#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;
int n,fa[N],dfn[N],siz[N],num,ans[N],l[N],r[N];
int c[N],f[N];
bool vis[N];
vector<int>e[N],vec,buc0,buc1;
int dep[N];
void dfs(int x){
	dep[x]=dep[fa[x]]+1;
	dfn[x]=++num,siz[x]=1;
	if(!(int)e[x].size())vec.pb(x);
	for(int y:e[x]){
		dfs(y);
		siz[x]+=siz[y];
	}
	l[x]=dfn[x],r[x]=dfn[x]+siz[x]-1;
}
void add(int x){
	for(;x<=n;x+=x&-x)c[x]++;
}
int ask(int x){
	int res=0;
	for(;x;x-=x&-x)res++;
	return res;
}
int calc(int x,int son){
	if(vis[x])return 0;
	bool flag=0;
	for(int y:e[x])if(y!=son){
		if(ask(r[y])-ask(l[y]-1)>0){
			flag=1;
			break;	
		}
	}
	if(flag)return x;
	return calc(fa[x],x);
}
void dfs2(int x,int v){
	if(!(int)e[x].size()){
		f[x]=v;
		buc1.pb(x);
	}
	for(int y:e[x])dfs2(y,v);
}
int find(int x){
	if(vis[x])return x;
	return find(fa[x]);
}
void dfs3(int x,int p){
	if(!(int)e[x].size()){
		int y=calc(x,0);
		if(y)f[x]=y;
		else {
			f[x]=0;
			buc0.pb(x);
		}
	}
	for(int y:e[x])dfs3(y,p);
}
int lca(int x,int y){
	if(dep[x]<dep[y])swap(x,y);
	while(dep[x]>dep[y])x=fa[x];
	if(x==y)return x;
	while(x!=y)x=fa[x],y=fa[y];
	return x;
}
/*
10
1 1 1 2 2 2 3 3 3
*/
int main()
{
	vis[0]=1;
	n=read();
	for(int i=2;i<=n;i++){
		fa[i]=read();
		e[fa[i]].pb(i);
	}
	dfs(1);
	int leaf=(int)vec.size();
	ans[1]=0,ans[2]=1;int LCA=lca(vec[0],vec.back());
	vis[dfn[LCA]]=1;
	add(dfn[vec[0]]);
	add(dfn[vec.back()]);
	for(int j=1;j<leaf-1;j++){
		int i=vec[j];
		
//		if(dfn[i]>r[LCA]||dfn[i]<l[LCA]){
//			buc0.pb(i);
//			continue;
//		}
		
		int x=calc(i,0);
		if(x){
			f[i]=x;
			buc1.pb(i);
		}
		else {
			buc0.pb(i);
		}
	}
	for(int i=3;i<=leaf;i++){
		while(buc1.size()&&!f[buc1.back()])buc1.pop_back();
		if((int)buc1.size()){
			int x=buc1.back();
			buc1.pop_back();
			int p=f[x];
			vis[p]=1;
			ans[i]=ans[i-1]+1;
			while(fa[x]!=p){
				int son=x;
				x=fa[x];
				for(int y:e[x])if(y!=son){
					dfs2(y,x);
				}
			}
			add(dfn[x]);
			dfs3(p,p);
		}
		else {
			while(buc0.size()&&f[buc0.back()])buc0.pop_back();
			ans[i]=ans[i-1];
			int x=buc0.back();
			buc0.pop_back();
			int p=find(x);
			while(fa[x]!=p){
				int son=x;
				x=fa[x];
				for(int y:e[x])if(y!=son){
					dfs2(y,x);
				}
			}
			add(dfn[x]);
		}
	}
	for(int i=1;i<=leaf;i++)printf("%d ",ans[i]+i);
	return 0;
}