#include<bits/stdc++.h>
#define pb push_back
using namespace std;
int read(){
	int x=0,f=1;char c;
	while(!isdigit(c=getchar()))if(c=='-')f=-1;
	while(isdigit(c))x=(x<<1)+(x<<3)+(c&15),c=getchar();
	return x*f;
}
const int N=2e5+10;
vector<int>e[N];
int n,leaf,f[N],g[N],s1[N],s2[N],ans[N];
struct node{
	int u;
	bool operator<(const node &A)const{return f[u]<f[A.u];}
};
priority_queue<node>q;
void dfs(int x){
	if(!(int)e[x].size()){
		leaf+=f[x]=1;
		return;
	}
	for(int y:e[x]){
		dfs(y);
		if(f[y]>f[s1[x]])s2[x]=s1[x],s1[x]=y;
		else if(f[y]>f[s2[x]])s2[x]=y;
	}
	f[x]=f[s1[x]]+f[s2[x]];
}
void ins(int x){
	for(int y:e[x])if(y!=s1[x]&&y!=s2[x])q.push((node){y});
	if(s1[x])ins(s1[x]);
	if(s2[x])ins(s2[x]);
}
int main()
{
	n=read();
	for(int i=2;i<=n;i++){
		int x=read();
		e[x].pb(i);
	}
	dfs(1);
	ins(1);
	int val=f[1],cost=0;
	while(q.size()){
		int x=q.top().u;
		q.pop();
		val+=f[x],cost++;
		ans[val]=cost;
		ins(x);
	}
	for(int i=1,pre=0;i<=leaf;i++){
		pre=max(pre,ans[i]);
		ans[i]=pre;
	}
	for(int i=1;i<=leaf;i++)printf("%d ",2*i-1-ans[i]);
	return 0;
}