#include "parks.h"
#include <bits/stdc++.h>
//#include "grader.cpp"
using namespace std;
typedef pair<int,int> pii;
map<pii,int> ind;
map<pii,int> ocup;
map<pii,int> match;
struct point
{
int x,y;
} v[200005];
int k;
vector<int> myy[200005];
vector<int> muchii[200005];
vector<pii> edges;
bool have[11][200005];
bool use[200005];
void dfs(int nod)
{
use[nod]=1;
for(int i:muchii[nod])
if(!use[i])
dfs(i);
}
int c[11][200005];
vector<int> U,V,A,B;
void addedge(int xa,int ya,int xb,int yb,int xc,int yc)
{
int a=ind[{xa,ya}];
int b=ind[{xb,yb}];
U.push_back(a);
V.push_back(b);
muchii[a].push_back(b);
muchii[b].push_back(a);
A.push_back(xc);
B.push_back(yc);
}
int diri[5]={-2,2,0,0};
int dirj[5]={0,0,-2,2};
int nr;
vector<int> cedge[800005];
int l[800005],r[800005];
vector<pii> who;
bool pairup(int nod)
{
if(use[nod])
return 0;
use[nod]=1;
for(int i:cedge[nod])
if(r[i]==0)
{
l[nod]=i;
r[i]=nod;
return 1;
}
for(int i:cedge[nod])
if(pairup(r[i]))
{
l[nod]=i;
r[i]=nod;
return 1;
}
return 0;
}
int comp[700005];
vector<int> dsu[700005];
void dsu_merge(int c1,int c2)
{
if(dsu[c1].size()<dsu[c2].size())
swap(c1,c2);
for(int i:dsu[c2])
{
comp[i]=c1;
dsu[c1].push_back(i);
}
dsu[c2].clear();
}
int construct_roads(std::vector<int> X, std::vector<int> Y)
{
k=X.size();
int xmax=0;
for(int i=0;i<k;i++)
{
v[i]={X[i],Y[i]};
ind[{X[i],Y[i]}]=i;
xmax=max(xmax,X[i]);
if(X[i]<=6)
{
myy[X[i]].push_back(Y[i]);
have[X[i]][Y[i]]=1;
}
}
if(xmax<=2)
{
sort(myy[2].begin(),myy[2].end());
vector<int> U,V,a,b;
for(int i=1;i<myy[2].size();i++)
{
if(myy[2][i]-myy[2][i-1]!=2)
return 0;
int x=2;
int yu=myy[2][i-1];
int yv=myy[2][i];
U.push_back(ind[{x,yu}]);
V.push_back(ind[{x,yv}]);
a.push_back(x-1);
b.push_back(yv-1);
}
build(U,V,a,b);
return 1;
}
if(xmax<=4)
{
sort(myy[2].begin(),myy[2].end());
sort(myy[4].begin(),myy[4].end());
vector<int> U,V,A,B;
for(int i=2;i<=200000;i+=2)
if(have[2][i]&&have[2][i-2])
{
int a=ind[{2,i}];
int b=ind[{2,i-2}];
U.push_back(a);
V.push_back(b);
muchii[a].push_back(b);
muchii[b].push_back(a);
A.push_back(1);
B.push_back(i-1);
}
for(int i=2;i<=200000;i+=2)
if(have[4][i]&&have[4][i-2])
{
int a=ind[{4,i}];
int b=ind[{4,i-2}];
U.push_back(a);
V.push_back(b);
muchii[a].push_back(b);
muchii[b].push_back(a);
A.push_back(5);
B.push_back(i-1);
}
for(int i=2;i<=200000;i+=2)
if(have[2][i]&&have[4][i])
{
int a=ind[{2,i}];
int b=ind[{4,i}];
U.push_back(a);
V.push_back(b);
muchii[a].push_back(b);
muchii[b].push_back(a);
A.push_back(3);
B.push_back(i+1);
}
dfs(0);
for(int i=0;i<k;i++)
if(!use[i])
return 0;
build(U,V,A,B);
return 1;
}
if(xmax<=6)
{
sort(myy[2].begin(),myy[2].end());
sort(myy[4].begin(),myy[4].end());
sort(myy[6].begin(),myy[6].end());
int nr=0;
for(int i=2;i<=200000;i+=2)
if(have[2][i])
{
if(have[2][i-2])
{
addedge(2,i,2,i-2,1,i-1);
c[2][i]=c[2][i-2];
}
else
{
nr++;
c[2][i]=nr;
}
}
