#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,dist[N],SZ[N],DIST[N];
vector<int> g[N],vec[N];
void dfs1(int u,int p){
SZ[u]=1;
for(auto v : g[u]){
if(v==p) continue ;
DIST[v]=DIST[u]+1;
dfs1(v,u);
SZ[u]+=SZ[v];
}
}
/*
int hoursRequired(int u,int v){
DIST[u]=0;
dfs1(u,u);
return DIST[v];
}
int attractionsBehind(int u,int v){
dfs1(u,u);
return SZ[v];
}
*/
int get1(int u,int v){
return hoursRequired(u,v);
}
int get2(int u,int v){
return attractionsBehind(u,v);
}
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;
}
}
}
vector<int> createFunTour(int _n, int Q) {
vector<int> adj;
n=_n;
findcentroid();
//eror(rt);
f(i,0,n){
dist[i]=get1(rt,i);
if(dist[i]==1) adj.pb(i);
}
//dbgv(adj);
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;
}
}
}
//eror(vec[0].size());
//eror(vec[1].size());
//eror(vec[2].size());
while(vec[2].size()){
int x=vec[2].back();
vec[2].pop_back();
if(vec[0].size()<=vec[1].size()) vec[0].pb(x);
else vec[1].pb(x);
}
sort(all(vec[0]),[&](int u,int v){ return dist[u]>dist[v]; });
sort(all(vec[1]),[&](int u,int v){ return dist[u]>dist[v]; });
//cout<<"vec0 = "; for(auto x : vec[0]) cout<<x<<" "; cout<<endl;
//cout<<"vec1 = "; for(auto x : vec[1]) cout<<x<<" "; cout<<endl;
vector<int> ans;
f(i,0,vec[0].size()){
ans.pb(vec[0][i]);
if(i<vec[1].size()) ans.pb(vec[1][i]);
}
ans.pb(rt);
return ans;
}
/*
int32_t main(){
ios:: sync_with_stdio(0), cin.tie(0), cout.tie(0);
int n;
cin>>n;
f(i,1,n){
int u,v;
cin>>u>>v;
g[u].pb(v);
g[v].pb(u);
}
vector<int> ans=createFunTour(n,n);
dbgv(ans);
}*/
/*
7
0 1
0 5
0 6
1 2
1 4
2 3
*/
