#include "fun.h"
#include<bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef pair<int,int> pi;
typedef vector<pi> vpi;
#define pb emplace_back
#define mp make_pair
#define f first
#define s second
#define ALL(x) x.begin(),x.end()
#define SZ(x) (int)x.size()
const int MAXN= 100100;
vi res;
vpi V[MAXN]; // pair(distance, node). Length is 0 for all nodes except neighbours of centroid
int pd[MAXN]; // distance from centroid
int mid3[MAXN]; // exclude the centroid + neighbours
int belg[MAXN]; // which subtree a node belongs to
std::vector<int> createFunTour(int N, int Q) {
int rt=0;
vpi T;
for(int i=1;i<N;++i){
T.pb(mp(attractionsBehind(0,i),i));
}
sort(ALL(T));reverse(ALL(T));
while(T.size()&&T.back().f<=N/2)T.pop_back();
int cent=rt;
if(SZ(T)==0)cent=rt;
else{
cent=T.back().s;
}
belg[cent]=-1;
vi adj;
for(int i=0;i<N;++i){
int d=hoursRequired(cent,i);
pd[i]=d;
if(d==1){
adj.pb(i);
mid3[i]=1;
}
}
mid3[cent]=1;
assert(SZ(adj)<=3);
for(int i=0;i<N;++i)if(!mid3[i]){
int done=0;
for(auto x:adj)if(x!=adj.back()){
int k=hoursRequired(x,i);
if(k==pd[i]-1){
V[x].pb(mp(pd[i],i));
done=1;
break;
}
}
if(!done)V[adj.back()].pb(mp(pd[i],i));
}
for(auto i:adj){
V[i].pb(mp(pd[i],i));
sort(ALL(V[i]));
}
for(auto i:adj)for(auto j:V[i]){
belg[j.s]=i;
}
int blk=-1;
int LFT=N;
while(SZ(res) < N){
int skip=0;
int biggst=adj[0];
for(auto i:adj)if(SZ(V[i]) > SZ(V[biggst]))biggst=i;
int rst=LFT-SZ(V[biggst]);
int tx=SZ(V[biggst]);
if(tx==rst)skip=1;
if(skip){ // Dominant case
int MAJ=adj[0];
for(auto i:adj)if(SZ(V[i]) > SZ(V[MAJ]))MAJ=i;
if(blk!=MAJ){
pi t=mp(-1,-1);
for(auto i:adj)if(i!=blk){
if(SZ(V[i])){
pi x=V[i].back();
t=max(t,x);
}
}
if(t.s!=MAJ && t.f!=-1 && SZ(res) && pd[res.back()] < t.f){
// Swap over to other, taller small branch
res.pb(t.s);
V[belg[t.s]].pop_back();
blk=-1;
}
}
vpi rest;
for(auto i:adj)if(i!=MAJ){
for(auto k:V[i])rest.pb(k);
}
rest.pb(-1,cent);
sort(ALL(rest));
while(SZ(res)<N){
if(blk==MAJ){
blk=-1;
res.pb(rest.back().s);
rest.pop_back();
}else{
res.pb(V[MAJ].back().s);
V[MAJ].pop_back();
blk=MAJ;
}
}
return res;
}
else{ // Greedily go to bigest branch that is not currently visited
int furtbst=-1;
int t=-1;
int tp=-1;
for(auto i:adj)if(SZ(V[i])){
if(i==blk)continue;
int k=V[i].back().s;
int cd=V[i].back().f;
if(cd>=furtbst){
furtbst=cd;
t=k;
tp=i;
}
}
if(t==-1){
res.pb(cent);
assert(SZ(res)==N);
return res;
}
blk=tp;
res.pb(t);
V[tp].pop_back();
}
--LFT;
}
return res;
}
