#include <bits/stdc++.h>

using namespace std;

#define ar array
#define ll long long
typedef int uci;
#define int long long
#define F first
#define S second
typedef complex<double> cd;

seed_seq seq{
    (uint64_t) chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count(),
    (uint64_t) __builtin_ia32_rdtsc(),
    (uint64_t) (uintptr_t) make_unique<char>().get()
};
mt19937 rng(seq);
// mt19937_64 lrng(seq);

struct debugger{
    template <typename T>
    debugger& operator<<(T &a){
        #ifdef DEBUG
            cerr << a;
        #endif
        return *this;
    }
    template <typename T>
    debugger& operator<<(T &&a){
        #ifdef DEBUG
            cerr << a;
        #endif
        return *this;
    }
} deb;

const double PI = acos(-1.0);
const int MAX_N = 1e5 + 1;
const int MOD = 1e9 + 7;
const int INF = 1e9;
const ll LINF = 1e18;

//! function insert

//THINK FIRST, CODE SECOND
//DON'T GET STUCK ON ONE STRATEGY
//CALM DOWNNN FOR ONCE IN YOUR LIFE
//REDUCE
//COUGH E??!?!?!! O.O
//uwu i see you ryan
int dp[200001];
bool seen[200001];

int preproc(int v, vector<vector<int>> &adj){
    if(adj[v].empty()){
        return dp[v] = 1;
    }
    ar<int, 2> bigs{};
    for(int i : adj[v]){
        int t = preproc(i, adj);
        if(t > bigs[0]){
            swap(bigs[0], bigs[1]);
            bigs[0] = t;
        }else if(t > bigs[1])
            bigs[1] = t;
    }
    return dp[v] = bigs[0]+bigs[1];
}

void mark(int v, set<ar<int, 2>> &poss, vector<vector<int>> &adj){
    ar<int, 2> bigs{};
    ar<int, 2> inds{-1, -1};
    seen[v] = true;
    for(int i : adj[v]){
        int t = dp[i];
        if(t > bigs[0]){
            swap(bigs[0], bigs[1]);
            swap(inds[0], inds[1]);
            bigs[0] = t;
            inds[0] = i;
        }else if(t > bigs[1]){
            bigs[1] = t;
            inds[1] = i;
        }
    }

    for(int i : adj[v]){
        if(i != inds[0] && i != inds[1]){
            poss.insert({-dp[i], i});
        }
    }
    if(inds[0] != -1)
        mark(inds[0], poss, adj);
    if(inds[1] != -1)
        mark(inds[1], poss, adj);
}

void solve() {
    int n;
    cin >> n;
    vector<vector<int>> adj(n);
    for(int i{1}; i < n; ++i){
        int t;
        cin >> t;
        t--;
        adj[t].push_back(i);
    }
    int lc{};
    for(int i{}; i < n; ++i){
        if(adj[i].size() == 0)
            lc++;
    }
    int leaves = preproc(0, adj);
    int cost{};

    vector<int> out(lc);
    set<ar<int, 2>> possible;
    mark(0, possible, adj);
    for(int i{1}; i <= lc; ++i){
        if(i > leaves){
            cost++;
            auto it = *possible.begin();
            possible.erase(possible.begin());
            leaves -= it[0];
            mark(it[1], possible, adj);
        }
        out[i-1] = 2*i-cost-1;
    }
    for(int i : out)
        cout << i << ' ';
    cout << '\n';
}

uci main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);

        // cout << "Case #" << t  << ": ";
        solve();
}

/*
    random number generator stuff
    num = rng(); gives integer number
    num = uniform_int_distribution<int>(a, b)(rng); -> bounds [a, b]
    num = uniform_real_distribution<double>(a, b)(rng); -> bounds [a, b)
    can also instantiate distributions and call on generator:
    uniform_int_distribution<int> thing(a, b);
    num = thing(rng);
*/
// struct custom_hash {
//     static uint64_t splitmix64(uint64_t x) {
//         // http://xorshift.di.unimi.it/splitmix64.c
//         x += 0x9e3779b97f4a7c15;
//         x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
//         x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
//         return x ^ (x >> 31);
//     }
//     size_t operator()(uint64_t x) const {
//         static const uint64_t FIXED_RANDOM = lrng();
//         return splitmix64(x + FIXED_RANDOM);
//     }
// };