#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


struct Heap {
  Heap *l, *r;
  int key;
  Heap(int key_ = 0) : l(nullptr), r(nullptr), key(key_) {}
};
// max heap
Heap *meld(Heap *a, Heap *b) {
  if (!a) return b;
  if (!b) return a;
  if (a->key < b->key) swap(a, b);
  a->r = meld(a->r, b);
  swap(a->l, a->r);
  return a;
}
void pop(Heap *&a) {
  a = meld(a->l, a->r);
}


int N;
vector<int> P;

vector<vector<int>> graph;

int nodesLen;
vector<Heap> nodes;

// x: +1 then x +2's
Heap *dfs(int u) {
  const int deg = graph[u].size();
  Heap *ret = nullptr;
  if (deg == 0) {
    ret = &(nodes[nodesLen++] = Heap(0));
  } else {
    vector<int> mxs;
    for (const int v : graph[u]) {
      Heap *res = dfs(v);
      if (deg >= 2) {
        mxs.push_back(res->key);
        pop(res);
      }
      ret = meld(ret, res);
    }
    if (deg >= 2) {
      nth_element(mxs.begin(), mxs.begin() + 2, mxs.end(), greater<int>{});
      ret = meld(ret, &(nodes[nodesLen++] = Heap(1 + mxs[0] + mxs[1])));
      for (int j = 2; j < deg; ++j) {
        ret = meld(ret, &(nodes[nodesLen++] = Heap(mxs[j])));
      }
    }
  }
  return ret;
}

int main() {
  for (; ~scanf("%d", &N); ) {
    P.assign(N, -1);
    for (int u = 1; u < N; ++u) {
      scanf("%d", &P[u]);
      --P[u];
    }
    
    graph.assign(N, {});
    for (int u = 1; u < N; ++u) {
      graph[P[u]].push_back(u);
    }
    
    nodesLen = 0;
    nodes.resize(2 * N);
    
    Heap *res = dfs(0);
    vector<int> ans{0};
    for (; res; pop(res)) {
      const int x = res->key;
      ans.push_back(ans.back() + 1);
      for (int y = 0; y < x; ++y) {
        ans.push_back(ans.back() + 2);
      }
    }
    
    for (int k = 1; k < (int)ans.size(); ++k) {
      if (k > 1) printf(" ");
      printf("%d", ans[k]);
    }
    puts("");
  }
  return 0;
}