#include <bits/stdc++.h>
using namespace std;
#define dbgv(v) cout<<#v<<" = "; f(i,0,v.size()) cout<<v[i]<<" "; cout<<endl
#define dbga(a,x,y) cout<<#a<<" = "; f(i,x,y) cout<<a[i]<<" "; cout<<endl
#define erorp(x) cout<<#x<<"={"<<x.F<<" , "<<x.S<<"}"<<endl
#define eror(x) cout<<#x<<'='<<(x)<<endl
#define f_(i,a,b) for(int i=a;i>=b;i--)
#define f(i,a,b) for(int i=a;i<b;i++)
#define nb(x) __builtin_popcount(x)
#define all(v) v.begin(),v.end()
#define bit(n,k) (((n)>>(k))&1)
#define Add(x,y) x=(x+y)%mod
#define maxm(a,b) a=max(a,b)
#define minm(a,b) a=min(a,b)
#define lst(x) x[x.size()-1]
#define sz(x) int(x.size())
#define mp make_pair
#define ll long long
#define pb push_back
#define S second
#define F first
#include "fun.h"
const int N=1e5+99;
int n,rt,lid,last[N],dist[N];
vector<int> ans,g[N],vec[N];
int cmp(int u,int v){
return dist[u]<dist[v];
}
int get1(int u,int v){
return hoursRequired(u,v);
}
int get2(int u,int v){
return attractionsBehind(u,v);
}
int get(int u){
if(vec[u].size()==0) return -N;
return dist[vec[u].back()];
}
void findcentroid(){
int sz=n+1;
rt=-1;
f(i,0,n){
int res=get2(0,i);
if(res>=(n+1)/2 && res<sz){
rt=i;
sz=res;
}
}
}
bool check(){
f(i,0,3){
int sum=0;
f(j,0,3) sum+=vec[j].size();
if(sum==2*sz(vec[i])){
return 1;
}
}
return 0;
}
vector<int> createFunTour(int _n, int Q) {
vector<int> adj;
n=_n;
findcentroid();
f(i,0,n){
dist[i]=get1(rt,i);
if(dist[i]==1) adj.pb(i);
}
f(i,0,n){
if(rt==i) continue ;
f(j,0,adj.size()){
if(j==adj.size()-1 || dist[i]==get1(adj[j],i)+1){
vec[j].pb(i);
break;
}
}
}
lid=3;
last[0]=last[1]=N;
f(i,0,3) sort(all(vec[i]),cmp);
f(i,1,3) if(vec[i].size()>vec[0].size()) swap(vec[i],vec[0]);
int i=0;
if(vec[1].size()+vec[2].size()<vec[0].size()){
while(vec[0].size()){
ans.pb(vec[0].back());
vec[0].pop_back();
if(vec[1].size() && (get(1)>=get(2))) ans.pb(vec[1].back()),vec[1].pop_back();
else if(vec[2].size()) ans.pb(vec[2].back()),vec[2].pop_back();
}
ans.pb(rt);
return ans;
}
while(check()==0){
int id=-1;
f(i,0,3) if(vec[i].size() && i!=lid && (id==-1 || get(id)<get(i))){
id=i;
}
last[i]=dist[vec[id].back()];
ans.pb(vec[id].back());
vec[id].pop_back();
lid=id;
i^=1;
}
f_(i,1,0){
if(vec[i].size()<vec[i+1].size()){
swap(vec[i],vec[i+1]);
if(lid==i || lid==i+1) lid^=i^(i+1);
}
}
if(get(0)<=last[i] && max(get(1),get(2))<=last[i^1]){
while(vec[0].size()){
ans.pb(vec[0].back());
vec[0].pop_back();
if(vec[2].size()==0 || (vec[1].size() && dist[vec[1].back()]>dist[vec[2].back()])){
ans.pb(vec[1].back());
vec[1].pop_back();
}
else{
ans.pb(vec[2].back());
vec[2].pop_back();
}
}
}
else if(get(0)<=last[i^1] && max(get(1),get(2))==get(3^lid) && max(get(1),get(2))<=last[i]){
while(vec[0].size()){
if(vec[2].size()==0 || (vec[1].size() && dist[vec[1].back()]>dist[vec[2].back()])){
ans.pb(vec[1].back());
vec[1].pop_back();
}
else{
ans.pb(vec[2].back());
vec[2].pop_back();
}
ans.pb(vec[0].back());
vec[0].pop_back();
}
}
else{
eror(2);
assert(0);
}
ans.pb(rt);
return ans;
}
