// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
- insert(x),erase(x)
- find_by_order(k): return iterator to the k-th smallest element
- order_of_key(x): the number of elements that are strictly smaller
*/

#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
uniform_real_distribution<> pp(0.0,1.0);
#define int long long
#define ld long double
#define pii pair<int,int>
#define piii pair<int,pii>
#define mpp make_pair
#define fi first
#define se second
const int inf=1e18;
const int mod=998244353;
const int maxn=200005;
const int bl=650;
const int maxs=655;
const int maxm=200005;
const int maxq=1000005;
const int maxl=25;
const int maxa=1000000;
const int root=3;
int power(int a,int n){
    int res=1;
    while(n){
        if(n&1) res=res*a%mod;
        a=a*a%mod;n>>=1;
    }
    return res;
}
const int iroot=power(3,mod-2);
const int base=131;

int n,total;
vector<int> edge[maxn];
priority_queue<int> pq[maxn];
int cnt[maxn],sz[maxn];

void dfs(int u){
    if(edge[u].empty()){
        sz[u]++;
        pq[u].push(1);
        return;
    }
    pii Max1={0,-1},Max2={0,-1};
    for(int v:edge[u]){
        dfs(v);sz[u]+=sz[v];
        int d=pq[v].top();
        if(mpp(d,v)>Max1) Max2=Max1,Max1=mpp(d,v);
        else if(mpp(d,v)>Max2) Max2=mpp(d,v);
    }
    pq[u].push(Max1.fi+Max2.fi);
    if(Max1.se!=-1){
        int v=Max1.se;
        pq[v].pop();
    }
    if(Max2.se!=-1){
        int v=Max2.se;
        pq[v].pop();
    }
    for(int v:edge[u]){
        if((int)pq[u].size()<(int)pq[v].size()) pq[u].swap(pq[v]);
        while(!pq[v].empty()){
            pq[u].push(pq[v].top());
            pq[v].pop();
        }
    }
}

void solve(){
    cin >> n;
    for(int i=2;i<=n;i++){
        int p;cin >> p;
        edge[p].push_back(i);
    }
    dfs(1);
    int cur=1;
    while(!pq[1].empty()){
        cnt[cur]--;
        cur+=pq[1].top();
        pq[1].pop();
    }
    for(int i=1;i<=sz[1];i++){
        cnt[i]+=cnt[i-1]+2;
        cout << cnt[i] << ' ';
    }
    cout << '\n';
}

signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);cout.tie(NULL);
    int test=1;//cin >> test;
    while(test--) solve();
}