//Shirasu Azusa 2024.6
#include <bits/stdc++.h>
#define fi first
#define se second
#define eb emplace_back
#define mp make_pair
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef __int128 i128;
template<class T,class S>
bool chmax(T &a,const S b) {return (a<b?a=b,1:0);}
template<class T,class S>
bool chmin(T &a,const S b) {return (a>b?a=b,1:0);}
int popcnt(int x) {return __builtin_popcount(x);}
int popcnt(ll x)  {return __builtin_popcountll(x);}
int topbit(int x) {return (x==0?-1:31-__builtin_clz(x));}
int topbit(ll x)  {return (x==0?-1:63-__builtin_clzll(x));}
int lowbit(int x) {return (x==0?-1:__builtin_ctz(x));}
int lowbit(ll x)  {return (x==0?-1:__builtin_ctzll(x));}

#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
typedef pair<int,int> pii;  
typedef vector<int> vi;
typedef vector<pii> vp;
typedef tuple<int,int,int> tiii;
int read() {
  int x=0,w=1; char c=getchar(); 
  while(!isdigit(c)) {if(c=='-') w=-1; c=getchar();}
  while(isdigit(c)) {x=x*10+(c-'0'); c=getchar();} 
  return x*w;
}

const int N=2e5+5;
int n,ans[N],lfc;
vi e[N];
priority_queue<int> f[N];

void merge(int u,int v) {
  if(f[u].size()<f[v].size()) swap(f[u],f[v]);
  while(!f[v].empty()) f[u].push(f[v].top()), f[v].pop();
}
void dfs(int u) {
  if(e[u].size()==0) {
    f[u].push(0); lfc++;
  } else {
    vi gg;
    for(int v:e[u]) {
      dfs(v); int x=f[v].top(); f[v].pop(); gg.eb(x);
      merge(u,v);
    }
    if(gg.size()>1) {
      sort(gg.begin(),gg.end(),greater<int>()); int m=gg.size();
      f[u].push(gg[0]+gg[1]+1);
      rep(i,2,m-1) f[u].push(gg[i]);
    } else {
      f[u].push(gg[0]);
    }
  }
}

void work() {
  n=read(); lfc=0;
  rep(i,1,n) while(f[i].size()) f[i].pop();
  rep(i,1,n) e[i].clear();
  rep(i,2,n) e[read()].eb(i);
  dfs(1); int tick=0;
  while(f[1].size()) {
    int x=f[1].top(); f[1].pop();
    ans[tick+1]=ans[tick]+1; tick++;
    rep(i,1,x) ans[tick+1]=ans[tick]+2, tick++;
  }
  assert(tick==lfc);
  rep(i,1,tick) printf("%d ",ans[i]); puts("");
}

signed main() {
  int T=1;
  while(T--) work();
  return 0;
}