for(int i=2;i<=200000;i+=2)
if(have[6][i])
{
if(have[6][i-2])
{
addedge(6,i,6,i-2,7,i-1);
c[6][i]=c[6][i-2];
}
else
{
nr++;
c[6][i]=nr;
}
}
int lft=1;
for(int i=2;i<=200000;i+=2)
if(have[4][i])
{
if(have[4][i-2])
{
if(lft==1)
{
addedge(4,i,4,i-2,3,i-1);
ocup[{3,i-1}]=1;
}
else
{
addedge(4,i,4,i-2,5,i-1);
ocup[{5,i-1}]=1;
}
lft^=1;
c[4][i]=c[4][i-2];
}
else
{
lft=1;
nr++;
c[4][i]=nr;
}
}
for(int i=2;i<=200000;i+=2)
if(have[2][i]&&have[4][i])
{
int a=c[2][i];
int b=c[4][i];
if(match[{a,b}]==0)
{
match[{a,b}]=1;
if(!ocup[{3,i-1}])
{
addedge(2,i,4,i,3,i-1);
ocup[{3,i-1}]=1;
}
else
{
addedge(2,i,4,i,3,i+1);
ocup[{3,i+1}]=1;
}
}
}
for(int i=2;i<=200000;i+=2)
if(have[4][i]&&have[6][i])
{
int a=c[4][i];
int b=c[6][i];
if(match[{a,b}]==0)
{
match[{a,b}]=1;
if(!ocup[{5,i-1}])
{
addedge(4,i,6,i,5,i-1);
ocup[{5,i-1}]=1;
}
else
{
addedge(4,i,6,i,5,i+1);
ocup[{5,i+1}]=1;
}
}
}
dfs(0);
for(int i=0;i<k;i++)
if(!use[i])
return 0;
build(U,V,A,B);
return 1;
}
vector<int> nodes;
for(int i=0;i<k;i++)
nodes.push_back(i);
int bulan=0;
nr=0;
while(bulan<=4)
{
random_shuffle(nodes.begin(),nodes.end());
bulan++;
bool good=1;
for(int i=0;i<k;i++)
{
comp[i]=i;
dsu[i].clear();
dsu[i].push_back(i);
muchii[i].clear();
use[i]=0;
}
edges.clear();
for(auto p:nodes)
{
int nod=p;
int x=X[nod];
int y=Y[nod];
for(int z=0;z<4;z++)
{
int lin=x+diri[z];
int col=y+dirj[z];
if(ind.count({lin,col})!=0)
{
int w=ind[{lin,col}];
if(comp[nod]!=comp[w])
{
dsu_merge(comp[nod],comp[w]);
muchii[nod].push_back(w);
muchii[w].push_back(nod);
edges.push_back({nod,w});
}
}
}
}
dfs(0);
for(int i=0;i<k;i++)
if(!use[i])
good=0;
if(good==0)
continue;
who.clear();
who.push_back({0,0});
for(int i=0;i<edges.size();i++)
{
cedge[i+1].clear();
int a=edges[i].first;
int b=edges[i].second;
int xa=X[a],ya=Y[a],xb=X[b],yb=Y[b];
if(xa==xb)
{
int x=xa+1;
int y=(ya+yb)/2;
if(ind[{x,y}]==0)
{
nr++;
ind[{x,y}]=nr;
who.push_back({x,y});
}
int nrm=ind[{x,y}];
cedge[i+1].push_back(nrm);
x=xa-1;
y=(ya+yb)/2;
if(ind[{x,y}]==0)
{
nr++;
ind[{x,y}]=nr;
who.push_back({x,y});
}
nrm=ind[{x,y}];
cedge[i+1].push_back(nrm);
}
else
{
int x=(xa+xb)/2;
int y=ya-1;
if(ind[{x,y}]==0)
{
nr++;
ind[{x,y}]=nr;
who.push_back({x,y});
}
int nrm=ind[{x,y}];
cedge[i+1].push_back(nrm);
x=(xa+xb)/2;
y=ya+1;
if(ind[{x,y}]==0)
{
nr++;
ind[{x,y}]=nr;
who.push_back({x,y});
}
nrm=ind[{x,y}];
cedge[i+1].push_back(nrm);
}
}
for(int i=1;i<=edges.size();i++)
l[i]=0;
for(int i=1;i<=nr;i++)
r[i]=0;
bool ok=0;
do
{
ok=0;
for(int i=1;i<=edges.size();i++)
use[i]=0;
for(int i=1;i<=edges.size();i++)
if(l[i]==0)
ok|=pairup(i);
}while(ok);
for(int i=1;i<=edges.size();i++)
if(l[i]==0)
good=0;
if(good==0)
continue;
for(int i=1;i<=edges.size();i++)
{
U.push_back(edges[i-1].first);
V.push_back(edges[i-1].second);
A.push_back(who[l[i]].first);
B.push_back(who[l[i]].second);
}
build(U,V,A,B);
return 1;
}
return 0;
}
