#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<ctime>
#include<random>
#include<assert.h>
#include<ext/pb_ds/priority_queue.hpp>
#define pb emplace_back
#define mp make_pair
#define fi first
#define se second
#define dbg(x) cerr<<"In Line "<< __LINE__<<" the "<<#x<<" = "<<x<<'\n'
#define dpi(x,y) cerr<<"In Line "<<__LINE__<<" the "<<#x<<" = "<<x<<" ; "<<"the "<<#y<<" = "<<y<<'\n'
#define DE(fmt,...) fprintf(stderr, "Line %d : " fmt "\n",__LINE__,##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int>pii;
typedef pair<ll,int>pli;
typedef pair<ll,ll>pll;
typedef pair<int,ll>pil;
typedef vector<int>vi;
typedef vector<ll>vll;
typedef vector<pii>vpii;
typedef vector<pll>vpll;
template<typename T>T cmax(T &x, T y){return x=x>y?x:y;}
template<typename T>T cmin(T &x, T y){return x=x<y?x:y;}
template<typename T>
T &read(T &r){
	r=0;bool w=0;char ch=getchar();
	while(ch<'0'||ch>'9')w=ch=='-'?1:0,ch=getchar();
	while(ch>='0'&&ch<='9')r=r*10+(ch^48),ch=getchar();
	return r=w?-r:r;
}
template<typename T1,typename... T2>
void read(T1 &x,T2& ...y){read(x);read(y...);}
const int mod=998244353;
inline void cadd(int &x,int y){x=(x+y>=mod)?(x+y-mod):(x+y);}
inline void cdel(int &x,int y){x=(x-y<0)?(x-y+mod):(x-y);}
inline int add(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
inline int del(int x,int y){return (x-y<0)?(x-y+mod):(x-y);}
int qpow(int x,int y){
	int s=1;
	while(y){
		if(y&1)s=1ll*s*x%mod;
		x=1ll*x*x%mod;
		y>>=1;
	}
	return s;
}
const int N=500010;
int n;
vi eg[N];
__gnu_pbds::priority_queue<int>q[N];
void dfs(int x){
	if(eg[x].empty()){
		q[x].push(1);
		return ;
	}
	for(auto v:eg[x])dfs(v);
	if((int)eg[x].size()==1)swap(q[x],q[eg[x][0]]);
	else{
		int mx[2]={0,0};
		for(auto v:eg[x]){
			int t=q[v].top();
			for(int i:{0,1})if(t>mx[i])swap(t,mx[i]);
		}
		q[x].push(mx[0]+mx[1]);
		for(auto v:eg[x]){
			int t=q[v].top();
			if(t==mx[0])q[v].pop(),mx[0]=0;
			else if(t==mx[1])q[v].pop(),mx[1]=0;
			q[x].join(q[v]);
		}
	}
}
signed main(){
	#ifdef do_while_true
//		assert(freopen("data.in","r",stdin));
//		assert(freopen("data.out","w",stdout));
	#endif
	read(n);
	for(int i=2;i<=n;i++){
		int x;read(x);
		eg[x].pb(i);
	}
	dfs(1);
	vi vec;
	int s=0;
	while(!q[1].empty()){
		int i=q[1].top();q[1].pop();
		vec.pb(++s);
		while(--i)vec.pb(s+=2);
	}
	for(auto i:vec)cout<<i<<' ';
    #ifdef do_while_true
//		cerr<<'\n'<<"Time:"<<1.0*clock()/CLOCKS_PER_SEC*1000<<" ms"<<'\n';
	#endif
	return 0;
}