#include "parks.h"
#include<bits/stdc++.h>
using namespace std;
typedef pair<pair<int,int>,int> pp;
int n;
///bench position
int bench_lr[200010]={},bench_ba[200010]={};
///above,below,left,right;
int a[200010],b[200010],l[200010],r[200010];
///sort to get a b l r
vector<pp> fo,fo2;
///go back to find links: traceback above and below (get the x coor)
int trace_a[200010],trace_b[200010];
///to get potential connected links (that shouldn't collide)
int cur_y[200010],cur_x[200010];
vector<pair<int,bool>> link;
vector<int> adj[400010];
int chosen[400010]={};
///check if every fountains are connected
vector<int> adj2[200010];
void changebench(int x)
{
if(x<0) return;
if(a[x]<0) return;
int temp=x;
while(temp>=0 && a[temp]>=0 && bench_lr[temp]==-1)
{
bench_lr[temp]=1;
temp=r[x];
}
}
void dfs(int v,int col)
{
chosen[v]=col;
for(int i=0;i<adj[v].size();i++)
{
if(!chosen[adj[v][i]]) dfs(adj[v][i],3-col);
}
}
int cou=0;
bool visited[200010]={};
void dfs_check(int v)
{
cou++;
for(int i=0;i<adj2[v].size();i++)
{
if(visited[adj2[v][i]]) continue;
visited[adj2[v][i]]=true;
dfs_check(adj2[v][i]);
}
}
int construct_roads(std::vector<int> x, std::vector<int> y) {
if (x.size() == 1) {
build({}, {}, {}, {});
return 1;
}
n=x.size();
for(int i=0;i<n;i++)
{
fo.push_back({{x[i],y[i]},i});
fo2.push_back({{y[i],x[i]},i});
a[i]=-1;
b[i]=-1;
l[i]=-1;
r[i]=-1;
}
for(int i=0;i<200010;i++) cur_x[i]=cur_y[i]=-2;
sort(fo.begin(),fo.end());
sort(fo2.begin(),fo2.end());
for(int i=0;i<n-1;i++)
{
if(fo[i].first.first==fo[i+1].first.first && fo[i].first.second==fo[i+1].first.second-2)
{
a[fo[i].second]=fo[i+1].second;
b[fo[i+1].second]=fo[i].second;
bench_lr[fo[i].second]=-1;
}
}
for(int i=0;i<n-1;i++)
{
if(fo2[i].first.first==fo2[i+1].first.first && fo2[i].first.second==fo2[i+1].first.second-2)
{
r[fo2[i].second]=fo2[i+1].second;
l[fo2[i+1].second]=fo2[i].second;
}
}
for(int i=0;i<n;i++)
{
if(a[i]>=0) adj2[i].push_back(a[i]);
if(b[i]>=0) adj2[i].push_back(b[i]);
if(l[i]>=0) adj2[i].push_back(l[i]);
if(r[i]>=0) adj2[i].push_back(r[i]);
}
visited[0]=true;
dfs_check(0);
if(cou<n) return 0;
int temp;
for(int i=0;i<n-1;i++)
{
temp=fo[i].second;
if(a[temp]<0)
{
trace_a[temp]=x[temp]+1;
}
else
{
if(l[temp]<0)
{
trace_a[temp]=x[temp]-1;
}
else
{
trace_a[temp]=trace_a[l[temp]];
}
}
if(b[temp]<0)
{
trace_b[temp]=x[temp]+1;
}
else
{
if(l[temp]<0) trace_b[temp]=x[temp]-1;
else trace_b[temp]=trace_b[l[temp]];
}
}
int temp2;
for(int i=0;i<n;i++)
{
temp=fo[i].second;
if(r[temp]<0) continue;
if(b[temp]<0 || b[r[temp]]<0)
{
link.push_back({temp,false});
if(cur_y[y[temp]-1]>=0)
{
temp2=link[cur_y[y[temp]-1]].first;
if(trace_b[temp]<=x[temp2]+1)
{
adj[link.size()-1].push_back(cur_y[y[temp]-1]);
adj[cur_y[y[temp]-1]].push_back(link.size()-1);
}
}
cur_y[y[temp]-1]=link.size()-1;
cur_x[x[temp]+1]=link.size()-1;
}
if(a[temp]<0 || a[r[temp]]<0)
{
link.push_back({temp,true});
if(cur_y[y[temp]+1]>=0)
{
temp2=link[cur_y[y[temp]+1]].first;
if(trace_a[temp]<=x[temp2]+1)
{
adj[link.size()-1].push_back(cur_y[y[temp]+1]);
adj[cur_y[y[temp]+1]].push_back(link.size()-1);
}
}
cur_y[y[temp]+1]=link.size()-1;
adj[link.size()-1].push_back(cur_x[x[temp]+1]);
adj[cur_x[x[temp]+1]].push_back(link.size()-1);
cur_x[x[temp]+1]=link.size()-1;
}
}
for(int i=0;i<link.size();i++)
{
if(chosen[i]) continue;
dfs(i,1);
}
for(int i=0;i<link.size();i++)
{
if(chosen[i]==1)
{
temp=link[i].first;
if(link[i].second)
{
bench_ba[temp]=1;
changebench(r[temp]);
}
else
{
bench_ba[temp]=-1;
changebench(b[r[temp]]);
}
}
}
vector<int> u,v,aa,bb;
for(int i=0;i<n;i++)
{
if(bench_lr[i])
{
u.push_back(i);
v.push_back(a[i]);
aa.push_back(x[i]+bench_lr[i]);
bb.push_back(y[i]+1);
}
if(bench_ba[i])
{
u.push_back(i);
v.push_back(r[i]);
aa.push_back(x[i]+1);
bb.push_back(y[i]+bench_ba[i]);
}
}
build(u,v,aa,bb);
return 1;
}
