x[i]-2][y[i]]);
}
}
int start = 0;
forn(1, i, n-1)
{
if(x[i] < x[start]) start = i;
else if(x[i] == x[start] && y[i] > y[start]) start = i;
}
dfs(start);
forn(0, i, n-1)
{
if(!used[i]) return 0;
}
for(auto i : edges)
{
if(y[i.f] == y[i.s])
{
vec.pb({max(x[i.f], x[i.s])-1, y[i.f] - 1});
vec.pb({max(x[i.f], x[i.s])-1, y[i.f] + 1});
}
else
{
vec.pb({x[i.f] - 1, max(y[i.f], y[i.s]) - 1});
vec.pb({x[i.f] + 1, max(y[i.f], y[i.s]) - 1});
}
}
sort(all(vec));
vec.erase(unique(all(vec)), vec.end());
// FOR(0, i, vec.size()) cout << vec[i].f << " " << vec[i].s << endl;
FOR(0, it, edges.size())
{
pii i = edges[it];
if(y[i.f] == y[i.s])
{
to[it][0] = lower_bound(all(vec), mp(max(x[i.f], x[i.s])-1, y[i.f] - 1))-vec.begin();
to[it][1] = lower_bound(all(vec), mp(max(x[i.f], x[i.s])-1, y[i.f] + 1))-vec.begin();
}
else
{
to[it][0] = lower_bound(all(vec), mp(x[i.f] - 1, max(y[i.f], y[i.s]) - 1))-vec.begin();
to[it][1] = lower_bound(all(vec), mp(x[i.f] + 1, max(y[i.f], y[i.s]) - 1))-vec.begin();
}
// cout << "E " << edges[it].f << " " << edges[it].s << " " << to[it][0] << " " << to[it][1] << endl;
}
FOR(0, i, vec.size()) mt[i] = -1;
FOR(0, j, edges.size()) used[j] = 0;
FOR(0, i, edges.size())
{
++timer;
try_kuhn(i);
}
/*while(true)
{
cout << "GO\n";
int ok = 0;
FOR(0, i, edges.size()) used[i] = 0;
FOR(0, i, edges.size())
{
if(used[i]) continue;
if(try_kuhn(i))
{
ok = 1;
}
}
if(!ok) break;
}*/
vector <int> ans1, ans2, ans3, ans4;
for(auto i : edges)
{
ans1.pb(i.f);
ans2.pb(i.s);
}
ans3.assign(edges.size(), 0);
ans4.assign(edges.size(), 0);
FOR(0, i, vec.size())
{
if(mt[i] == -1) continue;
ans3[mt[i]] = vec[i].f;
ans4[mt[i]] = vec[i].s;
}
build(ans1, ans2, ans3, ans4);
return 1;
}
