#include <bits/stdc++.h>
using namespace std;

#define ar array
#define F first
#define S second
typedef int uci;
#define int long long

void solve(){
    int n;
    cin >> n;
    vector<set<int>> adj(n);
    vector<int> par(n);
    for(int i{1}; i < n; ++i){
        cin >> par[i];
        par[i]--;
        adj[par[i]].insert(i);
    }
    int tot = n;
    for(int i{}; i < n; ++i){
        if(adj[i].size() == 1)
            tot--;
    }

    vector<bool> leaf(n);
    int lc{};
    for(int i{1}; i < n; ++i){
        if(adj[i].size() == 0){
            leaf[i] = true;
            lc++;
            while(par[i] > 0 && adj[par[i]].size() == 1){
                int p = par[i];
                adj[p].erase(adj[p].begin());
                par[i] = par[p];
                adj[par[i]].insert(i);
                adj[par[i]].erase(p);
            }
        }
    }
    vector<int> real(n), fake(n);
    set<ar<int, 2>> nodes;
    for(int i{}; i < n; ++i){
        for(int j : adj[i]){
            if(leaf[j]){
                real[i]++;
            }else
                fake[i]++;
        }
        if(real[i] > 0)
            nodes.insert({-real[i]-fake[i], i});
    }

    vector<int> out(lc, tot);
    for(int i{1}; i < lc; ++i){
        auto a = *nodes.begin();
        nodes.erase(nodes.begin());

        real[a[1]]--;
        a[0] *= -1;
        if(a[0] >= 3){
            tot--;
            if(real[a[1]] > 0){
                nodes.insert({-real[a[1]]-fake[a[1]], a[1]});
            }
        }else{
            tot -= 2;
            while(par[a[1]] > 0 && adj[par[a[1]]].size() == 1){
                int p = par[a[1]];
                par[a[1]] = par[p];
            }
            nodes.erase({-real[par[a[1]]]-fake[par[a[1]]], par[a[1]]});
            real[par[a[1]]]++;
            nodes.erase({-real[par[a[1]]]-fake[par[a[1]]], par[a[1]]});
        }
        out[i] = tot;
    }
    reverse(out.begin(), out.end());
    for(int i : out)
        cout << i << ' ';
    cout << '\n';
}

uci main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);
    solve();
}