#include<bits/stdc++.h>
#define int long long
#define db long double
using namespace std;
const int N=5e5+10;
int f[N],d[N];
vector<int> g[N],ye,w[N],q;
void dfs(int x,int fa){
	for(auto it:g[x])if(it!=fa){
		dfs(it,x);
		d[x]=min(d[it]+1,d[x]);
	}
	if(d[x]==1e18) d[x]=1,ye.push_back(x);
}
void dfss(int x,int fa){
	for(auto it:g[x]) if(it!=fa){
		dfss(it,x);
		w[x].push_back(-f[it]);
	}
	sort(w[x].begin(),w[x].end());
	if(!w[x].size()) f[x]=1;
	else if(w[x].size()==1) f[x]=-w[x][0];
	else f[x]=-w[x][0]-w[x][1];
	if(w[x].size()>2){
		for(int i=2;i<w[x].size();i++){
			q.push_back(-w[x][i]);
		}
	}
}
int s[N];
void solve(){
	int n;cin>>n;
	for(int i=1;i<=n;i++) d[i]=1e18;
	for(int i=2;i<=n;i++){
		int y;cin>>y;
		g[y].push_back(i);
		g[i].push_back(y);
	}
	dfs(1,0);
	dfss(1,0);
	int cnt=1;
	q.push_back(f[1]);
	sort(q.begin(),q.end());
	int m=q.size();
	for(int i=m-1;i>=0;i--){
		s[i]=s[i+1]+q[i];
	}
	int t=m-1;
	for(int i=1;i<=ye.size();i++){
		if(i==1){
			cout<<1<<" ";continue;
		}
		if(t<0){
			cnt++;cout<<cnt<<" ";continue;
		}
		if(i<=s[t]){
			cnt+=2;
		}
		else{
			cnt++;
			t--;
		}
		cout<<cnt<<" ";
	}
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(0);cout.tie(0); 
//	int T;cin>>T;
//	while(T--)
	solve();
}